proconlib
This documentation is automatically generated by competitive-verifier/competitive-verifier
tests/prime_factorization/severe_cases.test.cpp
- View this file on GitHub
- Last update: 2026-01-24 23:50:59+09:00
Depends on
- std::abs(x) extended for my library (tools/abs.hpp)
- Assertion macro (tools/assert_that.hpp)
- $2^{\left\lceil \log_2(x) \right\rceil}$ (tools/bit_ceil.hpp)
- $2^{\left\lfloor \log_2(x) \right\rfloor}$ (tools/bit_floor.hpp)
- Bit width required to represent a given integer (tools/bit_width.hpp)
- Number of trailing zeros (tools/countr_zero.hpp)
- tools/detail/int128_t_and_uint128_t.hpp
- $\left\lfloor \log_2(x) \right\rfloor$ (tools/floor_log2.hpp)
- std::gcd(m, n) extended for my library (tools/gcd.hpp)
- Check whether a given integer is $2^n$ (tools/has_single_bit.hpp)
- Combine hash values (tools/hash_combine.hpp)
- Concept for integral types including tools::int128_t and tools::uint128_t (tools/integral.hpp)
- std::is_integral extended for tools::int128_t and tools::uint128_t (tools/is_integral.hpp)
- Miller-Rabin primality test (tools/is_prime.hpp)
- std::is_signed extended for tools::int128_t and tools::uint128_t (tools/is_signed.hpp)
- std::is_unsigned extended for tools::int128_t and tools::uint128_t (tools/is_unsigned.hpp)
- std::make_signed extended for tools::int128_t and tools::uint128_t (tools/make_signed.hpp)
- std::make_unsigned extended for tools::int128_t and tools::uint128_t (tools/make_unsigned.hpp)
- Minimum non-negative reminder (tools/mod.hpp)
- tools::integral except for bool (tools/non_bool_integral.hpp)
- The number of nanoseconds that have elapsed since epoch (tools/now.hpp)
- Popcount (tools/popcount.hpp)
- $2^x$ (tools/pow2.hpp)
- $x^y \pmod{M}$ (tools/pow_mod.hpp)
- Pollard's rho algorithm (tools/prime_factorization.hpp)
- $x \cdot y \pmod{M}$ (tools/prod_mod.hpp)
- 128-bit unsigned integer (tools/uint128_t.hpp)
Code
// competitive-verifier: STANDALONE
#include <cstdint>
#include <iostream>
#include <vector>
#include "tools/assert_that.hpp"
#include "tools/prime_factorization.hpp"
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(1)) == std::vector<std::int8_t>{});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(2)) == std::vector<std::int8_t>{INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(3)) == std::vector<std::int8_t>{INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(4)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(5)) == std::vector<std::int8_t>{INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(6)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(7)) == std::vector<std::int8_t>{INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(8)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(9)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(10)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(11)) == std::vector<std::int8_t>{INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(12)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(13)) == std::vector<std::int8_t>{INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(14)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(15)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(16)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(17)) == std::vector<std::int8_t>{INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(18)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(19)) == std::vector<std::int8_t>{INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(20)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(21)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(22)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(23)) == std::vector<std::int8_t>{INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(24)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(25)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(26)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(27)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(28)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(29)) == std::vector<std::int8_t>{INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(30)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(31)) == std::vector<std::int8_t>{INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(32)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(33)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(34)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(35)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(36)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(37)) == std::vector<std::int8_t>{INT8_C(37)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(38)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(39)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(40)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(41)) == std::vector<std::int8_t>{INT8_C(41)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(42)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(43)) == std::vector<std::int8_t>{INT8_C(43)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(44)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(45)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(46)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(47)) == std::vector<std::int8_t>{INT8_C(47)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(48)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(49)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(50)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(51)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(52)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(53)) == std::vector<std::int8_t>{INT8_C(53)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(54)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(55)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(56)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(57)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(58)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(59)) == std::vector<std::int8_t>{INT8_C(59)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(60)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(61)) == std::vector<std::int8_t>{INT8_C(61)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(62)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(63)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(64)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(65)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(66)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(67)) == std::vector<std::int8_t>{INT8_C(67)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(68)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(69)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(70)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(71)) == std::vector<std::int8_t>{INT8_C(71)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(72)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(73)) == std::vector<std::int8_t>{INT8_C(73)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(74)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(37)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(75)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(76)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(77)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(78)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(79)) == std::vector<std::int8_t>{INT8_C(79)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(80)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(81)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(82)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(41)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(83)) == std::vector<std::int8_t>{INT8_C(83)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(84)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(85)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(86)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(43)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(87)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(88)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(89)) == std::vector<std::int8_t>{INT8_C(89)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(90)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(91)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(92)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(93)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(94)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(47)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(95)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(96)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(97)) == std::vector<std::int8_t>{INT8_C(97)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(98)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(7), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(99)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(100)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(101)) == std::vector<std::int8_t>{INT8_C(101)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(102)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(103)) == std::vector<std::int8_t>{INT8_C(103)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(104)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(105)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(5), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(106)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(53)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(107)) == std::vector<std::int8_t>{INT8_C(107)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(108)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(109)) == std::vector<std::int8_t>{INT8_C(109)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(110)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(111)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(37)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(112)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(113)) == std::vector<std::int8_t>{INT8_C(113)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(114)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(115)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(116)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(117)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(118)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(59)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(119)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(120)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(121)) == std::vector<std::int8_t>{INT8_C(11), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(122)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(61)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(123)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(41)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(124)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(125)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(126)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(127)) == std::vector<std::int8_t>{INT8_C(127)});
assert_that(tools::prime_factorization(INT32_C(1)) == std::vector<std::int32_t>{});
assert_that(tools::prime_factorization(INT32_C(2)) == std::vector{INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(3)) == std::vector{INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(4)) == std::vector{INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(5)) == std::vector{INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(6)) == std::vector{INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(7)) == std::vector{INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(8)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(9)) == std::vector{INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(10)) == std::vector{INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(11)) == std::vector{INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(12)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(13)) == std::vector{INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(14)) == std::vector{INT32_C(2), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(15)) == std::vector{INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(16)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(17)) == std::vector{INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(18)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(19)) == std::vector{INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(20)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(21)) == std::vector{INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(22)) == std::vector{INT32_C(2), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(23)) == std::vector{INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(24)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(25)) == std::vector{INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(26)) == std::vector{INT32_C(2), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(27)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(28)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(29)) == std::vector{INT32_C(29)});
assert_that(tools::prime_factorization(INT32_C(30)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(31)) == std::vector{INT32_C(31)});
assert_that(tools::prime_factorization(INT32_C(32)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(33)) == std::vector{INT32_C(3), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(34)) == std::vector{INT32_C(2), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(35)) == std::vector{INT32_C(5), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(36)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(37)) == std::vector{INT32_C(37)});
assert_that(tools::prime_factorization(INT32_C(38)) == std::vector{INT32_C(2), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(39)) == std::vector{INT32_C(3), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(40)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(41)) == std::vector{INT32_C(41)});
assert_that(tools::prime_factorization(INT32_C(42)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(43)) == std::vector{INT32_C(43)});
assert_that(tools::prime_factorization(INT32_C(44)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(45)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(46)) == std::vector{INT32_C(2), INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(47)) == std::vector{INT32_C(47)});
assert_that(tools::prime_factorization(INT32_C(48)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(49)) == std::vector{INT32_C(7), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(50)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(51)) == std::vector{INT32_C(3), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(52)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(53)) == std::vector{INT32_C(53)});
assert_that(tools::prime_factorization(INT32_C(54)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(55)) == std::vector{INT32_C(5), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(56)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(57)) == std::vector{INT32_C(3), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(58)) == std::vector{INT32_C(2), INT32_C(29)});
assert_that(tools::prime_factorization(INT32_C(59)) == std::vector{INT32_C(59)});
assert_that(tools::prime_factorization(INT32_C(60)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(61)) == std::vector{INT32_C(61)});
assert_that(tools::prime_factorization(INT32_C(62)) == std::vector{INT32_C(2), INT32_C(31)});
assert_that(tools::prime_factorization(INT32_C(63)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(64)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(65)) == std::vector{INT32_C(5), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(66)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(67)) == std::vector{INT32_C(67)});
assert_that(tools::prime_factorization(INT32_C(68)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(69)) == std::vector{INT32_C(3), INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(70)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(71)) == std::vector{INT32_C(71)});
assert_that(tools::prime_factorization(INT32_C(72)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(73)) == std::vector{INT32_C(73)});
assert_that(tools::prime_factorization(INT32_C(74)) == std::vector{INT32_C(2), INT32_C(37)});
assert_that(tools::prime_factorization(INT32_C(75)) == std::vector{INT32_C(3), INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(76)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(77)) == std::vector{INT32_C(7), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(78)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(79)) == std::vector{INT32_C(79)});
assert_that(tools::prime_factorization(INT32_C(80)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(81)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(82)) == std::vector{INT32_C(2), INT32_C(41)});
assert_that(tools::prime_factorization(INT32_C(83)) == std::vector{INT32_C(83)});
assert_that(tools::prime_factorization(INT32_C(84)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(85)) == std::vector{INT32_C(5), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(86)) == std::vector{INT32_C(2), INT32_C(43)});
assert_that(tools::prime_factorization(INT32_C(87)) == std::vector{INT32_C(3), INT32_C(29)});
assert_that(tools::prime_factorization(INT32_C(88)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(89)) == std::vector{INT32_C(89)});
assert_that(tools::prime_factorization(INT32_C(90)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(91)) == std::vector{INT32_C(7), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(92)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(93)) == std::vector{INT32_C(3), INT32_C(31)});
assert_that(tools::prime_factorization(INT32_C(94)) == std::vector{INT32_C(2), INT32_C(47)});
assert_that(tools::prime_factorization(INT32_C(95)) == std::vector{INT32_C(5), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(96)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(97)) == std::vector{INT32_C(97)});
assert_that(tools::prime_factorization(INT32_C(98)) == std::vector{INT32_C(2), INT32_C(7), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(99)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(100)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(2095133040)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(5), INT32_C(7), INT32_C(11), INT32_C(13), INT32_C(17), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(2147483548)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(7), INT32_C(76695841)});
assert_that(tools::prime_factorization(INT32_C(2147483549)) == std::vector{INT32_C(2147483549)});
assert_that(tools::prime_factorization(INT32_C(2147483550)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(5), INT32_C(5), INT32_C(19), INT32_C(23), INT32_C(181), INT32_C(181)});
assert_that(tools::prime_factorization(INT32_C(2147483551)) == std::vector{INT32_C(32063), INT32_C(66977)});
assert_that(tools::prime_factorization(INT32_C(2147483552)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(37), INT32_C(349), INT32_C(5197)});
assert_that(tools::prime_factorization(INT32_C(2147483553)) == std::vector{INT32_C(3), INT32_C(29), INT32_C(31), INT32_C(503), INT32_C(1583)});
assert_that(tools::prime_factorization(INT32_C(2147483554)) == std::vector{INT32_C(2), INT32_C(17), INT32_C(43), INT32_C(563), INT32_C(2609)});
assert_that(tools::prime_factorization(INT32_C(2147483555)) == std::vector{INT32_C(5), INT32_C(7), INT32_C(7), INT32_C(7), INT32_C(1252177)});
assert_that(tools::prime_factorization(INT32_C(2147483556)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(109), INT32_C(182423)});
assert_that(tools::prime_factorization(INT32_C(2147483557)) == std::vector{INT32_C(3181), INT32_C(675097)});
assert_that(tools::prime_factorization(INT32_C(2147483558)) == std::vector{INT32_C(2), INT32_C(11), INT32_C(11), INT32_C(139), INT32_C(63841)});
assert_that(tools::prime_factorization(INT32_C(2147483559)) == std::vector{INT32_C(3), INT32_C(13), INT32_C(73), INT32_C(754297)});
assert_that(tools::prime_factorization(INT32_C(2147483560)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(227), INT32_C(236507)});
assert_that(tools::prime_factorization(INT32_C(2147483561)) == std::vector{INT32_C(167), INT32_C(12859183)});
assert_that(tools::prime_factorization(INT32_C(2147483562)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(7), INT32_C(631), INT32_C(81031)});
assert_that(tools::prime_factorization(INT32_C(2147483563)) == std::vector{INT32_C(2147483563)});
assert_that(tools::prime_factorization(INT32_C(2147483564)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(6269), INT32_C(85639)});
assert_that(tools::prime_factorization(INT32_C(2147483565)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(5), INT32_C(103), INT32_C(463319)});
assert_that(tools::prime_factorization(INT32_C(2147483566)) == std::vector{INT32_C(2), INT32_C(1073741783)});
assert_that(tools::prime_factorization(INT32_C(2147483567)) == std::vector{INT32_C(11503), INT32_C(186689)});
assert_that(tools::prime_factorization(INT32_C(2147483568)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(41), INT32_C(83), INT32_C(13147)});
assert_that(tools::prime_factorization(INT32_C(2147483569)) == std::vector{INT32_C(7), INT32_C(11), INT32_C(19), INT32_C(1467863)});
assert_that(tools::prime_factorization(INT32_C(2147483570)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(214748357)});
assert_that(tools::prime_factorization(INT32_C(2147483571)) == std::vector{INT32_C(3), INT32_C(17), INT32_C(17), INT32_C(2476913)});
assert_that(tools::prime_factorization(INT32_C(2147483572)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(13), INT32_C(5641), INT32_C(7321)});
assert_that(tools::prime_factorization(INT32_C(2147483573)) == std::vector{INT32_C(23), INT32_C(93368851)});
assert_that(tools::prime_factorization(INT32_C(2147483574)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(53), INT32_C(2251031)});
assert_that(tools::prime_factorization(INT32_C(2147483575)) == std::vector{INT32_C(5), INT32_C(5), INT32_C(85899343)});
assert_that(tools::prime_factorization(INT32_C(2147483576)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(7), INT32_C(2341), INT32_C(16381)});
assert_that(tools::prime_factorization(INT32_C(2147483577)) == std::vector{INT32_C(3), INT32_C(10103), INT32_C(70853)});
assert_that(tools::prime_factorization(INT32_C(2147483578)) == std::vector{INT32_C(2), INT32_C(1073741789)});
assert_that(tools::prime_factorization(INT32_C(2147483579)) == std::vector{INT32_C(2147483579)});
assert_that(tools::prime_factorization(INT32_C(2147483580)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(5), INT32_C(11), INT32_C(47), INT32_C(107), INT32_C(647)});
assert_that(tools::prime_factorization(INT32_C(2147483581)) == std::vector{INT32_C(89), INT32_C(691), INT32_C(34919)});
assert_that(tools::prime_factorization(INT32_C(2147483582)) == std::vector{INT32_C(2), INT32_C(29), INT32_C(97), INT32_C(381707)});
assert_that(tools::prime_factorization(INT32_C(2147483583)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(7), INT32_C(1262483)});
assert_that(tools::prime_factorization(INT32_C(2147483584)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(31), INT32_C(601), INT32_C(1801)});
assert_that(tools::prime_factorization(INT32_C(2147483585)) == std::vector{INT32_C(5), INT32_C(13), INT32_C(179), INT32_C(184571)});
assert_that(tools::prime_factorization(INT32_C(2147483586)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(357913931)});
assert_that(tools::prime_factorization(INT32_C(2147483587)) == std::vector{INT32_C(2147483587)});
assert_that(tools::prime_factorization(INT32_C(2147483588)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(17), INT32_C(19), INT32_C(19), INT32_C(87481)});
assert_that(tools::prime_factorization(INT32_C(2147483589)) == std::vector{INT32_C(3), INT32_C(37), INT32_C(61), INT32_C(317159)});
assert_that(tools::prime_factorization(INT32_C(2147483590)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(7), INT32_C(877), INT32_C(34981)});
assert_that(tools::prime_factorization(INT32_C(2147483591)) == std::vector{INT32_C(11), INT32_C(195225781)});
assert_that(tools::prime_factorization(INT32_C(2147483592)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(4813), INT32_C(6197)});
assert_that(tools::prime_factorization(INT32_C(2147483593)) == std::vector{INT32_C(59), INT32_C(239), INT32_C(152293)});
assert_that(tools::prime_factorization(INT32_C(2147483594)) == std::vector{INT32_C(2), INT32_C(193), INT32_C(1021), INT32_C(5449)});
assert_that(tools::prime_factorization(INT32_C(2147483595)) == std::vector{INT32_C(3), INT32_C(5), INT32_C(143165573)});
assert_that(tools::prime_factorization(INT32_C(2147483596)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(23), INT32_C(23342213)});
assert_that(tools::prime_factorization(INT32_C(2147483597)) == std::vector{INT32_C(7), INT32_C(43), INT32_C(7134497)});
assert_that(tools::prime_factorization(INT32_C(2147483598)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(13), INT32_C(67), INT32_C(163), INT32_C(2521)});
assert_that(tools::prime_factorization(INT32_C(2147483599)) == std::vector{INT32_C(1657), INT32_C(1296007)});
assert_that(tools::prime_factorization(INT32_C(2147483600)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(5), INT32_C(173), INT32_C(31033)});
assert_that(tools::prime_factorization(INT32_C(2147483601)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(238609289)});
assert_that(tools::prime_factorization(INT32_C(2147483602)) == std::vector{INT32_C(2), INT32_C(11), INT32_C(97612891)});
assert_that(tools::prime_factorization(INT32_C(2147483603)) == std::vector{INT32_C(1187), INT32_C(1809169)});
assert_that(tools::prime_factorization(INT32_C(2147483604)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(7), INT32_C(7), INT32_C(197), INT32_C(18539)});
assert_that(tools::prime_factorization(INT32_C(2147483605)) == std::vector{INT32_C(5), INT32_C(17), INT32_C(25264513)});
assert_that(tools::prime_factorization(INT32_C(2147483606)) == std::vector{INT32_C(2), INT32_C(3671), INT32_C(292493)});
assert_that(tools::prime_factorization(INT32_C(2147483607)) == std::vector{INT32_C(3), INT32_C(19), INT32_C(571), INT32_C(65981)});
assert_that(tools::prime_factorization(INT32_C(2147483608)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(71), INT32_C(3780781)});
assert_that(tools::prime_factorization(INT32_C(2147483609)) == std::vector{INT32_C(41), INT32_C(52377649)});
assert_that(tools::prime_factorization(INT32_C(2147483610)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(5), INT32_C(313), INT32_C(25411)});
assert_that(tools::prime_factorization(INT32_C(2147483611)) == std::vector{INT32_C(7), INT32_C(13), INT32_C(29), INT32_C(813749)});
assert_that(tools::prime_factorization(INT32_C(2147483612)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(311), INT32_C(1726273)});
assert_that(tools::prime_factorization(INT32_C(2147483613)) == std::vector{INT32_C(3), INT32_C(11), INT32_C(2953), INT32_C(22037)});
assert_that(tools::prime_factorization(INT32_C(2147483614)) == std::vector{INT32_C(2), INT32_C(101), INT32_C(10631107)});
assert_that(tools::prime_factorization(INT32_C(2147483615)) == std::vector{INT32_C(5), INT32_C(31), INT32_C(13854733)});
assert_that(tools::prime_factorization(INT32_C(2147483616)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(2731), INT32_C(8191)});
assert_that(tools::prime_factorization(INT32_C(2147483617)) == std::vector{INT32_C(6733), INT32_C(318949)});
assert_that(tools::prime_factorization(INT32_C(2147483618)) == std::vector{INT32_C(2), INT32_C(7), INT32_C(367), INT32_C(417961)});
assert_that(tools::prime_factorization(INT32_C(2147483619)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(23), INT32_C(353), INT32_C(29389)});
assert_that(tools::prime_factorization(INT32_C(2147483620)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(4603), INT32_C(23327)});
assert_that(tools::prime_factorization(INT32_C(2147483621)) == std::vector{INT32_C(14741), INT32_C(145681)});
assert_that(tools::prime_factorization(INT32_C(2147483622)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(17), INT32_C(467), INT32_C(45083)});
assert_that(tools::prime_factorization(INT32_C(2147483623)) == std::vector{INT32_C(79), INT32_C(967), INT32_C(28111)});
assert_that(tools::prime_factorization(INT32_C(2147483624)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(11), INT32_C(13), INT32_C(1877171)});
assert_that(tools::prime_factorization(INT32_C(2147483625)) == std::vector{INT32_C(3), INT32_C(5), INT32_C(5), INT32_C(5), INT32_C(7), INT32_C(199), INT32_C(4111)});
assert_that(tools::prime_factorization(INT32_C(2147483626)) == std::vector{INT32_C(2), INT32_C(19), INT32_C(37), INT32_C(1527371)});
assert_that(tools::prime_factorization(INT32_C(2147483627)) == std::vector{INT32_C(47), INT32_C(53), INT32_C(862097)});
assert_that(tools::prime_factorization(INT32_C(2147483628)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(59652323)});
assert_that(tools::prime_factorization(INT32_C(2147483629)) == std::vector{INT32_C(2147483629)});
assert_that(tools::prime_factorization(INT32_C(2147483630)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(6553), INT32_C(32771)});
assert_that(tools::prime_factorization(INT32_C(2147483631)) == std::vector{INT32_C(3), INT32_C(137), INT32_C(263), INT32_C(19867)});
assert_that(tools::prime_factorization(INT32_C(2147483632)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(7), INT32_C(73), INT32_C(262657)});
assert_that(tools::prime_factorization(INT32_C(2147483633)) == std::vector{INT32_C(5843), INT32_C(367531)});
assert_that(tools::prime_factorization(INT32_C(2147483634)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(12097), INT32_C(29587)});
assert_that(tools::prime_factorization(INT32_C(2147483635)) == std::vector{INT32_C(5), INT32_C(11), INT32_C(337), INT32_C(115861)});
assert_that(tools::prime_factorization(INT32_C(2147483636)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(536870909)});
assert_that(tools::prime_factorization(INT32_C(2147483637)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(13), INT32_C(6118187)});
assert_that(tools::prime_factorization(INT32_C(2147483638)) == std::vector{INT32_C(2), INT32_C(2969), INT32_C(361651)});
assert_that(tools::prime_factorization(INT32_C(2147483639)) == std::vector{INT32_C(7), INT32_C(17), INT32_C(18046081)});
assert_that(tools::prime_factorization(INT32_C(2147483640)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(5), INT32_C(29), INT32_C(43), INT32_C(113), INT32_C(127)});
assert_that(tools::prime_factorization(INT32_C(2147483641)) == std::vector{INT32_C(2699), INT32_C(795659)});
assert_that(tools::prime_factorization(INT32_C(2147483642)) == std::vector{INT32_C(2), INT32_C(23), INT32_C(46684427)});
assert_that(tools::prime_factorization(INT32_C(2147483643)) == std::vector{INT32_C(3), INT32_C(715827881)});
assert_that(tools::prime_factorization(INT32_C(2147483644)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(233), INT32_C(1103), INT32_C(2089)});
assert_that(tools::prime_factorization(INT32_C(2147483645)) == std::vector{INT32_C(5), INT32_C(19), INT32_C(22605091)});
assert_that(tools::prime_factorization(INT32_C(2147483646)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(7), INT32_C(11), INT32_C(31), INT32_C(151), INT32_C(331)});
assert_that(tools::prime_factorization(INT32_C(2147483647)) == std::vector{INT32_C(2147483647)});
assert_that(tools::prime_factorization(UINT32_C(1)) == std::vector<std::uint32_t>{});
assert_that(tools::prime_factorization(UINT32_C(2)) == std::vector{UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(3)) == std::vector{UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(4)) == std::vector{UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(5)) == std::vector{UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(6)) == std::vector{UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(7)) == std::vector{UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(8)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(9)) == std::vector{UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(10)) == std::vector{UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(11)) == std::vector{UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(12)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(13)) == std::vector{UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(14)) == std::vector{UINT32_C(2), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(15)) == std::vector{UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(16)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(17)) == std::vector{UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(18)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(19)) == std::vector{UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(20)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(21)) == std::vector{UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(22)) == std::vector{UINT32_C(2), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(23)) == std::vector{UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(24)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(25)) == std::vector{UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(26)) == std::vector{UINT32_C(2), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(27)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(28)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(29)) == std::vector{UINT32_C(29)});
assert_that(tools::prime_factorization(UINT32_C(30)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(31)) == std::vector{UINT32_C(31)});
assert_that(tools::prime_factorization(UINT32_C(32)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(33)) == std::vector{UINT32_C(3), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(34)) == std::vector{UINT32_C(2), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(35)) == std::vector{UINT32_C(5), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(36)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(37)) == std::vector{UINT32_C(37)});
assert_that(tools::prime_factorization(UINT32_C(38)) == std::vector{UINT32_C(2), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(39)) == std::vector{UINT32_C(3), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(40)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(41)) == std::vector{UINT32_C(41)});
assert_that(tools::prime_factorization(UINT32_C(42)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(43)) == std::vector{UINT32_C(43)});
assert_that(tools::prime_factorization(UINT32_C(44)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(45)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(46)) == std::vector{UINT32_C(2), UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(47)) == std::vector{UINT32_C(47)});
assert_that(tools::prime_factorization(UINT32_C(48)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(49)) == std::vector{UINT32_C(7), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(50)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(51)) == std::vector{UINT32_C(3), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(52)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(53)) == std::vector{UINT32_C(53)});
assert_that(tools::prime_factorization(UINT32_C(54)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(55)) == std::vector{UINT32_C(5), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(56)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(57)) == std::vector{UINT32_C(3), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(58)) == std::vector{UINT32_C(2), UINT32_C(29)});
assert_that(tools::prime_factorization(UINT32_C(59)) == std::vector{UINT32_C(59)});
assert_that(tools::prime_factorization(UINT32_C(60)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(61)) == std::vector{UINT32_C(61)});
assert_that(tools::prime_factorization(UINT32_C(62)) == std::vector{UINT32_C(2), UINT32_C(31)});
assert_that(tools::prime_factorization(UINT32_C(63)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(64)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(65)) == std::vector{UINT32_C(5), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(66)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(67)) == std::vector{UINT32_C(67)});
assert_that(tools::prime_factorization(UINT32_C(68)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(69)) == std::vector{UINT32_C(3), UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(70)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(71)) == std::vector{UINT32_C(71)});
assert_that(tools::prime_factorization(UINT32_C(72)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(73)) == std::vector{UINT32_C(73)});
assert_that(tools::prime_factorization(UINT32_C(74)) == std::vector{UINT32_C(2), UINT32_C(37)});
assert_that(tools::prime_factorization(UINT32_C(75)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(76)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(77)) == std::vector{UINT32_C(7), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(78)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(79)) == std::vector{UINT32_C(79)});
assert_that(tools::prime_factorization(UINT32_C(80)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(81)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(82)) == std::vector{UINT32_C(2), UINT32_C(41)});
assert_that(tools::prime_factorization(UINT32_C(83)) == std::vector{UINT32_C(83)});
assert_that(tools::prime_factorization(UINT32_C(84)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(85)) == std::vector{UINT32_C(5), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(86)) == std::vector{UINT32_C(2), UINT32_C(43)});
assert_that(tools::prime_factorization(UINT32_C(87)) == std::vector{UINT32_C(3), UINT32_C(29)});
assert_that(tools::prime_factorization(UINT32_C(88)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(89)) == std::vector{UINT32_C(89)});
assert_that(tools::prime_factorization(UINT32_C(90)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(91)) == std::vector{UINT32_C(7), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(92)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(93)) == std::vector{UINT32_C(3), UINT32_C(31)});
assert_that(tools::prime_factorization(UINT32_C(94)) == std::vector{UINT32_C(2), UINT32_C(47)});
assert_that(tools::prime_factorization(UINT32_C(95)) == std::vector{UINT32_C(5), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(96)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(97)) == std::vector{UINT32_C(97)});
assert_that(tools::prime_factorization(UINT32_C(98)) == std::vector{UINT32_C(2), UINT32_C(7), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(99)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(100)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(3491888400)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(5), UINT32_C(5), UINT32_C(7), UINT32_C(11), UINT32_C(13), UINT32_C(17), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(4294967196)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(13), UINT32_C(67), UINT32_C(163), UINT32_C(2521)});
assert_that(tools::prime_factorization(UINT32_C(4294967197)) == std::vector{UINT32_C(4294967197)});
assert_that(tools::prime_factorization(UINT32_C(4294967198)) == std::vector{UINT32_C(2), UINT32_C(1657), UINT32_C(1296007)});
assert_that(tools::prime_factorization(UINT32_C(4294967199)) == std::vector{UINT32_C(3), UINT32_C(31), UINT32_C(46182443)});
assert_that(tools::prime_factorization(UINT32_C(4294967200)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(5), UINT32_C(173), UINT32_C(31033)});
assert_that(tools::prime_factorization(UINT32_C(4294967201)) == std::vector{UINT32_C(7), UINT32_C(53), UINT32_C(11576731)});
assert_that(tools::prime_factorization(UINT32_C(4294967202)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(238609289)});
assert_that(tools::prime_factorization(UINT32_C(4294967203)) == std::vector{UINT32_C(157), UINT32_C(1051), UINT32_C(26029)});
assert_that(tools::prime_factorization(UINT32_C(4294967204)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(11), UINT32_C(97612891)});
assert_that(tools::prime_factorization(UINT32_C(4294967205)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(286331147)});
assert_that(tools::prime_factorization(UINT32_C(4294967206)) == std::vector{UINT32_C(2), UINT32_C(1187), UINT32_C(1809169)});
assert_that(tools::prime_factorization(UINT32_C(4294967207)) == std::vector{UINT32_C(47), UINT32_C(91382281)});
assert_that(tools::prime_factorization(UINT32_C(4294967208)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(7), UINT32_C(7), UINT32_C(197), UINT32_C(18539)});
assert_that(tools::prime_factorization(UINT32_C(4294967209)) == std::vector{UINT32_C(13), UINT32_C(677), UINT32_C(488009)});
assert_that(tools::prime_factorization(UINT32_C(4294967210)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(17), UINT32_C(25264513)});
assert_that(tools::prime_factorization(UINT32_C(4294967211)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(477218579)});
assert_that(tools::prime_factorization(UINT32_C(4294967212)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3671), UINT32_C(292493)});
assert_that(tools::prime_factorization(UINT32_C(4294967213)) == std::vector{UINT32_C(57139), UINT32_C(75167)});
assert_that(tools::prime_factorization(UINT32_C(4294967214)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(19), UINT32_C(571), UINT32_C(65981)});
assert_that(tools::prime_factorization(UINT32_C(4294967215)) == std::vector{UINT32_C(5), UINT32_C(7), UINT32_C(11), UINT32_C(23), UINT32_C(37), UINT32_C(13109)});
assert_that(tools::prime_factorization(UINT32_C(4294967216)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(71), UINT32_C(3780781)});
assert_that(tools::prime_factorization(UINT32_C(4294967217)) == std::vector{UINT32_C(3), UINT32_C(1431655739)});
assert_that(tools::prime_factorization(UINT32_C(4294967218)) == std::vector{UINT32_C(2), UINT32_C(41), UINT32_C(52377649)});
assert_that(tools::prime_factorization(UINT32_C(4294967219)) == std::vector{UINT32_C(83), UINT32_C(4327), UINT32_C(11959)});
assert_that(tools::prime_factorization(UINT32_C(4294967220)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(5), UINT32_C(313), UINT32_C(25411)});
assert_that(tools::prime_factorization(UINT32_C(4294967221)) == std::vector{UINT32_C(109), UINT32_C(39403369)});
assert_that(tools::prime_factorization(UINT32_C(4294967222)) == std::vector{UINT32_C(2), UINT32_C(7), UINT32_C(13), UINT32_C(29), UINT32_C(813749)});
assert_that(tools::prime_factorization(UINT32_C(4294967223)) == std::vector{UINT32_C(3), UINT32_C(359), UINT32_C(1291), UINT32_C(3089)});
assert_that(tools::prime_factorization(UINT32_C(4294967224)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(311), UINT32_C(1726273)});
assert_that(tools::prime_factorization(UINT32_C(4294967225)) == std::vector{UINT32_C(5), UINT32_C(5), UINT32_C(743), UINT32_C(231223)});
assert_that(tools::prime_factorization(UINT32_C(4294967226)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(11), UINT32_C(2953), UINT32_C(22037)});
assert_that(tools::prime_factorization(UINT32_C(4294967227)) == std::vector{UINT32_C(17), UINT32_C(252645131)});
assert_that(tools::prime_factorization(UINT32_C(4294967228)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(101), UINT32_C(10631107)});
assert_that(tools::prime_factorization(UINT32_C(4294967229)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(7), UINT32_C(977), UINT32_C(69779)});
assert_that(tools::prime_factorization(UINT32_C(4294967230)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(31), UINT32_C(13854733)});
assert_that(tools::prime_factorization(UINT32_C(4294967231)) == std::vector{UINT32_C(4294967231)});
assert_that(tools::prime_factorization(UINT32_C(4294967232)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(2731), UINT32_C(8191)});
assert_that(tools::prime_factorization(UINT32_C(4294967233)) == std::vector{UINT32_C(19), UINT32_C(103), UINT32_C(617), UINT32_C(3557)});
assert_that(tools::prime_factorization(UINT32_C(4294967234)) == std::vector{UINT32_C(2), UINT32_C(6733), UINT32_C(318949)});
assert_that(tools::prime_factorization(UINT32_C(4294967235)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(13), UINT32_C(22025473)});
assert_that(tools::prime_factorization(UINT32_C(4294967236)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(7), UINT32_C(367), UINT32_C(417961)});
assert_that(tools::prime_factorization(UINT32_C(4294967237)) == std::vector{UINT32_C(11), UINT32_C(11), UINT32_C(43), UINT32_C(825479)});
assert_that(tools::prime_factorization(UINT32_C(4294967238)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(23), UINT32_C(353), UINT32_C(29389)});
assert_that(tools::prime_factorization(UINT32_C(4294967239)) == std::vector{UINT32_C(61), UINT32_C(70409299)});
assert_that(tools::prime_factorization(UINT32_C(4294967240)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(4603), UINT32_C(23327)});
assert_that(tools::prime_factorization(UINT32_C(4294967241)) == std::vector{UINT32_C(3), UINT32_C(1431655747)});
assert_that(tools::prime_factorization(UINT32_C(4294967242)) == std::vector{UINT32_C(2), UINT32_C(14741), UINT32_C(145681)});
assert_that(tools::prime_factorization(UINT32_C(4294967243)) == std::vector{UINT32_C(7), UINT32_C(991), UINT32_C(619139)});
assert_that(tools::prime_factorization(UINT32_C(4294967244)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(17), UINT32_C(467), UINT32_C(45083)});
assert_that(tools::prime_factorization(UINT32_C(4294967245)) == std::vector{UINT32_C(5), UINT32_C(59), UINT32_C(211), UINT32_C(69001)});
assert_that(tools::prime_factorization(UINT32_C(4294967246)) == std::vector{UINT32_C(2), UINT32_C(79), UINT32_C(967), UINT32_C(28111)});
assert_that(tools::prime_factorization(UINT32_C(4294967247)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(809), UINT32_C(65543)});
assert_that(tools::prime_factorization(UINT32_C(4294967248)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(11), UINT32_C(13), UINT32_C(1877171)});
assert_that(tools::prime_factorization(UINT32_C(4294967249)) == std::vector{UINT32_C(269), UINT32_C(15966421)});
assert_that(tools::prime_factorization(UINT32_C(4294967250)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(5), UINT32_C(5), UINT32_C(5), UINT32_C(7), UINT32_C(199), UINT32_C(4111)});
assert_that(tools::prime_factorization(UINT32_C(4294967251)) == std::vector{UINT32_C(29), UINT32_C(89), UINT32_C(1664071)});
assert_that(tools::prime_factorization(UINT32_C(4294967252)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(19), UINT32_C(37), UINT32_C(1527371)});
assert_that(tools::prime_factorization(UINT32_C(4294967253)) == std::vector{UINT32_C(3), UINT32_C(1431655751)});
assert_that(tools::prime_factorization(UINT32_C(4294967254)) == std::vector{UINT32_C(2), UINT32_C(47), UINT32_C(53), UINT32_C(862097)});
assert_that(tools::prime_factorization(UINT32_C(4294967255)) == std::vector{UINT32_C(5), UINT32_C(139), UINT32_C(1451), UINT32_C(4259)});
assert_that(tools::prime_factorization(UINT32_C(4294967256)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(59652323)});
assert_that(tools::prime_factorization(UINT32_C(4294967257)) == std::vector{UINT32_C(7), UINT32_C(7), UINT32_C(1061), UINT32_C(82613)});
assert_that(tools::prime_factorization(UINT32_C(4294967258)) == std::vector{UINT32_C(2), UINT32_C(2147483629)});
assert_that(tools::prime_factorization(UINT32_C(4294967259)) == std::vector{UINT32_C(3), UINT32_C(11), UINT32_C(41), UINT32_C(659), UINT32_C(4817)});
assert_that(tools::prime_factorization(UINT32_C(4294967260)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(6553), UINT32_C(32771)});
assert_that(tools::prime_factorization(UINT32_C(4294967261)) == std::vector{UINT32_C(13), UINT32_C(17), UINT32_C(23), UINT32_C(31), UINT32_C(97), UINT32_C(281)});
assert_that(tools::prime_factorization(UINT32_C(4294967262)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(137), UINT32_C(263), UINT32_C(19867)});
assert_that(tools::prime_factorization(UINT32_C(4294967263)) == std::vector{UINT32_C(67), UINT32_C(64103989)});
assert_that(tools::prime_factorization(UINT32_C(4294967264)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(7), UINT32_C(73), UINT32_C(262657)});
assert_that(tools::prime_factorization(UINT32_C(4294967265)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(5), UINT32_C(95443717)});
assert_that(tools::prime_factorization(UINT32_C(4294967266)) == std::vector{UINT32_C(2), UINT32_C(5843), UINT32_C(367531)});
assert_that(tools::prime_factorization(UINT32_C(4294967267)) == std::vector{UINT32_C(107), UINT32_C(1069), UINT32_C(37549)});
assert_that(tools::prime_factorization(UINT32_C(4294967268)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(12097), UINT32_C(29587)});
assert_that(tools::prime_factorization(UINT32_C(4294967269)) == std::vector{UINT32_C(277), UINT32_C(433), UINT32_C(35809)});
assert_that(tools::prime_factorization(UINT32_C(4294967270)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(11), UINT32_C(337), UINT32_C(115861)});
assert_that(tools::prime_factorization(UINT32_C(4294967271)) == std::vector{UINT32_C(3), UINT32_C(7), UINT32_C(19), UINT32_C(3121), UINT32_C(3449)});
assert_that(tools::prime_factorization(UINT32_C(4294967272)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(536870909)});
assert_that(tools::prime_factorization(UINT32_C(4294967273)) == std::vector{UINT32_C(10847), UINT32_C(395959)});
assert_that(tools::prime_factorization(UINT32_C(4294967274)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(13), UINT32_C(6118187)});
assert_that(tools::prime_factorization(UINT32_C(4294967275)) == std::vector{UINT32_C(5), UINT32_C(5), UINT32_C(171798691)});
assert_that(tools::prime_factorization(UINT32_C(4294967276)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2969), UINT32_C(361651)});
assert_that(tools::prime_factorization(UINT32_C(4294967277)) == std::vector{UINT32_C(3), UINT32_C(769), UINT32_C(1861711)});
assert_that(tools::prime_factorization(UINT32_C(4294967278)) == std::vector{UINT32_C(2), UINT32_C(7), UINT32_C(17), UINT32_C(18046081)});
assert_that(tools::prime_factorization(UINT32_C(4294967279)) == std::vector{UINT32_C(4294967279)});
assert_that(tools::prime_factorization(UINT32_C(4294967280)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(5), UINT32_C(29), UINT32_C(43), UINT32_C(113), UINT32_C(127)});
assert_that(tools::prime_factorization(UINT32_C(4294967281)) == std::vector{UINT32_C(11), UINT32_C(181), UINT32_C(241), UINT32_C(8951)});
assert_that(tools::prime_factorization(UINT32_C(4294967282)) == std::vector{UINT32_C(2), UINT32_C(2699), UINT32_C(795659)});
assert_that(tools::prime_factorization(UINT32_C(4294967283)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(389), UINT32_C(1226783)});
assert_that(tools::prime_factorization(UINT32_C(4294967284)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(23), UINT32_C(46684427)});
assert_that(tools::prime_factorization(UINT32_C(4294967285)) == std::vector{UINT32_C(5), UINT32_C(7), UINT32_C(122713351)});
assert_that(tools::prime_factorization(UINT32_C(4294967286)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(715827881)});
assert_that(tools::prime_factorization(UINT32_C(4294967287)) == std::vector{UINT32_C(13), UINT32_C(71), UINT32_C(71), UINT32_C(65539)});
assert_that(tools::prime_factorization(UINT32_C(4294967288)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(233), UINT32_C(1103), UINT32_C(2089)});
assert_that(tools::prime_factorization(UINT32_C(4294967289)) == std::vector{UINT32_C(3), UINT32_C(37), UINT32_C(167), UINT32_C(223), UINT32_C(1039)});
assert_that(tools::prime_factorization(UINT32_C(4294967290)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(19), UINT32_C(22605091)});
assert_that(tools::prime_factorization(UINT32_C(4294967291)) == std::vector{UINT32_C(4294967291)});
assert_that(tools::prime_factorization(UINT32_C(4294967292)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(7), UINT32_C(11), UINT32_C(31), UINT32_C(151), UINT32_C(331)});
assert_that(tools::prime_factorization(UINT32_C(4294967293)) == std::vector{UINT32_C(9241), UINT32_C(464773)});
assert_that(tools::prime_factorization(UINT32_C(4294967294)) == std::vector{UINT32_C(2), UINT32_C(2147483647)});
assert_that(tools::prime_factorization(UINT32_C(4294967295)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(17), UINT32_C(257), UINT32_C(65537)});
assert_that(tools::prime_factorization(INT64_C(1)) == std::vector<std::int64_t>{});
assert_that(tools::prime_factorization(INT64_C(2)) == std::vector{INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(3)) == std::vector{INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(4)) == std::vector{INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(5)) == std::vector{INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(6)) == std::vector{INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(7)) == std::vector{INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(8)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(9)) == std::vector{INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(10)) == std::vector{INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(11)) == std::vector{INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(12)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(13)) == std::vector{INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(14)) == std::vector{INT64_C(2), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(15)) == std::vector{INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(16)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(17)) == std::vector{INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(18)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(19)) == std::vector{INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(20)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(21)) == std::vector{INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(22)) == std::vector{INT64_C(2), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(23)) == std::vector{INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(24)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(25)) == std::vector{INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(26)) == std::vector{INT64_C(2), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(27)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(28)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(29)) == std::vector{INT64_C(29)});
assert_that(tools::prime_factorization(INT64_C(30)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(31)) == std::vector{INT64_C(31)});
assert_that(tools::prime_factorization(INT64_C(32)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(33)) == std::vector{INT64_C(3), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(34)) == std::vector{INT64_C(2), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(35)) == std::vector{INT64_C(5), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(36)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(37)) == std::vector{INT64_C(37)});
assert_that(tools::prime_factorization(INT64_C(38)) == std::vector{INT64_C(2), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(39)) == std::vector{INT64_C(3), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(40)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(41)) == std::vector{INT64_C(41)});
assert_that(tools::prime_factorization(INT64_C(42)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(43)) == std::vector{INT64_C(43)});
assert_that(tools::prime_factorization(INT64_C(44)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(45)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(46)) == std::vector{INT64_C(2), INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(47)) == std::vector{INT64_C(47)});
assert_that(tools::prime_factorization(INT64_C(48)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(49)) == std::vector{INT64_C(7), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(50)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(51)) == std::vector{INT64_C(3), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(52)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(53)) == std::vector{INT64_C(53)});
assert_that(tools::prime_factorization(INT64_C(54)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(55)) == std::vector{INT64_C(5), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(56)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(57)) == std::vector{INT64_C(3), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(58)) == std::vector{INT64_C(2), INT64_C(29)});
assert_that(tools::prime_factorization(INT64_C(59)) == std::vector{INT64_C(59)});
assert_that(tools::prime_factorization(INT64_C(60)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(61)) == std::vector{INT64_C(61)});
assert_that(tools::prime_factorization(INT64_C(62)) == std::vector{INT64_C(2), INT64_C(31)});
assert_that(tools::prime_factorization(INT64_C(63)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(64)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(65)) == std::vector{INT64_C(5), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(66)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(67)) == std::vector{INT64_C(67)});
assert_that(tools::prime_factorization(INT64_C(68)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(69)) == std::vector{INT64_C(3), INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(70)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(71)) == std::vector{INT64_C(71)});
assert_that(tools::prime_factorization(INT64_C(72)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(73)) == std::vector{INT64_C(73)});
assert_that(tools::prime_factorization(INT64_C(74)) == std::vector{INT64_C(2), INT64_C(37)});
assert_that(tools::prime_factorization(INT64_C(75)) == std::vector{INT64_C(3), INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(76)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(77)) == std::vector{INT64_C(7), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(78)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(79)) == std::vector{INT64_C(79)});
assert_that(tools::prime_factorization(INT64_C(80)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(81)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(82)) == std::vector{INT64_C(2), INT64_C(41)});
assert_that(tools::prime_factorization(INT64_C(83)) == std::vector{INT64_C(83)});
assert_that(tools::prime_factorization(INT64_C(84)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(85)) == std::vector{INT64_C(5), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(86)) == std::vector{INT64_C(2), INT64_C(43)});
assert_that(tools::prime_factorization(INT64_C(87)) == std::vector{INT64_C(3), INT64_C(29)});
assert_that(tools::prime_factorization(INT64_C(88)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(89)) == std::vector{INT64_C(89)});
assert_that(tools::prime_factorization(INT64_C(90)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(91)) == std::vector{INT64_C(7), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(92)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(93)) == std::vector{INT64_C(3), INT64_C(31)});
assert_that(tools::prime_factorization(INT64_C(94)) == std::vector{INT64_C(2), INT64_C(47)});
assert_that(tools::prime_factorization(INT64_C(95)) == std::vector{INT64_C(5), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(96)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(97)) == std::vector{INT64_C(97)});
assert_that(tools::prime_factorization(INT64_C(98)) == std::vector{INT64_C(2), INT64_C(7), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(99)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(100)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(9200527969062830400)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(5), INT64_C(7), INT64_C(7), INT64_C(11), INT64_C(13), INT64_C(17), INT64_C(19), INT64_C(23), INT64_C(29), INT64_C(31), INT64_C(37), INT64_C(41)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775708)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(1319), INT64_C(1748175139661633)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775709)) == std::vector{INT64_C(7), INT64_C(7), INT64_C(13), INT64_C(29), INT64_C(2729), INT64_C(182956886477)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775710)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(131), INT64_C(2699), INT64_C(364289), INT64_C(795659)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775711)) == std::vector{INT64_C(1171), INT64_C(16573), INT64_C(475260479017)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775712)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(11), INT64_C(26202761468337431)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775713)) == std::vector{INT64_C(3), INT64_C(23), INT64_C(133672058505141677)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775714)) == std::vector{INT64_C(2), INT64_C(17), INT64_C(19), INT64_C(215153), INT64_C(66360523403)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775715)) == std::vector{INT64_C(5), INT64_C(1844674407370955143)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775716)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(7), INT64_C(1607), INT64_C(2067431), INT64_C(33049397)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775717)) == std::vector{INT64_C(59), INT64_C(156328339607708063)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775718)) == std::vector{INT64_C(2), INT64_C(41), INT64_C(101), INT64_C(4051), INT64_C(6199), INT64_C(44347651)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775719)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(1024819115206086191)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775720)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(4229), INT64_C(54524545027517)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775721)) == std::vector{INT64_C(53), INT64_C(1791191), INT64_C(97156521827)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775722)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(13), INT64_C(3109), INT64_C(38034210179111)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775723)) == std::vector{INT64_C(7), INT64_C(11), INT64_C(43), INT64_C(27109), INT64_C(234293), INT64_C(438589)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775724)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(124367), INT64_C(18540633843493)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775725)) == std::vector{INT64_C(3), INT64_C(5), INT64_C(5), INT64_C(47), INT64_C(47), INT64_C(55671477512327)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775726)) == std::vector{INT64_C(2), INT64_C(1087), INT64_C(4242581433695849)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775727)) == std::vector{INT64_C(11113), INT64_C(829962389710679)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775728)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(37), INT64_C(34519), INT64_C(83717), INT64_C(199679)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775729)) == std::vector{INT64_C(97), INT64_C(103), INT64_C(2707), INT64_C(32233), INT64_C(10580149)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775730)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(7), INT64_C(89), INT64_C(1480477052464651)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775731)) == std::vector{INT64_C(3), INT64_C(17), INT64_C(319856591), INT64_C(565410991)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775732)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(71), INT64_C(139), INT64_C(1193693), INT64_C(195732949)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775733)) == std::vector{INT64_C(19), INT64_C(239), INT64_C(6197), INT64_C(8209), INT64_C(39926981)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775734)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(11), INT64_C(73), INT64_C(3527), INT64_C(542772044869)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775735)) == std::vector{INT64_C(5), INT64_C(13), INT64_C(141898031336227319)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775736)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(23), INT64_C(46684427), INT64_C(1073741827)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775737)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(7), INT64_C(313), INT64_C(68329), INT64_C(6845414887)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775738)) == std::vector{INT64_C(2), INT64_C(29), INT64_C(31), INT64_C(17597), INT64_C(33289), INT64_C(8757107)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775739)) == std::vector{INT64_C(61), INT64_C(3264649), INT64_C(46315184351)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775740)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(5), INT64_C(153722867280912929)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775741)) == std::vector{INT64_C(75883), INT64_C(299881), INT64_C(405318367)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775742)) == std::vector{INT64_C(2), INT64_C(252449), INT64_C(18267792775679)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775743)) == std::vector{INT64_C(3), INT64_C(79), INT64_C(116533), INT64_C(333958463183)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775744)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(7), INT64_C(32377), INT64_C(524287), INT64_C(1212847)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775745)) == std::vector{INT64_C(5), INT64_C(11), INT64_C(199), INT64_C(11587), INT64_C(72728219243)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775746)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(179), INT64_C(23021), INT64_C(124348343983)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775747)) == std::vector{INT64_C(677), INT64_C(78919), INT64_C(172631277569)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775748)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(13), INT64_C(17), INT64_C(37359691), INT64_C(279276367)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775749)) == std::vector{INT64_C(3), INT64_C(8447), INT64_C(363970326224489)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775750)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(5), INT64_C(5), INT64_C(36893488147419103)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775751)) == std::vector{INT64_C(7), INT64_C(17659), INT64_C(74614903261427)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775752)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(19), INT64_C(93053), INT64_C(217367447189)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775753)) == std::vector{INT64_C(266416229), INT64_C(34620158357)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775754)) == std::vector{INT64_C(2), INT64_C(343242169), INT64_C(13435662733)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775755)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(68321274347072413)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775756)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(11), INT64_C(227), INT64_C(263), INT64_C(18341), INT64_C(191439889)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775757)) == std::vector{INT64_C(149), INT64_C(5987), INT64_C(10339372933139)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775758)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(7), INT64_C(7), INT64_C(43826197), INT64_C(715827881)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775759)) == std::vector{INT64_C(23), INT64_C(41), INT64_C(620441), INT64_C(15764403593)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775760)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(2663), INT64_C(43294085790719)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775761)) == std::vector{INT64_C(3), INT64_C(13), INT64_C(13), INT64_C(619), INT64_C(739), INT64_C(39769184003)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775762)) == std::vector{INT64_C(2), INT64_C(107), INT64_C(1117), INT64_C(38585379884599)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775763)) == std::vector{INT64_C(4481), INT64_C(63601), INT64_C(32363153923)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775764)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(256204778801521549)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775765)) == std::vector{INT64_C(5), INT64_C(7), INT64_C(17), INT64_C(37), INT64_C(418958529950251)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775766)) == std::vector{INT64_C(2), INT64_C(43), INT64_C(67), INT64_C(193), INT64_C(809383), INT64_C(10247197)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775767)) == std::vector{INT64_C(3), INT64_C(11), INT64_C(29), INT64_C(19473149), INT64_C(494927519)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775768)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(409), INT64_C(1793599), INT64_C(1571632781)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775769)) == std::vector{INT64_C(31), INT64_C(10037), INT64_C(29643133428427)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775770)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(5), INT64_C(986507), INT64_C(311650839337)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775771)) == std::vector{INT64_C(19), INT64_C(485440633518672409)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775772)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(7), INT64_C(47), INT64_C(8627903), INT64_C(812322689)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775773)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(1024819115206086197)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775774)) == std::vector{INT64_C(2), INT64_C(13), INT64_C(53), INT64_C(6693303364916383)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775775)) == std::vector{INT64_C(5), INT64_C(5), INT64_C(109), INT64_C(57881), INT64_C(58477284139)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775776)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(59), INT64_C(233), INT64_C(1103), INT64_C(2089), INT64_C(3033169)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775777)) == std::vector{INT64_C(584911), INT64_C(15768846947407)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775778)) == std::vector{INT64_C(2), INT64_C(11), INT64_C(137), INT64_C(547), INT64_C(5594472617641)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775779)) == std::vector{INT64_C(3), INT64_C(7), INT64_C(439208192231179799)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775780)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(461168601842738789)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775781)) == std::vector{INT64_C(773), INT64_C(2713), INT64_C(19993), INT64_C(219979633)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775782)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(17), INT64_C(23), INT64_C(319279), INT64_C(456065899)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775783)) == std::vector{INT64_C(9223372036854775783)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775784)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(1177067), INT64_C(979486728119)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775785)) == std::vector{INT64_C(3), INT64_C(5), INT64_C(24097), INT64_C(25517345276327)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775786)) == std::vector{INT64_C(2), INT64_C(7), INT64_C(181), INT64_C(229), INT64_C(3697), INT64_C(4299304283)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775787)) == std::vector{INT64_C(13), INT64_C(440303), INT64_C(1611367982233)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775788)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(643), INT64_C(1195356666259043)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775789)) == std::vector{INT64_C(11), INT64_C(3931), INT64_C(213301543369829)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775790)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(19), INT64_C(83), INT64_C(1277), INT64_C(20261), INT64_C(22605091)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775791)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(14737), INT64_C(4837853), INT64_C(14374259)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775792)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(179951), INT64_C(3203431780337)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775793)) == std::vector{INT64_C(7), INT64_C(113), INT64_C(5647), INT64_C(2064883032409)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775794)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3491), INT64_C(440340496364689)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775795)) == std::vector{INT64_C(5), INT64_C(191), INT64_C(421), INT64_C(90679), INT64_C(252986611)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775796)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(29), INT64_C(79511827903920481)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775797)) == std::vector{INT64_C(3), INT64_C(3074457345618258599)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775798)) == std::vector{INT64_C(2), INT64_C(34421), INT64_C(133978850655919)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775799)) == std::vector{INT64_C(17), INT64_C(17), INT64_C(17), INT64_C(2927), INT64_C(641387128649)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775800)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(5), INT64_C(7), INT64_C(11), INT64_C(13), INT64_C(31), INT64_C(41), INT64_C(61), INT64_C(151), INT64_C(331), INT64_C(1321)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775801)) == std::vector{INT64_C(157), INT64_C(1973), INT64_C(29775769179641)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775802)) == std::vector{INT64_C(2), INT64_C(37), INT64_C(9902437), INT64_C(12586817029)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775803)) == std::vector{INT64_C(3), INT64_C(71), INT64_C(42013), INT64_C(1030686124187)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775804)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2305843009213693951)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775805)) == std::vector{INT64_C(5), INT64_C(23), INT64_C(53301701), INT64_C(1504703107)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775806)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(715827883), INT64_C(2147483647)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775807)) == std::vector{INT64_C(7), INT64_C(7), INT64_C(73), INT64_C(127), INT64_C(337), INT64_C(92737), INT64_C(649657)});
assert_that(tools::prime_factorization(UINT64_C(1)) == std::vector<std::uint64_t>{});
assert_that(tools::prime_factorization(UINT64_C(2)) == std::vector{UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(3)) == std::vector{UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(4)) == std::vector{UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(5)) == std::vector{UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(6)) == std::vector{UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(7)) == std::vector{UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(8)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(9)) == std::vector{UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(10)) == std::vector{UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(11)) == std::vector{UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(12)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(13)) == std::vector{UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(14)) == std::vector{UINT64_C(2), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(15)) == std::vector{UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(16)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(17)) == std::vector{UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(18)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(19)) == std::vector{UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(20)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(21)) == std::vector{UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(22)) == std::vector{UINT64_C(2), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(23)) == std::vector{UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(24)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(25)) == std::vector{UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(26)) == std::vector{UINT64_C(2), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(27)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(28)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(29)) == std::vector{UINT64_C(29)});
assert_that(tools::prime_factorization(UINT64_C(30)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(31)) == std::vector{UINT64_C(31)});
assert_that(tools::prime_factorization(UINT64_C(32)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(33)) == std::vector{UINT64_C(3), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(34)) == std::vector{UINT64_C(2), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(35)) == std::vector{UINT64_C(5), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(36)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(37)) == std::vector{UINT64_C(37)});
assert_that(tools::prime_factorization(UINT64_C(38)) == std::vector{UINT64_C(2), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(39)) == std::vector{UINT64_C(3), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(40)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(41)) == std::vector{UINT64_C(41)});
assert_that(tools::prime_factorization(UINT64_C(42)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(43)) == std::vector{UINT64_C(43)});
assert_that(tools::prime_factorization(UINT64_C(44)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(45)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(46)) == std::vector{UINT64_C(2), UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(47)) == std::vector{UINT64_C(47)});
assert_that(tools::prime_factorization(UINT64_C(48)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(49)) == std::vector{UINT64_C(7), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(50)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(51)) == std::vector{UINT64_C(3), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(52)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(53)) == std::vector{UINT64_C(53)});
assert_that(tools::prime_factorization(UINT64_C(54)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(55)) == std::vector{UINT64_C(5), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(56)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(57)) == std::vector{UINT64_C(3), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(58)) == std::vector{UINT64_C(2), UINT64_C(29)});
assert_that(tools::prime_factorization(UINT64_C(59)) == std::vector{UINT64_C(59)});
assert_that(tools::prime_factorization(UINT64_C(60)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(61)) == std::vector{UINT64_C(61)});
assert_that(tools::prime_factorization(UINT64_C(62)) == std::vector{UINT64_C(2), UINT64_C(31)});
assert_that(tools::prime_factorization(UINT64_C(63)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(64)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(65)) == std::vector{UINT64_C(5), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(66)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(67)) == std::vector{UINT64_C(67)});
assert_that(tools::prime_factorization(UINT64_C(68)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(69)) == std::vector{UINT64_C(3), UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(70)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(71)) == std::vector{UINT64_C(71)});
assert_that(tools::prime_factorization(UINT64_C(72)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(73)) == std::vector{UINT64_C(73)});
assert_that(tools::prime_factorization(UINT64_C(74)) == std::vector{UINT64_C(2), UINT64_C(37)});
assert_that(tools::prime_factorization(UINT64_C(75)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(76)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(77)) == std::vector{UINT64_C(7), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(78)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(79)) == std::vector{UINT64_C(79)});
assert_that(tools::prime_factorization(UINT64_C(80)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(81)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(82)) == std::vector{UINT64_C(2), UINT64_C(41)});
assert_that(tools::prime_factorization(UINT64_C(83)) == std::vector{UINT64_C(83)});
assert_that(tools::prime_factorization(UINT64_C(84)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(85)) == std::vector{UINT64_C(5), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(86)) == std::vector{UINT64_C(2), UINT64_C(43)});
assert_that(tools::prime_factorization(UINT64_C(87)) == std::vector{UINT64_C(3), UINT64_C(29)});
assert_that(tools::prime_factorization(UINT64_C(88)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(89)) == std::vector{UINT64_C(89)});
assert_that(tools::prime_factorization(UINT64_C(90)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(91)) == std::vector{UINT64_C(7), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(92)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(93)) == std::vector{UINT64_C(3), UINT64_C(31)});
assert_that(tools::prime_factorization(UINT64_C(94)) == std::vector{UINT64_C(2), UINT64_C(47)});
assert_that(tools::prime_factorization(UINT64_C(95)) == std::vector{UINT64_C(5), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(96)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(97)) == std::vector{UINT64_C(97)});
assert_that(tools::prime_factorization(UINT64_C(98)) == std::vector{UINT64_C(2), UINT64_C(7), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(99)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(100)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(18401055938125660800)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(5), UINT64_C(5), UINT64_C(7), UINT64_C(7), UINT64_C(11), UINT64_C(13), UINT64_C(17), UINT64_C(19), UINT64_C(23), UINT64_C(29), UINT64_C(31), UINT64_C(37), UINT64_C(41)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551516)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(7), UINT64_C(7), UINT64_C(43826197), UINT64_C(715827881)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551517)) == std::vector{UINT64_C(397), UINT64_C(46465350311610961)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551518)) == std::vector{UINT64_C(2), UINT64_C(23), UINT64_C(41), UINT64_C(620441), UINT64_C(15764403593)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551519)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(307), UINT64_C(405029), UINT64_C(16483624697)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551520)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(2663), UINT64_C(43294085790719)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551521)) == std::vector{UINT64_C(18446744073709551521)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551522)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(13), UINT64_C(13), UINT64_C(619), UINT64_C(739), UINT64_C(39769184003)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551523)) == std::vector{UINT64_C(7), UINT64_C(11), UINT64_C(11), UINT64_C(19), UINT64_C(6897409), UINT64_C(166186879)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551524)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(107), UINT64_C(1117), UINT64_C(38585379884599)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551525)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(5), UINT64_C(4441), UINT64_C(55383154165607)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551526)) == std::vector{UINT64_C(2), UINT64_C(4481), UINT64_C(63601), UINT64_C(32363153923)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551527)) == std::vector{UINT64_C(17099), UINT64_C(1078820052266773)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551528)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(256204778801521549)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551529)) == std::vector{UINT64_C(14843), UINT64_C(13973891), UINT64_C(88936633)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551530)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(7), UINT64_C(17), UINT64_C(37), UINT64_C(418958529950251)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551531)) == std::vector{UINT64_C(3), UINT64_C(962165251), UINT64_C(6390705427)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551532)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(43), UINT64_C(67), UINT64_C(193), UINT64_C(809383), UINT64_C(10247197)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551533)) == std::vector{UINT64_C(18446744073709551533)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551534)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(11), UINT64_C(29), UINT64_C(19473149), UINT64_C(494927519)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551535)) == std::vector{UINT64_C(5), UINT64_C(13), UINT64_C(71), UINT64_C(71), UINT64_C(9629), UINT64_C(65539), UINT64_C(89209)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551536)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(409), UINT64_C(1793599), UINT64_C(1571632781)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551537)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(7), UINT64_C(101), UINT64_C(7623919), UINT64_C(126753007)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551538)) == std::vector{UINT64_C(2), UINT64_C(31), UINT64_C(10037), UINT64_C(29643133428427)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551539)) == std::vector{UINT64_C(61), UINT64_C(268909), UINT64_C(1124564966411)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551540)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(5), UINT64_C(986507), UINT64_C(311650839337)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551541)) == std::vector{UINT64_C(23), UINT64_C(73), UINT64_C(7283), UINT64_C(1508546551513)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551542)) == std::vector{UINT64_C(2), UINT64_C(19), UINT64_C(485440633518672409)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551543)) == std::vector{UINT64_C(3), UINT64_C(839), UINT64_C(7328861372153179)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551544)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(7), UINT64_C(47), UINT64_C(8627903), UINT64_C(812322689)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551545)) == std::vector{UINT64_C(5), UINT64_C(11), UINT64_C(3319), UINT64_C(36871), UINT64_C(2740721231)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551546)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(1024819115206086197)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551547)) == std::vector{UINT64_C(17), UINT64_C(211), UINT64_C(251), UINT64_C(1101431), UINT64_C(18601901)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551548)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(13), UINT64_C(53), UINT64_C(6693303364916383)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551549)) == std::vector{UINT64_C(3), UINT64_C(89), UINT64_C(69088929115017047)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551550)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(5), UINT64_C(109), UINT64_C(57881), UINT64_C(58477284139)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551551)) == std::vector{UINT64_C(7), UINT64_C(131), UINT64_C(20116405751046403)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551552)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(59), UINT64_C(233), UINT64_C(1103), UINT64_C(2089), UINT64_C(3033169)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551553)) == std::vector{UINT64_C(401), UINT64_C(119241217), UINT64_C(385788209)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551554)) == std::vector{UINT64_C(2), UINT64_C(584911), UINT64_C(15768846947407)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551555)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(5), UINT64_C(97), UINT64_C(197), UINT64_C(325957), UINT64_C(65812583)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551556)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(11), UINT64_C(137), UINT64_C(547), UINT64_C(5594472617641)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551557)) == std::vector{UINT64_C(18446744073709551557)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551558)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(7), UINT64_C(439208192231179799)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551559)) == std::vector{UINT64_C(41), UINT64_C(163), UINT64_C(269), UINT64_C(8807), UINT64_C(1165112831)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551560)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(461168601842738789)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551561)) == std::vector{UINT64_C(3), UINT64_C(13), UINT64_C(19), UINT64_C(103), UINT64_C(1811), UINT64_C(133458377137)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551562)) == std::vector{UINT64_C(2), UINT64_C(773), UINT64_C(2713), UINT64_C(19993), UINT64_C(219979633)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551563)) == std::vector{UINT64_C(29), UINT64_C(74187931), UINT64_C(8574098437)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551564)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(17), UINT64_C(23), UINT64_C(319279), UINT64_C(456065899)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551565)) == std::vector{UINT64_C(5), UINT64_C(7), UINT64_C(7), UINT64_C(79), UINT64_C(599), UINT64_C(659), UINT64_C(2414428283)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551566)) == std::vector{UINT64_C(2), UINT64_C(9223372036854775783)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551567)) == std::vector{UINT64_C(3), UINT64_C(11), UINT64_C(37), UINT64_C(167), UINT64_C(223), UINT64_C(1039), UINT64_C(6323), UINT64_C(61751)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551568)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(1177067), UINT64_C(979486728119)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551569)) == std::vector{UINT64_C(31), UINT64_C(173), UINT64_C(9419), UINT64_C(439771), UINT64_C(830387)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551570)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(5), UINT64_C(24097), UINT64_C(25517345276327)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551571)) == std::vector{UINT64_C(11071), UINT64_C(844709), UINT64_C(1972539689)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551572)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(7), UINT64_C(181), UINT64_C(229), UINT64_C(3697), UINT64_C(4299304283)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551573)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(31799), UINT64_C(64456059323003)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551574)) == std::vector{UINT64_C(2), UINT64_C(13), UINT64_C(440303), UINT64_C(1611367982233)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551575)) == std::vector{UINT64_C(5), UINT64_C(5), UINT64_C(43), UINT64_C(122099), UINT64_C(140539741759)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551576)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(643), UINT64_C(1195356666259043)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551577)) == std::vector{UINT64_C(139646831), UINT64_C(132095686967)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551578)) == std::vector{UINT64_C(2), UINT64_C(11), UINT64_C(3931), UINT64_C(213301543369829)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551579)) == std::vector{UINT64_C(3), UINT64_C(7), UINT64_C(57906439), UINT64_C(15169580441)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551580)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(19), UINT64_C(83), UINT64_C(1277), UINT64_C(20261), UINT64_C(22605091)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551581)) == std::vector{UINT64_C(17), UINT64_C(72786899), UINT64_C(14907938207)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551582)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(14737), UINT64_C(4837853), UINT64_C(14374259)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551583)) == std::vector{UINT64_C(827), UINT64_C(3894899), UINT64_C(5726879071)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551584)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(179951), UINT64_C(3203431780337)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551585)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(499), UINT64_C(2593), UINT64_C(950441521877)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551586)) == std::vector{UINT64_C(2), UINT64_C(7), UINT64_C(113), UINT64_C(5647), UINT64_C(2064883032409)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551587)) == std::vector{UINT64_C(13), UINT64_C(23), UINT64_C(23), UINT64_C(16561661), UINT64_C(161963371)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551588)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3491), UINT64_C(440340496364689)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551589)) == std::vector{UINT64_C(11), UINT64_C(13177), UINT64_C(127265442359687)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551590)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(191), UINT64_C(421), UINT64_C(90679), UINT64_C(252986611)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551591)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(47), UINT64_C(3384529), UINT64_C(4294967291)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551592)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(29), UINT64_C(79511827903920481)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551593)) == std::vector{UINT64_C(7), UINT64_C(16547), UINT64_C(159258424692517)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551594)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3074457345618258599)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551595)) == std::vector{UINT64_C(5), UINT64_C(373), UINT64_C(3301), UINT64_C(2996369460503)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551596)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(34421), UINT64_C(133978850655919)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551597)) == std::vector{UINT64_C(3), UINT64_C(6148914691236517199)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551598)) == std::vector{UINT64_C(2), UINT64_C(17), UINT64_C(17), UINT64_C(17), UINT64_C(2927), UINT64_C(641387128649)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551599)) == std::vector{UINT64_C(19), UINT64_C(67), UINT64_C(14490765179661863)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551600)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(5), UINT64_C(5), UINT64_C(7), UINT64_C(11), UINT64_C(13), UINT64_C(31), UINT64_C(41), UINT64_C(61), UINT64_C(151), UINT64_C(331), UINT64_C(1321)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551601)) == std::vector{UINT64_C(53), UINT64_C(348051774975651917)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551602)) == std::vector{UINT64_C(2), UINT64_C(157), UINT64_C(1973), UINT64_C(29775769179641)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551603)) == std::vector{UINT64_C(3), UINT64_C(139), UINT64_C(2306123), UINT64_C(19182323033)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551604)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(37), UINT64_C(9902437), UINT64_C(12586817029)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551605)) == std::vector{UINT64_C(5), UINT64_C(2551), UINT64_C(1446236305269271)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551606)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(71), UINT64_C(42013), UINT64_C(1030686124187)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551607)) == std::vector{UINT64_C(7), UINT64_C(9241), UINT64_C(464773), UINT64_C(613566757)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551608)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2305843009213693951)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551609)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(818923289), UINT64_C(2502845209)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551610)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(23), UINT64_C(53301701), UINT64_C(1504703107)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551611)) == std::vector{UINT64_C(11), UINT64_C(59), UINT64_C(98818999), UINT64_C(287630261)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551612)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(715827883), UINT64_C(2147483647)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551613)) == std::vector{UINT64_C(13), UINT64_C(3889), UINT64_C(364870227143809)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551614)) == std::vector{UINT64_C(2), UINT64_C(7), UINT64_C(7), UINT64_C(73), UINT64_C(127), UINT64_C(337), UINT64_C(92737), UINT64_C(649657)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551615)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(17), UINT64_C(257), UINT64_C(641), UINT64_C(65537), UINT64_C(6700417)});
return 0;
}
#line 1 "tests/prime_factorization/severe_cases.test.cpp"
// competitive-verifier: STANDALONE
#include <cstdint>
#include <iostream>
#include <vector>
#line 1 "tools/assert_that.hpp"
#line 5 "tools/assert_that.hpp"
#include <cstdlib>
#define assert_that_impl(cond, file, line, func) do {\
if (!cond) {\
std::cerr << file << ':' << line << ": " << func << ": Assertion `" << #cond << "' failed." << '\n';\
std::exit(EXIT_FAILURE);\
}\
} while (false)
#define assert_that(...) assert_that_impl((__VA_ARGS__), __FILE__, __LINE__, __func__)
#line 1 "tools/prime_factorization.hpp"
#include <algorithm>
#include <cassert>
#include <concepts>
#include <numeric>
#include <queue>
#include <tuple>
#include <utility>
#line 1 "tools/floor_log2.hpp"
#line 1 "tools/bit_width.hpp"
#include <bit>
#line 6 "tools/bit_width.hpp"
#include <type_traits>
#line 1 "tools/is_signed.hpp"
#line 5 "tools/is_signed.hpp"
namespace tools {
template <typename T>
struct is_signed : std::is_signed<T> {};
template <typename T>
inline constexpr bool is_signed_v = tools::is_signed<T>::value;
}
#line 1 "tools/is_unsigned.hpp"
#line 5 "tools/is_unsigned.hpp"
namespace tools {
template <typename T>
struct is_unsigned : std::is_unsigned<T> {};
template <typename T>
inline constexpr bool is_unsigned_v = tools::is_unsigned<T>::value;
}
#line 1 "tools/make_unsigned.hpp"
#line 5 "tools/make_unsigned.hpp"
namespace tools {
template <typename T>
struct make_unsigned : std::make_unsigned<T> {};
template <typename T>
using make_unsigned_t = typename tools::make_unsigned<T>::type;
}
#line 1 "tools/non_bool_integral.hpp"
#line 1 "tools/integral.hpp"
#line 1 "tools/is_integral.hpp"
#line 5 "tools/is_integral.hpp"
namespace tools {
template <typename T>
struct is_integral : std::is_integral<T> {};
template <typename T>
inline constexpr bool is_integral_v = tools::is_integral<T>::value;
}
#line 5 "tools/integral.hpp"
namespace tools {
template <typename T>
concept integral = tools::is_integral_v<T>;
}
#line 7 "tools/non_bool_integral.hpp"
namespace tools {
template <typename T>
concept non_bool_integral = tools::integral<T> && !std::same_as<std::remove_cv_t<T>, bool>;
}
#line 12 "tools/bit_width.hpp"
namespace tools {
namespace detail::bit_width {
template <tools::non_bool_integral T>
struct impl {
constexpr int operator()(const T x) const noexcept(noexcept(impl<tools::make_unsigned_t<T>>{}(x))) requires tools::is_signed_v<T> {
assert(x >= 0);
return impl<tools::make_unsigned_t<T>>{}(x);
}
constexpr int operator()(const T x) const noexcept(noexcept(std::bit_width(x))) requires tools::is_unsigned_v<T> {
return std::bit_width(x);
}
};
}
template <typename T>
constexpr decltype(auto) bit_width(T&& x) noexcept(noexcept(tools::detail::bit_width::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x)))) {
return tools::detail::bit_width::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x));
}
}
#line 6 "tools/floor_log2.hpp"
namespace tools {
template <typename T>
constexpr T floor_log2(T x) noexcept {
assert(x > 0);
return tools::bit_width(x) - 1;
}
}
#line 1 "tools/is_prime.hpp"
#include <array>
#line 1 "tools/prod_mod.hpp"
#line 1 "tools/uint128_t.hpp"
#line 1 "tools/detail/int128_t_and_uint128_t.hpp"
#line 6 "tools/detail/int128_t_and_uint128_t.hpp"
#include <cstddef>
#line 8 "tools/detail/int128_t_and_uint128_t.hpp"
#include <functional>
#line 10 "tools/detail/int128_t_and_uint128_t.hpp"
#include <limits>
#include <string>
#include <string_view>
#line 1 "tools/abs.hpp"
#include <cmath>
#line 7 "tools/abs.hpp"
namespace tools {
namespace detail::abs {
template <typename T>
struct impl {
constexpr decltype(auto) operator()(const T x) const noexcept(noexcept(std::abs(x))) {
return std::abs(x);
}
};
}
template <typename T>
constexpr decltype(auto) abs(T&& x) noexcept(noexcept(tools::detail::abs::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x)))) {
return tools::detail::abs::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x));
}
}
#line 1 "tools/bit_ceil.hpp"
#line 12 "tools/bit_ceil.hpp"
namespace tools {
namespace detail::bit_ceil {
template <tools::non_bool_integral T>
struct impl {
constexpr T operator()(const T x) const noexcept(noexcept(impl<tools::make_unsigned_t<T>>{}(x))) requires tools::is_signed_v<T> {
assert(x >= 0);
return impl<tools::make_unsigned_t<T>>{}(x);
}
constexpr T operator()(const T x) const noexcept(noexcept(std::bit_ceil(x))) requires tools::is_unsigned_v<T> {
return std::bit_ceil(x);
}
};
}
template <typename T>
constexpr decltype(auto) bit_ceil(T&& x) noexcept(noexcept(tools::detail::bit_ceil::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x)))) {
return tools::detail::bit_ceil::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x));
}
}
#line 1 "tools/bit_floor.hpp"
#line 12 "tools/bit_floor.hpp"
namespace tools {
namespace detail::bit_floor {
template <tools::non_bool_integral T>
struct impl {
constexpr T operator()(const T x) const noexcept(noexcept(impl<tools::make_unsigned_t<T>>{}(x))) requires tools::is_signed_v<T> {
assert(x >= 0);
return impl<tools::make_unsigned_t<T>>{}(x);
}
constexpr T operator()(const T x) const noexcept(noexcept(std::bit_floor(x))) requires tools::is_unsigned_v<T> {
return std::bit_floor(x);
}
};
}
template <typename T>
constexpr decltype(auto) bit_floor(T&& x) noexcept(noexcept(tools::detail::bit_floor::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x)))) {
return tools::detail::bit_floor::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x));
}
}
#line 1 "tools/countr_zero.hpp"
#line 14 "tools/countr_zero.hpp"
namespace tools {
namespace detail::countr_zero {
template <tools::non_bool_integral T>
struct impl {
constexpr int operator()(const T x) const noexcept(noexcept(impl<tools::make_unsigned_t<T>>{}(x))) requires tools::is_signed_v<T> {
assert(x >= 0);
return std::min(impl<tools::make_unsigned_t<T>>{}(x), std::numeric_limits<T>::digits);
}
constexpr int operator()(const T x) const noexcept(noexcept(std::countr_zero(x))) requires tools::is_unsigned_v<T> {
return std::countr_zero(x);
}
};
}
template <typename T>
constexpr decltype(auto) countr_zero(T&& x) noexcept(noexcept(tools::detail::countr_zero::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x)))) {
return tools::detail::countr_zero::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x));
}
}
#line 1 "tools/gcd.hpp"
#line 7 "tools/gcd.hpp"
namespace tools {
namespace detail::gcd {
template <typename M, typename N>
struct impl {
constexpr decltype(auto) operator()(const M m, const N n) const noexcept(noexcept(std::gcd(m, n))) {
return std::gcd(m, n);
}
};
}
template <typename M, typename N>
constexpr decltype(auto) gcd(M&& m, N&& n) noexcept(noexcept(tools::detail::gcd::impl<std::remove_cvref_t<M>, std::remove_cvref_t<N>>{}(std::forward<M>(m), std::forward<N>(n)))) {
return tools::detail::gcd::impl<std::remove_cvref_t<M>, std::remove_cvref_t<N>>{}(std::forward<M>(m), std::forward<N>(n));
}
}
#line 1 "tools/has_single_bit.hpp"
#line 12 "tools/has_single_bit.hpp"
namespace tools {
namespace detail::has_single_bit {
template <tools::non_bool_integral T>
struct impl {
constexpr bool operator()(const T x) const noexcept(noexcept(impl<tools::make_unsigned_t<T>>{}(x))) requires tools::is_signed_v<T> {
assert(x >= 0);
return impl<tools::make_unsigned_t<T>>{}(x);
}
constexpr bool operator()(const T x) const noexcept(noexcept(std::has_single_bit(x))) requires tools::is_unsigned_v<T> {
return std::has_single_bit(x);
}
};
}
template <typename T>
constexpr decltype(auto) has_single_bit(T&& x) noexcept(noexcept(tools::detail::has_single_bit::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x)))) {
return tools::detail::has_single_bit::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x));
}
}
#line 1 "tools/hash_combine.hpp"
#line 6 "tools/hash_combine.hpp"
// Source: https://github.com/google/cityhash/blob/f5dc54147fcce12cefd16548c8e760d68ac04226/src/city.h
// License: MIT
// Author: Google Inc.
// Copyright (c) 2011 Google, Inc.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
namespace tools {
template <typename T>
void hash_combine(std::size_t& seed, const T& v) {
static const std::hash<T> hasher;
static constexpr std::size_t k_mul = 0x9ddfea08eb382d69ULL;
std::size_t a = (hasher(v) ^ seed) * k_mul;
a ^= (a >> 47);
std::size_t b = (seed ^ a) * k_mul;
b ^= (b >> 47);
seed = b * k_mul;
}
}
#line 1 "tools/make_signed.hpp"
#line 5 "tools/make_signed.hpp"
namespace tools {
template <typename T>
struct make_signed : std::make_signed<T> {};
template <typename T>
using make_signed_t = typename tools::make_signed<T>::type;
}
#line 1 "tools/now.hpp"
#include <chrono>
namespace tools {
inline long long now() {
return std::chrono::duration_cast<std::chrono::nanoseconds>(std::chrono::high_resolution_clock::now().time_since_epoch()).count();
}
}
#line 1 "tools/popcount.hpp"
#line 12 "tools/popcount.hpp"
namespace tools {
namespace detail::popcount {
template <tools::non_bool_integral T>
struct impl {
constexpr int operator()(const T x) const noexcept(noexcept(impl<tools::make_unsigned_t<T>>{}(x))) requires tools::is_signed_v<T> {
assert(x >= 0);
return impl<tools::make_unsigned_t<T>>{}(x);
}
constexpr int operator()(const T x) const noexcept(noexcept(std::popcount(x))) requires tools::is_unsigned_v<T> {
return std::popcount(x);
}
};
}
template <typename T>
constexpr decltype(auto) popcount(T&& x) noexcept(noexcept(tools::detail::popcount::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x)))) {
return tools::detail::popcount::impl<std::remove_cvref_t<T>>{}(std::forward<T>(x));
}
}
#line 31 "tools/detail/int128_t_and_uint128_t.hpp"
namespace tools {
using uint128_t = unsigned __int128;
using int128_t = __int128;
template <>
struct is_integral<tools::int128_t> : std::true_type {};
template <>
struct is_integral<tools::uint128_t> : std::true_type {};
template <>
struct is_integral<const tools::int128_t> : std::true_type {};
template <>
struct is_integral<const tools::uint128_t> : std::true_type {};
template <>
struct is_integral<volatile tools::int128_t> : std::true_type {};
template <>
struct is_integral<volatile tools::uint128_t> : std::true_type {};
template <>
struct is_integral<const volatile tools::int128_t> : std::true_type {};
template <>
struct is_integral<const volatile tools::uint128_t> : std::true_type {};
template <>
struct is_signed<tools::int128_t> : std::true_type {};
template <>
struct is_signed<tools::uint128_t> : std::false_type {};
template <>
struct is_signed<const tools::int128_t> : std::true_type {};
template <>
struct is_signed<const tools::uint128_t> : std::false_type {};
template <>
struct is_signed<volatile tools::int128_t> : std::true_type {};
template <>
struct is_signed<volatile tools::uint128_t> : std::false_type {};
template <>
struct is_signed<const volatile tools::int128_t> : std::true_type {};
template <>
struct is_signed<const volatile tools::uint128_t> : std::false_type {};
template <>
struct is_unsigned<tools::int128_t> : std::false_type {};
template <>
struct is_unsigned<tools::uint128_t> : std::true_type {};
template <>
struct is_unsigned<const tools::int128_t> : std::false_type {};
template <>
struct is_unsigned<const tools::uint128_t> : std::true_type {};
template <>
struct is_unsigned<volatile tools::int128_t> : std::false_type {};
template <>
struct is_unsigned<volatile tools::uint128_t> : std::true_type {};
template <>
struct is_unsigned<const volatile tools::int128_t> : std::false_type {};
template <>
struct is_unsigned<const volatile tools::uint128_t> : std::true_type {};
template <>
struct make_signed<tools::int128_t> {
using type = tools::int128_t;
};
template <>
struct make_signed<tools::uint128_t> {
using type = tools::int128_t;
};
template <>
struct make_signed<const tools::int128_t> {
using type = const tools::int128_t;
};
template <>
struct make_signed<const tools::uint128_t> {
using type = const tools::int128_t;
};
template <>
struct make_signed<volatile tools::int128_t> {
using type = volatile tools::int128_t;
};
template <>
struct make_signed<volatile tools::uint128_t> {
using type = volatile tools::int128_t;
};
template <>
struct make_signed<const volatile tools::int128_t> {
using type = const volatile tools::int128_t;
};
template <>
struct make_signed<const volatile tools::uint128_t> {
using type = const volatile tools::int128_t;
};
template <>
struct make_unsigned<tools::int128_t> {
using type = tools::uint128_t;
};
template <>
struct make_unsigned<tools::uint128_t> {
using type = tools::uint128_t;
};
template <>
struct make_unsigned<const tools::int128_t> {
using type = const tools::uint128_t;
};
template <>
struct make_unsigned<const tools::uint128_t> {
using type = const tools::uint128_t;
};
template <>
struct make_unsigned<volatile tools::int128_t> {
using type = volatile tools::uint128_t;
};
template <>
struct make_unsigned<volatile tools::uint128_t> {
using type = volatile tools::uint128_t;
};
template <>
struct make_unsigned<const volatile tools::int128_t> {
using type = const volatile tools::uint128_t;
};
template <>
struct make_unsigned<const volatile tools::uint128_t> {
using type = const volatile tools::uint128_t;
};
namespace detail::int128_t {
constexpr tools::uint128_t parse_unsigned(const std::string_view s) noexcept {
assert(!s.empty());
tools::uint128_t x = 0;
std::size_t i = s[0] == '+';
if (i + 1 < s.size() && s[i] == '0' && (s[i + 1] == 'x' || s[i + 1] == 'X')) {
for (i += 2; i < s.size(); ++i) {
assert(('0' <= s[i] && s[i] <= '9') || ('a' <= s[i] && s[i] <= 'f') || ('A' <= s[i] && s[i] <= 'F'));
x <<= 4;
if ('0' <= s[i] && s[i] <= '9') {
x |= s[i] - '0';
} else if ('a' <= s[i] && s[i] <= 'f') {
x |= s[i] - 'a' + 10;
} else {
x |= s[i] - 'A' + 10;
}
}
} else {
for (; i < s.size(); ++i) {
assert('0' <= s[i] && s[i] <= '9');
x *= 10;
x += s[i] - '0';
}
}
return x;
}
constexpr tools::int128_t parse_signed(const std::string_view s) noexcept {
assert(!s.empty());
tools::int128_t x = 0;
if (s[0] == '-') {
std::size_t i = 1;
if (i + 1 < s.size() && s[i] == '0' && (s[i + 1] == 'x' || s[i + 1] == 'X')) {
for (i += 2; i < s.size(); ++i) {
assert(('0' <= s[i] && s[i] <= '9') || ('a' <= s[i] && s[i] <= 'f') || ('A' <= s[i] && s[i] <= 'F'));
x *= 16;
if ('0' <= s[i] && s[i] <= '9') {
x -= s[i] - '0';
} else if ('a' <= s[i] && s[i] <= 'f') {
x -= s[i] - 'a' + 10;
} else {
x -= s[i] - 'A' + 10;
}
}
} else {
for (; i < s.size(); ++i) {
assert('0' <= s[i] && s[i] <= '9');
x *= 10;
x -= s[i] - '0';
}
}
} else {
std::size_t i = s[0] == '+';
if (i + 1 < s.size() && s[i] == '0' && (s[i + 1] == 'x' || s[i + 1] == 'X')) {
for (i += 2; i < s.size(); ++i) {
assert(('0' <= s[i] && s[i] <= '9') || ('a' <= s[i] && s[i] <= 'f') || ('A' <= s[i] && s[i] <= 'F'));
x <<= 4;
if ('0' <= s[i] && s[i] <= '9') {
x |= s[i] - '0';
} else if ('a' <= s[i] && s[i] <= 'f') {
x |= s[i] - 'a' + 10;
} else {
x |= s[i] - 'A' + 10;
}
}
} else {
for (; i < s.size(); ++i) {
assert('0' <= s[i] && s[i] <= '9');
x *= 10;
x += s[i] - '0';
}
}
}
return x;
}
}
}
#define UINT128_C(c) tools::detail::int128_t::parse_unsigned(#c)
#define INT128_C(c) tools::detail::int128_t::parse_signed(#c)
inline std::istream& operator>>(std::istream& is, tools::uint128_t& x) {
std::string s;
is >> s;
x = tools::detail::int128_t::parse_unsigned(s);
return is;
}
inline std::istream& operator>>(std::istream& is, tools::int128_t& x) {
std::string s;
is >> s;
x = tools::detail::int128_t::parse_signed(s);
return is;
}
inline std::ostream& operator<<(std::ostream& os, tools::uint128_t x) {
std::string s;
if (x > 0) {
while (x > 0) {
s.push_back('0' + x % 10);
x /= 10;
}
} else {
s.push_back('0');
}
std::ranges::reverse(s);
return os << s;
}
inline std::ostream& operator<<(std::ostream& os, tools::int128_t x) {
std::string s;
if (x > 0) {
while (x > 0) {
s.push_back('0' + x % 10);
x /= 10;
}
} else if (x < 0) {
while (x < 0) {
s.push_back('0' + (-(x % 10)));
x /= 10;
}
s.push_back('-');
} else {
s.push_back('0');
}
std::ranges::reverse(s);
return os << s;
}
#if defined(__GLIBCXX__) && defined(__STRICT_ANSI__)
namespace std {
template <>
struct hash<tools::uint128_t> {
std::size_t operator()(const tools::uint128_t& x) const {
static const std::size_t seed = tools::now();
std::size_t hash = seed;
tools::hash_combine(hash, static_cast<std::uint64_t>(x >> 64));
tools::hash_combine(hash, static_cast<std::uint64_t>(x & ((UINT128_C(1) << 64) - 1)));
return hash;
}
};
template <>
struct hash<tools::int128_t> {
std::size_t operator()(const tools::int128_t& x) const {
static std::hash<tools::uint128_t> hasher;
return hasher(static_cast<tools::uint128_t>(x));
}
};
}
#endif
namespace tools {
template <>
struct detail::abs::impl<tools::int128_t> {
constexpr tools::int128_t operator()(const tools::int128_t& x) const noexcept {
return x >= 0 ? x : -x;
}
};
#if defined(__GLIBCXX__) && defined(__STRICT_ANSI__)
template <>
struct detail::bit_ceil::impl<tools::uint128_t> {
constexpr tools::uint128_t operator()(tools::uint128_t x) const noexcept {
if (x <= 1) return 1;
--x;
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
x |= x >> 32;
x |= x >> 64;
return ++x;
}
};
template <>
struct detail::bit_floor::impl<tools::uint128_t> {
constexpr tools::uint128_t operator()(tools::uint128_t x) const noexcept {
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
x |= x >> 32;
x |= x >> 64;
return x & ~(x >> 1);
}
};
template <>
struct detail::bit_width::impl<tools::uint128_t> {
constexpr int operator()(tools::uint128_t x) const noexcept {
int w = 0;
if (x & UINT128_C(0xffffffffffffffff0000000000000000)) {
x >>= 64;
w += 64;
}
if (x & UINT128_C(0xffffffff00000000)) {
x >>= 32;
w += 32;
}
if (x & UINT128_C(0xffff0000)) {
x >>= 16;
w += 16;
}
if (x & UINT128_C(0xff00)) {
x >>= 8;
w += 8;
}
if (x & UINT128_C(0xf0)) {
x >>= 4;
w += 4;
}
if (x & UINT128_C(0xc)) {
x >>= 2;
w += 2;
}
if (x & UINT128_C(0x2)) {
x >>= 1;
w += 1;
}
w += x;
return w;
}
};
template <>
class detail::countr_zero::impl<tools::uint128_t> {
using type = tools::uint128_t;
static constexpr int shift = 120;
static constexpr type magic = UINT128_C(0x01061438916347932a5cd9d3ead7b77f);
static constexpr int ntz_table[255] = {
128, 0, 1, -1, 2, -1, 8, -1, 3, -1, 15, -1, 9, -1, 22, -1,
4, -1, 29, -1, 16, -1, 36, -1, 10, -1, 43, -1, 23, -1, 50, -1,
5, -1, 33, -1, 30, -1, 57, -1, 17, -1, 64, -1, 37, -1, 71, -1,
11, -1, 60, -1, 44, -1, 78, -1, 24, -1, 85, -1, 51, -1, 92, -1,
-1, 6, -1, 20, -1, 34, -1, 48, 31, -1, -1, 69, 58, -1, -1, 90,
18, -1, 67, -1, 65, -1, 99, -1, 38, -1, 101, -1, 72, -1, 106, -1,
-1, 12, -1, 40, -1, 61, -1, 82, 45, -1, -1, 103, 79, -1, 113, -1,
-1, 25, -1, 74, 86, -1, -1, 116, -1, 52, -1, 108, -1, 93, -1, 120,
127, -1, -1, 7, -1, 14, -1, 21, -1, 28, -1, 35, -1, 42, -1, 49,
-1, 32, -1, 56, -1, 63, -1, 70, -1, 59, -1, 77, -1, 84, -1, 91,
-1, 19, -1, 47, -1, 68, -1, 89, -1, 66, -1, 98, -1, 100, -1, 105,
-1, 39, -1, 81, -1, 102, -1, 112, -1, 73, -1, 115, -1, 107, -1, 119,
126, -1, 13, -1, 27, -1, 41, -1, -1, 55, 62, -1, -1, 76, 83, -1,
-1, 46, -1, 88, -1, 97, -1, 104, -1, 80, -1, 111, -1, 114, -1, 118,
125, -1, 26, -1, 54, -1, 75, -1, -1, 87, 96, -1, -1, 110, -1, 117,
124, -1, 53, -1, -1, 95, 109, -1, 123, -1, 94, -1, 122, -1, 121
};
public:
constexpr int operator()(const type& x) const noexcept {
return ntz_table[static_cast<type>(magic * static_cast<type>(x & -x)) >> shift];
}
};
namespace detail::gcd {
template <>
struct impl<tools::uint128_t, tools::uint128_t> {
constexpr tools::uint128_t operator()(tools::uint128_t m, tools::uint128_t n) const noexcept {
while (n != 0) {
m %= n;
std::swap(m, n);
}
return m;
};
};
template <typename T>
concept non_bool_integral_at_most_128bit = tools::non_bool_integral<T> && std::numeric_limits<T>::digits <= 128;
template <typename T>
concept non_bool_integral_at_most_64bit = tools::non_bool_integral<T> && std::numeric_limits<T>::digits <= 64;
template <typename M, typename N> requires (
(non_bool_integral_at_most_128bit<M> && non_bool_integral_at_most_128bit<N>)
&& !(non_bool_integral_at_most_64bit<M> && non_bool_integral_at_most_64bit<N>)
&& !(std::same_as<M, tools::uint128_t> && std::same_as<N, tools::uint128_t>)
)
struct impl<M, N> {
constexpr std::common_type_t<M, N> operator()(const M m, const N n) const noexcept {
return std::common_type_t<M, N>(
tools::gcd(
m >= 0 ? tools::uint128_t(m) : tools::uint128_t(-(m + 1)) + 1,
n >= 0 ? tools::uint128_t(n) : tools::uint128_t(-(n + 1)) + 1
)
);
}
};
}
template <>
struct detail::has_single_bit::impl<tools::uint128_t> {
constexpr bool operator()(tools::uint128_t x) const noexcept {
return x != 0 && (x & (x - 1)) == 0;
}
};
template <>
struct detail::popcount::impl<tools::uint128_t> {
constexpr int operator()(tools::uint128_t x) const noexcept {
x = (x & UINT128_C(0x55555555555555555555555555555555)) + (x >> 1 & UINT128_C(0x55555555555555555555555555555555));
x = (x & UINT128_C(0x33333333333333333333333333333333)) + (x >> 2 & UINT128_C(0x33333333333333333333333333333333));
x = (x & UINT128_C(0x0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f)) + (x >> 4 & UINT128_C(0x0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f));
x = (x & UINT128_C(0x00ff00ff00ff00ff00ff00ff00ff00ff)) + (x >> 8 & UINT128_C(0x00ff00ff00ff00ff00ff00ff00ff00ff));
x = (x & UINT128_C(0x0000ffff0000ffff0000ffff0000ffff)) + (x >> 16 & UINT128_C(0x0000ffff0000ffff0000ffff0000ffff));
x = (x & UINT128_C(0x00000000ffffffff00000000ffffffff)) + (x >> 32 & UINT128_C(0x00000000ffffffff00000000ffffffff));
x = (x & UINT128_C(0x0000000000000000ffffffffffffffff)) + (x >> 64 & UINT128_C(0x0000000000000000ffffffffffffffff));
return x;
}
};
#endif
}
#line 5 "tools/uint128_t.hpp"
#line 5 "tools/prod_mod.hpp"
namespace tools {
template <typename T1, typename T2, typename T3>
constexpr T3 prod_mod(const T1 x, const T2 y, const T3 m) {
using u128 = tools::uint128_t;
u128 prod_mod = u128(x >= 0 ? x : -x) * u128(y >= 0 ? y : -y) % u128(m);
if ((x >= 0) ^ (y >= 0)) prod_mod = u128(m) - prod_mod;
return prod_mod;
}
}
#line 1 "tools/pow_mod.hpp"
#line 1 "tools/mod.hpp"
#line 7 "tools/mod.hpp"
namespace tools {
template <tools::non_bool_integral M, tools::non_bool_integral N>
constexpr std::common_type_t<M, N> mod(const M a, const N b) noexcept {
assert(b != 0);
using UM = tools::make_unsigned_t<M>;
using UN = tools::make_unsigned_t<N>;
const UM ua = a >= 0 ? a : static_cast<UM>(-(a + 1)) + 1;
const UN ub = b >= 0 ? b : static_cast<UN>(-(b + 1)) + 1;
auto r = ua % ub;
if (a < 0 && r > 0) {
r = ub - r;
}
return r;
}
}
#line 6 "tools/pow_mod.hpp"
namespace tools {
template <typename T1, typename T2, typename T3>
constexpr T3 pow_mod(const T1 x, T2 n, const T3 m) {
if (m == 1) return 0;
T3 r = 1;
T3 y = tools::mod(x, m);
while (n > 0) {
if ((n & 1) > 0) {
r = tools::prod_mod(r, y, m);
}
y = tools::prod_mod(y, y, m);
n /= 2;
}
return r;
}
}
#line 7 "tools/is_prime.hpp"
namespace tools {
constexpr bool is_prime(const unsigned long long n) {
constexpr std::array<unsigned long long, 7> bases = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
if (n <= 1) return false;
if (n == 2) return true;
if (n % 2 == 0) return false;
auto d = n - 1;
for (; d % 2 == 0; d /= 2);
for (const auto a : bases) {
if (a % n == 0) return true;
auto power = d;
auto target = tools::pow_mod(a, power, n);
bool is_composite = true;
if (target == 1) is_composite = false;
for (; is_composite && power != n - 1; power *= 2, target = tools::prod_mod(target, target, n)) {
if (target == n - 1) is_composite = false;
}
if (is_composite) {
return false;
}
}
return true;
}
}
#line 1 "tools/pow2.hpp"
#line 7 "tools/pow2.hpp"
namespace tools {
template <tools::integral T>
constexpr T pow2(const T x) noexcept {
assert(0 <= x && x < std::numeric_limits<T>::digits);
return T(1) << x;
}
}
#line 16 "tools/prime_factorization.hpp"
namespace tools {
template <std::integral T>
std::vector<T> prime_factorization(T n) {
assert(n >= 1);
std::vector<T> res;
if (n == 1) return res;
std::queue<std::pair<T, T>> factors;
factors.emplace(n, 1);
while (!factors.empty()) {
const auto [factor, occurrences] = factors.front();
factors.pop();
if (tools::is_prime(factor)) {
for (T i = 0; i < occurrences; ++i) {
res.push_back(factor);
}
} else {
const T m = tools::pow2((tools::floor_log2(factor) + 1) / 8);
for (T c = 1; ; ++c) {
const auto f = [&](T& x) {
x = tools::prod_mod(x, x, factor);
// (x + c) mod factor s.t. 0 <= x < factor and 1 <= c < factor
if (x >= factor - c) {
x -= factor - c;
} else {
x += c;
}
};
T y = 2;
T r = 1;
T q = 1;
T x, g, ys;
do {
x = y;
for (T i = 0; i < r; ++i) {
f(y);
}
T k = 0;
do {
ys = y;
for (T i = 0; i < std::min<T>(m, r - k); ++i) {
f(y);
q = tools::prod_mod(q, std::max(x, y) - std::min(x, y), factor);
}
g = std::gcd(q, factor);
k += m;
} while (k < r && g == 1);
r *= 2;
} while (g == 1);
if (g == factor) {
do {
f(ys);
g = std::gcd(std::max(x, ys) - std::min(x, ys), factor);
} while (g == 1);
}
if (g < factor) {
T h = factor / g;
std::tie(g, h) = std::minmax({g, h});
T n = 1;
while (h % g == 0) {
h /= g;
++n;
}
factors.emplace(g, occurrences * n);
if (h > 1) factors.emplace(h, occurrences);
break;
}
}
}
}
std::ranges::sort(res);
return res;
}
}
#line 8 "tests/prime_factorization/severe_cases.test.cpp"
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(1)) == std::vector<std::int8_t>{});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(2)) == std::vector<std::int8_t>{INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(3)) == std::vector<std::int8_t>{INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(4)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(5)) == std::vector<std::int8_t>{INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(6)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(7)) == std::vector<std::int8_t>{INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(8)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(9)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(10)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(11)) == std::vector<std::int8_t>{INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(12)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(13)) == std::vector<std::int8_t>{INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(14)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(15)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(16)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(17)) == std::vector<std::int8_t>{INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(18)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(19)) == std::vector<std::int8_t>{INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(20)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(21)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(22)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(23)) == std::vector<std::int8_t>{INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(24)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(25)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(26)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(27)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(28)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(29)) == std::vector<std::int8_t>{INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(30)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(31)) == std::vector<std::int8_t>{INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(32)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(33)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(34)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(35)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(36)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(37)) == std::vector<std::int8_t>{INT8_C(37)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(38)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(39)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(40)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(41)) == std::vector<std::int8_t>{INT8_C(41)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(42)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(43)) == std::vector<std::int8_t>{INT8_C(43)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(44)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(45)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(46)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(47)) == std::vector<std::int8_t>{INT8_C(47)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(48)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(49)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(50)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(51)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(52)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(53)) == std::vector<std::int8_t>{INT8_C(53)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(54)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(55)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(56)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(57)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(58)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(59)) == std::vector<std::int8_t>{INT8_C(59)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(60)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(61)) == std::vector<std::int8_t>{INT8_C(61)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(62)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(63)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(64)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(65)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(66)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(67)) == std::vector<std::int8_t>{INT8_C(67)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(68)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(69)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(70)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(71)) == std::vector<std::int8_t>{INT8_C(71)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(72)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(73)) == std::vector<std::int8_t>{INT8_C(73)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(74)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(37)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(75)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(76)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(77)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(78)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(79)) == std::vector<std::int8_t>{INT8_C(79)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(80)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(81)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(82)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(41)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(83)) == std::vector<std::int8_t>{INT8_C(83)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(84)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(85)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(86)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(43)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(87)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(88)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(89)) == std::vector<std::int8_t>{INT8_C(89)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(90)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(91)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(92)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(93)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(94)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(47)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(95)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(96)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(97)) == std::vector<std::int8_t>{INT8_C(97)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(98)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(7), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(99)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(100)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(101)) == std::vector<std::int8_t>{INT8_C(101)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(102)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(103)) == std::vector<std::int8_t>{INT8_C(103)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(104)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(105)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(5), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(106)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(53)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(107)) == std::vector<std::int8_t>{INT8_C(107)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(108)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(3)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(109)) == std::vector<std::int8_t>{INT8_C(109)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(110)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(5), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(111)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(37)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(112)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(113)) == std::vector<std::int8_t>{INT8_C(113)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(114)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(19)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(115)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(23)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(116)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(29)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(117)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(3), INT8_C(13)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(118)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(59)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(119)) == std::vector<std::int8_t>{INT8_C(7), INT8_C(17)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(120)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(2), INT8_C(3), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(121)) == std::vector<std::int8_t>{INT8_C(11), INT8_C(11)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(122)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(61)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(123)) == std::vector<std::int8_t>{INT8_C(3), INT8_C(41)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(124)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(2), INT8_C(31)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(125)) == std::vector<std::int8_t>{INT8_C(5), INT8_C(5), INT8_C(5)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(126)) == std::vector<std::int8_t>{INT8_C(2), INT8_C(3), INT8_C(3), INT8_C(7)});
assert_that(tools::prime_factorization<std::int8_t>(INT8_C(127)) == std::vector<std::int8_t>{INT8_C(127)});
assert_that(tools::prime_factorization(INT32_C(1)) == std::vector<std::int32_t>{});
assert_that(tools::prime_factorization(INT32_C(2)) == std::vector{INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(3)) == std::vector{INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(4)) == std::vector{INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(5)) == std::vector{INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(6)) == std::vector{INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(7)) == std::vector{INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(8)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(9)) == std::vector{INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(10)) == std::vector{INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(11)) == std::vector{INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(12)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(13)) == std::vector{INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(14)) == std::vector{INT32_C(2), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(15)) == std::vector{INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(16)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(17)) == std::vector{INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(18)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(19)) == std::vector{INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(20)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(21)) == std::vector{INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(22)) == std::vector{INT32_C(2), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(23)) == std::vector{INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(24)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(25)) == std::vector{INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(26)) == std::vector{INT32_C(2), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(27)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(28)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(29)) == std::vector{INT32_C(29)});
assert_that(tools::prime_factorization(INT32_C(30)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(31)) == std::vector{INT32_C(31)});
assert_that(tools::prime_factorization(INT32_C(32)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(33)) == std::vector{INT32_C(3), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(34)) == std::vector{INT32_C(2), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(35)) == std::vector{INT32_C(5), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(36)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(37)) == std::vector{INT32_C(37)});
assert_that(tools::prime_factorization(INT32_C(38)) == std::vector{INT32_C(2), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(39)) == std::vector{INT32_C(3), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(40)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(41)) == std::vector{INT32_C(41)});
assert_that(tools::prime_factorization(INT32_C(42)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(43)) == std::vector{INT32_C(43)});
assert_that(tools::prime_factorization(INT32_C(44)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(45)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(46)) == std::vector{INT32_C(2), INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(47)) == std::vector{INT32_C(47)});
assert_that(tools::prime_factorization(INT32_C(48)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(49)) == std::vector{INT32_C(7), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(50)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(51)) == std::vector{INT32_C(3), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(52)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(53)) == std::vector{INT32_C(53)});
assert_that(tools::prime_factorization(INT32_C(54)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(55)) == std::vector{INT32_C(5), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(56)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(57)) == std::vector{INT32_C(3), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(58)) == std::vector{INT32_C(2), INT32_C(29)});
assert_that(tools::prime_factorization(INT32_C(59)) == std::vector{INT32_C(59)});
assert_that(tools::prime_factorization(INT32_C(60)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(61)) == std::vector{INT32_C(61)});
assert_that(tools::prime_factorization(INT32_C(62)) == std::vector{INT32_C(2), INT32_C(31)});
assert_that(tools::prime_factorization(INT32_C(63)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(64)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2)});
assert_that(tools::prime_factorization(INT32_C(65)) == std::vector{INT32_C(5), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(66)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(67)) == std::vector{INT32_C(67)});
assert_that(tools::prime_factorization(INT32_C(68)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(69)) == std::vector{INT32_C(3), INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(70)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(71)) == std::vector{INT32_C(71)});
assert_that(tools::prime_factorization(INT32_C(72)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(73)) == std::vector{INT32_C(73)});
assert_that(tools::prime_factorization(INT32_C(74)) == std::vector{INT32_C(2), INT32_C(37)});
assert_that(tools::prime_factorization(INT32_C(75)) == std::vector{INT32_C(3), INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(76)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(77)) == std::vector{INT32_C(7), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(78)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(79)) == std::vector{INT32_C(79)});
assert_that(tools::prime_factorization(INT32_C(80)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(81)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(82)) == std::vector{INT32_C(2), INT32_C(41)});
assert_that(tools::prime_factorization(INT32_C(83)) == std::vector{INT32_C(83)});
assert_that(tools::prime_factorization(INT32_C(84)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(85)) == std::vector{INT32_C(5), INT32_C(17)});
assert_that(tools::prime_factorization(INT32_C(86)) == std::vector{INT32_C(2), INT32_C(43)});
assert_that(tools::prime_factorization(INT32_C(87)) == std::vector{INT32_C(3), INT32_C(29)});
assert_that(tools::prime_factorization(INT32_C(88)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(89)) == std::vector{INT32_C(89)});
assert_that(tools::prime_factorization(INT32_C(90)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(91)) == std::vector{INT32_C(7), INT32_C(13)});
assert_that(tools::prime_factorization(INT32_C(92)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(23)});
assert_that(tools::prime_factorization(INT32_C(93)) == std::vector{INT32_C(3), INT32_C(31)});
assert_that(tools::prime_factorization(INT32_C(94)) == std::vector{INT32_C(2), INT32_C(47)});
assert_that(tools::prime_factorization(INT32_C(95)) == std::vector{INT32_C(5), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(96)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3)});
assert_that(tools::prime_factorization(INT32_C(97)) == std::vector{INT32_C(97)});
assert_that(tools::prime_factorization(INT32_C(98)) == std::vector{INT32_C(2), INT32_C(7), INT32_C(7)});
assert_that(tools::prime_factorization(INT32_C(99)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(11)});
assert_that(tools::prime_factorization(INT32_C(100)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(5)});
assert_that(tools::prime_factorization(INT32_C(2095133040)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(5), INT32_C(7), INT32_C(11), INT32_C(13), INT32_C(17), INT32_C(19)});
assert_that(tools::prime_factorization(INT32_C(2147483548)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(7), INT32_C(76695841)});
assert_that(tools::prime_factorization(INT32_C(2147483549)) == std::vector{INT32_C(2147483549)});
assert_that(tools::prime_factorization(INT32_C(2147483550)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(5), INT32_C(5), INT32_C(19), INT32_C(23), INT32_C(181), INT32_C(181)});
assert_that(tools::prime_factorization(INT32_C(2147483551)) == std::vector{INT32_C(32063), INT32_C(66977)});
assert_that(tools::prime_factorization(INT32_C(2147483552)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(37), INT32_C(349), INT32_C(5197)});
assert_that(tools::prime_factorization(INT32_C(2147483553)) == std::vector{INT32_C(3), INT32_C(29), INT32_C(31), INT32_C(503), INT32_C(1583)});
assert_that(tools::prime_factorization(INT32_C(2147483554)) == std::vector{INT32_C(2), INT32_C(17), INT32_C(43), INT32_C(563), INT32_C(2609)});
assert_that(tools::prime_factorization(INT32_C(2147483555)) == std::vector{INT32_C(5), INT32_C(7), INT32_C(7), INT32_C(7), INT32_C(1252177)});
assert_that(tools::prime_factorization(INT32_C(2147483556)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(109), INT32_C(182423)});
assert_that(tools::prime_factorization(INT32_C(2147483557)) == std::vector{INT32_C(3181), INT32_C(675097)});
assert_that(tools::prime_factorization(INT32_C(2147483558)) == std::vector{INT32_C(2), INT32_C(11), INT32_C(11), INT32_C(139), INT32_C(63841)});
assert_that(tools::prime_factorization(INT32_C(2147483559)) == std::vector{INT32_C(3), INT32_C(13), INT32_C(73), INT32_C(754297)});
assert_that(tools::prime_factorization(INT32_C(2147483560)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(227), INT32_C(236507)});
assert_that(tools::prime_factorization(INT32_C(2147483561)) == std::vector{INT32_C(167), INT32_C(12859183)});
assert_that(tools::prime_factorization(INT32_C(2147483562)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(7), INT32_C(631), INT32_C(81031)});
assert_that(tools::prime_factorization(INT32_C(2147483563)) == std::vector{INT32_C(2147483563)});
assert_that(tools::prime_factorization(INT32_C(2147483564)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(6269), INT32_C(85639)});
assert_that(tools::prime_factorization(INT32_C(2147483565)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(5), INT32_C(103), INT32_C(463319)});
assert_that(tools::prime_factorization(INT32_C(2147483566)) == std::vector{INT32_C(2), INT32_C(1073741783)});
assert_that(tools::prime_factorization(INT32_C(2147483567)) == std::vector{INT32_C(11503), INT32_C(186689)});
assert_that(tools::prime_factorization(INT32_C(2147483568)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(41), INT32_C(83), INT32_C(13147)});
assert_that(tools::prime_factorization(INT32_C(2147483569)) == std::vector{INT32_C(7), INT32_C(11), INT32_C(19), INT32_C(1467863)});
assert_that(tools::prime_factorization(INT32_C(2147483570)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(214748357)});
assert_that(tools::prime_factorization(INT32_C(2147483571)) == std::vector{INT32_C(3), INT32_C(17), INT32_C(17), INT32_C(2476913)});
assert_that(tools::prime_factorization(INT32_C(2147483572)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(13), INT32_C(5641), INT32_C(7321)});
assert_that(tools::prime_factorization(INT32_C(2147483573)) == std::vector{INT32_C(23), INT32_C(93368851)});
assert_that(tools::prime_factorization(INT32_C(2147483574)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(53), INT32_C(2251031)});
assert_that(tools::prime_factorization(INT32_C(2147483575)) == std::vector{INT32_C(5), INT32_C(5), INT32_C(85899343)});
assert_that(tools::prime_factorization(INT32_C(2147483576)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(7), INT32_C(2341), INT32_C(16381)});
assert_that(tools::prime_factorization(INT32_C(2147483577)) == std::vector{INT32_C(3), INT32_C(10103), INT32_C(70853)});
assert_that(tools::prime_factorization(INT32_C(2147483578)) == std::vector{INT32_C(2), INT32_C(1073741789)});
assert_that(tools::prime_factorization(INT32_C(2147483579)) == std::vector{INT32_C(2147483579)});
assert_that(tools::prime_factorization(INT32_C(2147483580)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(5), INT32_C(11), INT32_C(47), INT32_C(107), INT32_C(647)});
assert_that(tools::prime_factorization(INT32_C(2147483581)) == std::vector{INT32_C(89), INT32_C(691), INT32_C(34919)});
assert_that(tools::prime_factorization(INT32_C(2147483582)) == std::vector{INT32_C(2), INT32_C(29), INT32_C(97), INT32_C(381707)});
assert_that(tools::prime_factorization(INT32_C(2147483583)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(7), INT32_C(1262483)});
assert_that(tools::prime_factorization(INT32_C(2147483584)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(31), INT32_C(601), INT32_C(1801)});
assert_that(tools::prime_factorization(INT32_C(2147483585)) == std::vector{INT32_C(5), INT32_C(13), INT32_C(179), INT32_C(184571)});
assert_that(tools::prime_factorization(INT32_C(2147483586)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(357913931)});
assert_that(tools::prime_factorization(INT32_C(2147483587)) == std::vector{INT32_C(2147483587)});
assert_that(tools::prime_factorization(INT32_C(2147483588)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(17), INT32_C(19), INT32_C(19), INT32_C(87481)});
assert_that(tools::prime_factorization(INT32_C(2147483589)) == std::vector{INT32_C(3), INT32_C(37), INT32_C(61), INT32_C(317159)});
assert_that(tools::prime_factorization(INT32_C(2147483590)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(7), INT32_C(877), INT32_C(34981)});
assert_that(tools::prime_factorization(INT32_C(2147483591)) == std::vector{INT32_C(11), INT32_C(195225781)});
assert_that(tools::prime_factorization(INT32_C(2147483592)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(4813), INT32_C(6197)});
assert_that(tools::prime_factorization(INT32_C(2147483593)) == std::vector{INT32_C(59), INT32_C(239), INT32_C(152293)});
assert_that(tools::prime_factorization(INT32_C(2147483594)) == std::vector{INT32_C(2), INT32_C(193), INT32_C(1021), INT32_C(5449)});
assert_that(tools::prime_factorization(INT32_C(2147483595)) == std::vector{INT32_C(3), INT32_C(5), INT32_C(143165573)});
assert_that(tools::prime_factorization(INT32_C(2147483596)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(23), INT32_C(23342213)});
assert_that(tools::prime_factorization(INT32_C(2147483597)) == std::vector{INT32_C(7), INT32_C(43), INT32_C(7134497)});
assert_that(tools::prime_factorization(INT32_C(2147483598)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(13), INT32_C(67), INT32_C(163), INT32_C(2521)});
assert_that(tools::prime_factorization(INT32_C(2147483599)) == std::vector{INT32_C(1657), INT32_C(1296007)});
assert_that(tools::prime_factorization(INT32_C(2147483600)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(5), INT32_C(173), INT32_C(31033)});
assert_that(tools::prime_factorization(INT32_C(2147483601)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(238609289)});
assert_that(tools::prime_factorization(INT32_C(2147483602)) == std::vector{INT32_C(2), INT32_C(11), INT32_C(97612891)});
assert_that(tools::prime_factorization(INT32_C(2147483603)) == std::vector{INT32_C(1187), INT32_C(1809169)});
assert_that(tools::prime_factorization(INT32_C(2147483604)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(7), INT32_C(7), INT32_C(197), INT32_C(18539)});
assert_that(tools::prime_factorization(INT32_C(2147483605)) == std::vector{INT32_C(5), INT32_C(17), INT32_C(25264513)});
assert_that(tools::prime_factorization(INT32_C(2147483606)) == std::vector{INT32_C(2), INT32_C(3671), INT32_C(292493)});
assert_that(tools::prime_factorization(INT32_C(2147483607)) == std::vector{INT32_C(3), INT32_C(19), INT32_C(571), INT32_C(65981)});
assert_that(tools::prime_factorization(INT32_C(2147483608)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(71), INT32_C(3780781)});
assert_that(tools::prime_factorization(INT32_C(2147483609)) == std::vector{INT32_C(41), INT32_C(52377649)});
assert_that(tools::prime_factorization(INT32_C(2147483610)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(5), INT32_C(313), INT32_C(25411)});
assert_that(tools::prime_factorization(INT32_C(2147483611)) == std::vector{INT32_C(7), INT32_C(13), INT32_C(29), INT32_C(813749)});
assert_that(tools::prime_factorization(INT32_C(2147483612)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(311), INT32_C(1726273)});
assert_that(tools::prime_factorization(INT32_C(2147483613)) == std::vector{INT32_C(3), INT32_C(11), INT32_C(2953), INT32_C(22037)});
assert_that(tools::prime_factorization(INT32_C(2147483614)) == std::vector{INT32_C(2), INT32_C(101), INT32_C(10631107)});
assert_that(tools::prime_factorization(INT32_C(2147483615)) == std::vector{INT32_C(5), INT32_C(31), INT32_C(13854733)});
assert_that(tools::prime_factorization(INT32_C(2147483616)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(2731), INT32_C(8191)});
assert_that(tools::prime_factorization(INT32_C(2147483617)) == std::vector{INT32_C(6733), INT32_C(318949)});
assert_that(tools::prime_factorization(INT32_C(2147483618)) == std::vector{INT32_C(2), INT32_C(7), INT32_C(367), INT32_C(417961)});
assert_that(tools::prime_factorization(INT32_C(2147483619)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(23), INT32_C(353), INT32_C(29389)});
assert_that(tools::prime_factorization(INT32_C(2147483620)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(5), INT32_C(4603), INT32_C(23327)});
assert_that(tools::prime_factorization(INT32_C(2147483621)) == std::vector{INT32_C(14741), INT32_C(145681)});
assert_that(tools::prime_factorization(INT32_C(2147483622)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(17), INT32_C(467), INT32_C(45083)});
assert_that(tools::prime_factorization(INT32_C(2147483623)) == std::vector{INT32_C(79), INT32_C(967), INT32_C(28111)});
assert_that(tools::prime_factorization(INT32_C(2147483624)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(11), INT32_C(13), INT32_C(1877171)});
assert_that(tools::prime_factorization(INT32_C(2147483625)) == std::vector{INT32_C(3), INT32_C(5), INT32_C(5), INT32_C(5), INT32_C(7), INT32_C(199), INT32_C(4111)});
assert_that(tools::prime_factorization(INT32_C(2147483626)) == std::vector{INT32_C(2), INT32_C(19), INT32_C(37), INT32_C(1527371)});
assert_that(tools::prime_factorization(INT32_C(2147483627)) == std::vector{INT32_C(47), INT32_C(53), INT32_C(862097)});
assert_that(tools::prime_factorization(INT32_C(2147483628)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(59652323)});
assert_that(tools::prime_factorization(INT32_C(2147483629)) == std::vector{INT32_C(2147483629)});
assert_that(tools::prime_factorization(INT32_C(2147483630)) == std::vector{INT32_C(2), INT32_C(5), INT32_C(6553), INT32_C(32771)});
assert_that(tools::prime_factorization(INT32_C(2147483631)) == std::vector{INT32_C(3), INT32_C(137), INT32_C(263), INT32_C(19867)});
assert_that(tools::prime_factorization(INT32_C(2147483632)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(7), INT32_C(73), INT32_C(262657)});
assert_that(tools::prime_factorization(INT32_C(2147483633)) == std::vector{INT32_C(5843), INT32_C(367531)});
assert_that(tools::prime_factorization(INT32_C(2147483634)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(12097), INT32_C(29587)});
assert_that(tools::prime_factorization(INT32_C(2147483635)) == std::vector{INT32_C(5), INT32_C(11), INT32_C(337), INT32_C(115861)});
assert_that(tools::prime_factorization(INT32_C(2147483636)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(536870909)});
assert_that(tools::prime_factorization(INT32_C(2147483637)) == std::vector{INT32_C(3), INT32_C(3), INT32_C(3), INT32_C(13), INT32_C(6118187)});
assert_that(tools::prime_factorization(INT32_C(2147483638)) == std::vector{INT32_C(2), INT32_C(2969), INT32_C(361651)});
assert_that(tools::prime_factorization(INT32_C(2147483639)) == std::vector{INT32_C(7), INT32_C(17), INT32_C(18046081)});
assert_that(tools::prime_factorization(INT32_C(2147483640)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(2), INT32_C(3), INT32_C(5), INT32_C(29), INT32_C(43), INT32_C(113), INT32_C(127)});
assert_that(tools::prime_factorization(INT32_C(2147483641)) == std::vector{INT32_C(2699), INT32_C(795659)});
assert_that(tools::prime_factorization(INT32_C(2147483642)) == std::vector{INT32_C(2), INT32_C(23), INT32_C(46684427)});
assert_that(tools::prime_factorization(INT32_C(2147483643)) == std::vector{INT32_C(3), INT32_C(715827881)});
assert_that(tools::prime_factorization(INT32_C(2147483644)) == std::vector{INT32_C(2), INT32_C(2), INT32_C(233), INT32_C(1103), INT32_C(2089)});
assert_that(tools::prime_factorization(INT32_C(2147483645)) == std::vector{INT32_C(5), INT32_C(19), INT32_C(22605091)});
assert_that(tools::prime_factorization(INT32_C(2147483646)) == std::vector{INT32_C(2), INT32_C(3), INT32_C(3), INT32_C(7), INT32_C(11), INT32_C(31), INT32_C(151), INT32_C(331)});
assert_that(tools::prime_factorization(INT32_C(2147483647)) == std::vector{INT32_C(2147483647)});
assert_that(tools::prime_factorization(UINT32_C(1)) == std::vector<std::uint32_t>{});
assert_that(tools::prime_factorization(UINT32_C(2)) == std::vector{UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(3)) == std::vector{UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(4)) == std::vector{UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(5)) == std::vector{UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(6)) == std::vector{UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(7)) == std::vector{UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(8)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(9)) == std::vector{UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(10)) == std::vector{UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(11)) == std::vector{UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(12)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(13)) == std::vector{UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(14)) == std::vector{UINT32_C(2), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(15)) == std::vector{UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(16)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(17)) == std::vector{UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(18)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(19)) == std::vector{UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(20)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(21)) == std::vector{UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(22)) == std::vector{UINT32_C(2), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(23)) == std::vector{UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(24)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(25)) == std::vector{UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(26)) == std::vector{UINT32_C(2), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(27)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(28)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(29)) == std::vector{UINT32_C(29)});
assert_that(tools::prime_factorization(UINT32_C(30)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(31)) == std::vector{UINT32_C(31)});
assert_that(tools::prime_factorization(UINT32_C(32)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(33)) == std::vector{UINT32_C(3), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(34)) == std::vector{UINT32_C(2), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(35)) == std::vector{UINT32_C(5), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(36)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(37)) == std::vector{UINT32_C(37)});
assert_that(tools::prime_factorization(UINT32_C(38)) == std::vector{UINT32_C(2), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(39)) == std::vector{UINT32_C(3), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(40)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(41)) == std::vector{UINT32_C(41)});
assert_that(tools::prime_factorization(UINT32_C(42)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(43)) == std::vector{UINT32_C(43)});
assert_that(tools::prime_factorization(UINT32_C(44)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(45)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(46)) == std::vector{UINT32_C(2), UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(47)) == std::vector{UINT32_C(47)});
assert_that(tools::prime_factorization(UINT32_C(48)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(49)) == std::vector{UINT32_C(7), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(50)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(51)) == std::vector{UINT32_C(3), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(52)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(53)) == std::vector{UINT32_C(53)});
assert_that(tools::prime_factorization(UINT32_C(54)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(55)) == std::vector{UINT32_C(5), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(56)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(57)) == std::vector{UINT32_C(3), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(58)) == std::vector{UINT32_C(2), UINT32_C(29)});
assert_that(tools::prime_factorization(UINT32_C(59)) == std::vector{UINT32_C(59)});
assert_that(tools::prime_factorization(UINT32_C(60)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(61)) == std::vector{UINT32_C(61)});
assert_that(tools::prime_factorization(UINT32_C(62)) == std::vector{UINT32_C(2), UINT32_C(31)});
assert_that(tools::prime_factorization(UINT32_C(63)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(64)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2)});
assert_that(tools::prime_factorization(UINT32_C(65)) == std::vector{UINT32_C(5), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(66)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(67)) == std::vector{UINT32_C(67)});
assert_that(tools::prime_factorization(UINT32_C(68)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(69)) == std::vector{UINT32_C(3), UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(70)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(71)) == std::vector{UINT32_C(71)});
assert_that(tools::prime_factorization(UINT32_C(72)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(73)) == std::vector{UINT32_C(73)});
assert_that(tools::prime_factorization(UINT32_C(74)) == std::vector{UINT32_C(2), UINT32_C(37)});
assert_that(tools::prime_factorization(UINT32_C(75)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(76)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(77)) == std::vector{UINT32_C(7), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(78)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(79)) == std::vector{UINT32_C(79)});
assert_that(tools::prime_factorization(UINT32_C(80)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(81)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(82)) == std::vector{UINT32_C(2), UINT32_C(41)});
assert_that(tools::prime_factorization(UINT32_C(83)) == std::vector{UINT32_C(83)});
assert_that(tools::prime_factorization(UINT32_C(84)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(85)) == std::vector{UINT32_C(5), UINT32_C(17)});
assert_that(tools::prime_factorization(UINT32_C(86)) == std::vector{UINT32_C(2), UINT32_C(43)});
assert_that(tools::prime_factorization(UINT32_C(87)) == std::vector{UINT32_C(3), UINT32_C(29)});
assert_that(tools::prime_factorization(UINT32_C(88)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(89)) == std::vector{UINT32_C(89)});
assert_that(tools::prime_factorization(UINT32_C(90)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(91)) == std::vector{UINT32_C(7), UINT32_C(13)});
assert_that(tools::prime_factorization(UINT32_C(92)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(23)});
assert_that(tools::prime_factorization(UINT32_C(93)) == std::vector{UINT32_C(3), UINT32_C(31)});
assert_that(tools::prime_factorization(UINT32_C(94)) == std::vector{UINT32_C(2), UINT32_C(47)});
assert_that(tools::prime_factorization(UINT32_C(95)) == std::vector{UINT32_C(5), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(96)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3)});
assert_that(tools::prime_factorization(UINT32_C(97)) == std::vector{UINT32_C(97)});
assert_that(tools::prime_factorization(UINT32_C(98)) == std::vector{UINT32_C(2), UINT32_C(7), UINT32_C(7)});
assert_that(tools::prime_factorization(UINT32_C(99)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(11)});
assert_that(tools::prime_factorization(UINT32_C(100)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(5)});
assert_that(tools::prime_factorization(UINT32_C(3491888400)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(5), UINT32_C(5), UINT32_C(7), UINT32_C(11), UINT32_C(13), UINT32_C(17), UINT32_C(19)});
assert_that(tools::prime_factorization(UINT32_C(4294967196)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(13), UINT32_C(67), UINT32_C(163), UINT32_C(2521)});
assert_that(tools::prime_factorization(UINT32_C(4294967197)) == std::vector{UINT32_C(4294967197)});
assert_that(tools::prime_factorization(UINT32_C(4294967198)) == std::vector{UINT32_C(2), UINT32_C(1657), UINT32_C(1296007)});
assert_that(tools::prime_factorization(UINT32_C(4294967199)) == std::vector{UINT32_C(3), UINT32_C(31), UINT32_C(46182443)});
assert_that(tools::prime_factorization(UINT32_C(4294967200)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(5), UINT32_C(173), UINT32_C(31033)});
assert_that(tools::prime_factorization(UINT32_C(4294967201)) == std::vector{UINT32_C(7), UINT32_C(53), UINT32_C(11576731)});
assert_that(tools::prime_factorization(UINT32_C(4294967202)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(238609289)});
assert_that(tools::prime_factorization(UINT32_C(4294967203)) == std::vector{UINT32_C(157), UINT32_C(1051), UINT32_C(26029)});
assert_that(tools::prime_factorization(UINT32_C(4294967204)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(11), UINT32_C(97612891)});
assert_that(tools::prime_factorization(UINT32_C(4294967205)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(286331147)});
assert_that(tools::prime_factorization(UINT32_C(4294967206)) == std::vector{UINT32_C(2), UINT32_C(1187), UINT32_C(1809169)});
assert_that(tools::prime_factorization(UINT32_C(4294967207)) == std::vector{UINT32_C(47), UINT32_C(91382281)});
assert_that(tools::prime_factorization(UINT32_C(4294967208)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(7), UINT32_C(7), UINT32_C(197), UINT32_C(18539)});
assert_that(tools::prime_factorization(UINT32_C(4294967209)) == std::vector{UINT32_C(13), UINT32_C(677), UINT32_C(488009)});
assert_that(tools::prime_factorization(UINT32_C(4294967210)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(17), UINT32_C(25264513)});
assert_that(tools::prime_factorization(UINT32_C(4294967211)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(477218579)});
assert_that(tools::prime_factorization(UINT32_C(4294967212)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3671), UINT32_C(292493)});
assert_that(tools::prime_factorization(UINT32_C(4294967213)) == std::vector{UINT32_C(57139), UINT32_C(75167)});
assert_that(tools::prime_factorization(UINT32_C(4294967214)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(19), UINT32_C(571), UINT32_C(65981)});
assert_that(tools::prime_factorization(UINT32_C(4294967215)) == std::vector{UINT32_C(5), UINT32_C(7), UINT32_C(11), UINT32_C(23), UINT32_C(37), UINT32_C(13109)});
assert_that(tools::prime_factorization(UINT32_C(4294967216)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(71), UINT32_C(3780781)});
assert_that(tools::prime_factorization(UINT32_C(4294967217)) == std::vector{UINT32_C(3), UINT32_C(1431655739)});
assert_that(tools::prime_factorization(UINT32_C(4294967218)) == std::vector{UINT32_C(2), UINT32_C(41), UINT32_C(52377649)});
assert_that(tools::prime_factorization(UINT32_C(4294967219)) == std::vector{UINT32_C(83), UINT32_C(4327), UINT32_C(11959)});
assert_that(tools::prime_factorization(UINT32_C(4294967220)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(5), UINT32_C(313), UINT32_C(25411)});
assert_that(tools::prime_factorization(UINT32_C(4294967221)) == std::vector{UINT32_C(109), UINT32_C(39403369)});
assert_that(tools::prime_factorization(UINT32_C(4294967222)) == std::vector{UINT32_C(2), UINT32_C(7), UINT32_C(13), UINT32_C(29), UINT32_C(813749)});
assert_that(tools::prime_factorization(UINT32_C(4294967223)) == std::vector{UINT32_C(3), UINT32_C(359), UINT32_C(1291), UINT32_C(3089)});
assert_that(tools::prime_factorization(UINT32_C(4294967224)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(311), UINT32_C(1726273)});
assert_that(tools::prime_factorization(UINT32_C(4294967225)) == std::vector{UINT32_C(5), UINT32_C(5), UINT32_C(743), UINT32_C(231223)});
assert_that(tools::prime_factorization(UINT32_C(4294967226)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(11), UINT32_C(2953), UINT32_C(22037)});
assert_that(tools::prime_factorization(UINT32_C(4294967227)) == std::vector{UINT32_C(17), UINT32_C(252645131)});
assert_that(tools::prime_factorization(UINT32_C(4294967228)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(101), UINT32_C(10631107)});
assert_that(tools::prime_factorization(UINT32_C(4294967229)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(7), UINT32_C(977), UINT32_C(69779)});
assert_that(tools::prime_factorization(UINT32_C(4294967230)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(31), UINT32_C(13854733)});
assert_that(tools::prime_factorization(UINT32_C(4294967231)) == std::vector{UINT32_C(4294967231)});
assert_that(tools::prime_factorization(UINT32_C(4294967232)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(2731), UINT32_C(8191)});
assert_that(tools::prime_factorization(UINT32_C(4294967233)) == std::vector{UINT32_C(19), UINT32_C(103), UINT32_C(617), UINT32_C(3557)});
assert_that(tools::prime_factorization(UINT32_C(4294967234)) == std::vector{UINT32_C(2), UINT32_C(6733), UINT32_C(318949)});
assert_that(tools::prime_factorization(UINT32_C(4294967235)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(13), UINT32_C(22025473)});
assert_that(tools::prime_factorization(UINT32_C(4294967236)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(7), UINT32_C(367), UINT32_C(417961)});
assert_that(tools::prime_factorization(UINT32_C(4294967237)) == std::vector{UINT32_C(11), UINT32_C(11), UINT32_C(43), UINT32_C(825479)});
assert_that(tools::prime_factorization(UINT32_C(4294967238)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(23), UINT32_C(353), UINT32_C(29389)});
assert_that(tools::prime_factorization(UINT32_C(4294967239)) == std::vector{UINT32_C(61), UINT32_C(70409299)});
assert_that(tools::prime_factorization(UINT32_C(4294967240)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(4603), UINT32_C(23327)});
assert_that(tools::prime_factorization(UINT32_C(4294967241)) == std::vector{UINT32_C(3), UINT32_C(1431655747)});
assert_that(tools::prime_factorization(UINT32_C(4294967242)) == std::vector{UINT32_C(2), UINT32_C(14741), UINT32_C(145681)});
assert_that(tools::prime_factorization(UINT32_C(4294967243)) == std::vector{UINT32_C(7), UINT32_C(991), UINT32_C(619139)});
assert_that(tools::prime_factorization(UINT32_C(4294967244)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(17), UINT32_C(467), UINT32_C(45083)});
assert_that(tools::prime_factorization(UINT32_C(4294967245)) == std::vector{UINT32_C(5), UINT32_C(59), UINT32_C(211), UINT32_C(69001)});
assert_that(tools::prime_factorization(UINT32_C(4294967246)) == std::vector{UINT32_C(2), UINT32_C(79), UINT32_C(967), UINT32_C(28111)});
assert_that(tools::prime_factorization(UINT32_C(4294967247)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(809), UINT32_C(65543)});
assert_that(tools::prime_factorization(UINT32_C(4294967248)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(11), UINT32_C(13), UINT32_C(1877171)});
assert_that(tools::prime_factorization(UINT32_C(4294967249)) == std::vector{UINT32_C(269), UINT32_C(15966421)});
assert_that(tools::prime_factorization(UINT32_C(4294967250)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(5), UINT32_C(5), UINT32_C(5), UINT32_C(7), UINT32_C(199), UINT32_C(4111)});
assert_that(tools::prime_factorization(UINT32_C(4294967251)) == std::vector{UINT32_C(29), UINT32_C(89), UINT32_C(1664071)});
assert_that(tools::prime_factorization(UINT32_C(4294967252)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(19), UINT32_C(37), UINT32_C(1527371)});
assert_that(tools::prime_factorization(UINT32_C(4294967253)) == std::vector{UINT32_C(3), UINT32_C(1431655751)});
assert_that(tools::prime_factorization(UINT32_C(4294967254)) == std::vector{UINT32_C(2), UINT32_C(47), UINT32_C(53), UINT32_C(862097)});
assert_that(tools::prime_factorization(UINT32_C(4294967255)) == std::vector{UINT32_C(5), UINT32_C(139), UINT32_C(1451), UINT32_C(4259)});
assert_that(tools::prime_factorization(UINT32_C(4294967256)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(59652323)});
assert_that(tools::prime_factorization(UINT32_C(4294967257)) == std::vector{UINT32_C(7), UINT32_C(7), UINT32_C(1061), UINT32_C(82613)});
assert_that(tools::prime_factorization(UINT32_C(4294967258)) == std::vector{UINT32_C(2), UINT32_C(2147483629)});
assert_that(tools::prime_factorization(UINT32_C(4294967259)) == std::vector{UINT32_C(3), UINT32_C(11), UINT32_C(41), UINT32_C(659), UINT32_C(4817)});
assert_that(tools::prime_factorization(UINT32_C(4294967260)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(5), UINT32_C(6553), UINT32_C(32771)});
assert_that(tools::prime_factorization(UINT32_C(4294967261)) == std::vector{UINT32_C(13), UINT32_C(17), UINT32_C(23), UINT32_C(31), UINT32_C(97), UINT32_C(281)});
assert_that(tools::prime_factorization(UINT32_C(4294967262)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(137), UINT32_C(263), UINT32_C(19867)});
assert_that(tools::prime_factorization(UINT32_C(4294967263)) == std::vector{UINT32_C(67), UINT32_C(64103989)});
assert_that(tools::prime_factorization(UINT32_C(4294967264)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(7), UINT32_C(73), UINT32_C(262657)});
assert_that(tools::prime_factorization(UINT32_C(4294967265)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(5), UINT32_C(95443717)});
assert_that(tools::prime_factorization(UINT32_C(4294967266)) == std::vector{UINT32_C(2), UINT32_C(5843), UINT32_C(367531)});
assert_that(tools::prime_factorization(UINT32_C(4294967267)) == std::vector{UINT32_C(107), UINT32_C(1069), UINT32_C(37549)});
assert_that(tools::prime_factorization(UINT32_C(4294967268)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(12097), UINT32_C(29587)});
assert_that(tools::prime_factorization(UINT32_C(4294967269)) == std::vector{UINT32_C(277), UINT32_C(433), UINT32_C(35809)});
assert_that(tools::prime_factorization(UINT32_C(4294967270)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(11), UINT32_C(337), UINT32_C(115861)});
assert_that(tools::prime_factorization(UINT32_C(4294967271)) == std::vector{UINT32_C(3), UINT32_C(7), UINT32_C(19), UINT32_C(3121), UINT32_C(3449)});
assert_that(tools::prime_factorization(UINT32_C(4294967272)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(536870909)});
assert_that(tools::prime_factorization(UINT32_C(4294967273)) == std::vector{UINT32_C(10847), UINT32_C(395959)});
assert_that(tools::prime_factorization(UINT32_C(4294967274)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(3), UINT32_C(13), UINT32_C(6118187)});
assert_that(tools::prime_factorization(UINT32_C(4294967275)) == std::vector{UINT32_C(5), UINT32_C(5), UINT32_C(171798691)});
assert_that(tools::prime_factorization(UINT32_C(4294967276)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2969), UINT32_C(361651)});
assert_that(tools::prime_factorization(UINT32_C(4294967277)) == std::vector{UINT32_C(3), UINT32_C(769), UINT32_C(1861711)});
assert_that(tools::prime_factorization(UINT32_C(4294967278)) == std::vector{UINT32_C(2), UINT32_C(7), UINT32_C(17), UINT32_C(18046081)});
assert_that(tools::prime_factorization(UINT32_C(4294967279)) == std::vector{UINT32_C(4294967279)});
assert_that(tools::prime_factorization(UINT32_C(4294967280)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(5), UINT32_C(29), UINT32_C(43), UINT32_C(113), UINT32_C(127)});
assert_that(tools::prime_factorization(UINT32_C(4294967281)) == std::vector{UINT32_C(11), UINT32_C(181), UINT32_C(241), UINT32_C(8951)});
assert_that(tools::prime_factorization(UINT32_C(4294967282)) == std::vector{UINT32_C(2), UINT32_C(2699), UINT32_C(795659)});
assert_that(tools::prime_factorization(UINT32_C(4294967283)) == std::vector{UINT32_C(3), UINT32_C(3), UINT32_C(389), UINT32_C(1226783)});
assert_that(tools::prime_factorization(UINT32_C(4294967284)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(23), UINT32_C(46684427)});
assert_that(tools::prime_factorization(UINT32_C(4294967285)) == std::vector{UINT32_C(5), UINT32_C(7), UINT32_C(122713351)});
assert_that(tools::prime_factorization(UINT32_C(4294967286)) == std::vector{UINT32_C(2), UINT32_C(3), UINT32_C(715827881)});
assert_that(tools::prime_factorization(UINT32_C(4294967287)) == std::vector{UINT32_C(13), UINT32_C(71), UINT32_C(71), UINT32_C(65539)});
assert_that(tools::prime_factorization(UINT32_C(4294967288)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(2), UINT32_C(233), UINT32_C(1103), UINT32_C(2089)});
assert_that(tools::prime_factorization(UINT32_C(4294967289)) == std::vector{UINT32_C(3), UINT32_C(37), UINT32_C(167), UINT32_C(223), UINT32_C(1039)});
assert_that(tools::prime_factorization(UINT32_C(4294967290)) == std::vector{UINT32_C(2), UINT32_C(5), UINT32_C(19), UINT32_C(22605091)});
assert_that(tools::prime_factorization(UINT32_C(4294967291)) == std::vector{UINT32_C(4294967291)});
assert_that(tools::prime_factorization(UINT32_C(4294967292)) == std::vector{UINT32_C(2), UINT32_C(2), UINT32_C(3), UINT32_C(3), UINT32_C(7), UINT32_C(11), UINT32_C(31), UINT32_C(151), UINT32_C(331)});
assert_that(tools::prime_factorization(UINT32_C(4294967293)) == std::vector{UINT32_C(9241), UINT32_C(464773)});
assert_that(tools::prime_factorization(UINT32_C(4294967294)) == std::vector{UINT32_C(2), UINT32_C(2147483647)});
assert_that(tools::prime_factorization(UINT32_C(4294967295)) == std::vector{UINT32_C(3), UINT32_C(5), UINT32_C(17), UINT32_C(257), UINT32_C(65537)});
assert_that(tools::prime_factorization(INT64_C(1)) == std::vector<std::int64_t>{});
assert_that(tools::prime_factorization(INT64_C(2)) == std::vector{INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(3)) == std::vector{INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(4)) == std::vector{INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(5)) == std::vector{INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(6)) == std::vector{INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(7)) == std::vector{INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(8)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(9)) == std::vector{INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(10)) == std::vector{INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(11)) == std::vector{INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(12)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(13)) == std::vector{INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(14)) == std::vector{INT64_C(2), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(15)) == std::vector{INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(16)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(17)) == std::vector{INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(18)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(19)) == std::vector{INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(20)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(21)) == std::vector{INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(22)) == std::vector{INT64_C(2), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(23)) == std::vector{INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(24)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(25)) == std::vector{INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(26)) == std::vector{INT64_C(2), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(27)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(28)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(29)) == std::vector{INT64_C(29)});
assert_that(tools::prime_factorization(INT64_C(30)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(31)) == std::vector{INT64_C(31)});
assert_that(tools::prime_factorization(INT64_C(32)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(33)) == std::vector{INT64_C(3), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(34)) == std::vector{INT64_C(2), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(35)) == std::vector{INT64_C(5), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(36)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(37)) == std::vector{INT64_C(37)});
assert_that(tools::prime_factorization(INT64_C(38)) == std::vector{INT64_C(2), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(39)) == std::vector{INT64_C(3), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(40)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(41)) == std::vector{INT64_C(41)});
assert_that(tools::prime_factorization(INT64_C(42)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(43)) == std::vector{INT64_C(43)});
assert_that(tools::prime_factorization(INT64_C(44)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(45)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(46)) == std::vector{INT64_C(2), INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(47)) == std::vector{INT64_C(47)});
assert_that(tools::prime_factorization(INT64_C(48)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(49)) == std::vector{INT64_C(7), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(50)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(51)) == std::vector{INT64_C(3), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(52)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(53)) == std::vector{INT64_C(53)});
assert_that(tools::prime_factorization(INT64_C(54)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(55)) == std::vector{INT64_C(5), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(56)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(57)) == std::vector{INT64_C(3), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(58)) == std::vector{INT64_C(2), INT64_C(29)});
assert_that(tools::prime_factorization(INT64_C(59)) == std::vector{INT64_C(59)});
assert_that(tools::prime_factorization(INT64_C(60)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(61)) == std::vector{INT64_C(61)});
assert_that(tools::prime_factorization(INT64_C(62)) == std::vector{INT64_C(2), INT64_C(31)});
assert_that(tools::prime_factorization(INT64_C(63)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(64)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2)});
assert_that(tools::prime_factorization(INT64_C(65)) == std::vector{INT64_C(5), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(66)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(67)) == std::vector{INT64_C(67)});
assert_that(tools::prime_factorization(INT64_C(68)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(69)) == std::vector{INT64_C(3), INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(70)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(71)) == std::vector{INT64_C(71)});
assert_that(tools::prime_factorization(INT64_C(72)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(73)) == std::vector{INT64_C(73)});
assert_that(tools::prime_factorization(INT64_C(74)) == std::vector{INT64_C(2), INT64_C(37)});
assert_that(tools::prime_factorization(INT64_C(75)) == std::vector{INT64_C(3), INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(76)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(77)) == std::vector{INT64_C(7), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(78)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(79)) == std::vector{INT64_C(79)});
assert_that(tools::prime_factorization(INT64_C(80)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(81)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(82)) == std::vector{INT64_C(2), INT64_C(41)});
assert_that(tools::prime_factorization(INT64_C(83)) == std::vector{INT64_C(83)});
assert_that(tools::prime_factorization(INT64_C(84)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(85)) == std::vector{INT64_C(5), INT64_C(17)});
assert_that(tools::prime_factorization(INT64_C(86)) == std::vector{INT64_C(2), INT64_C(43)});
assert_that(tools::prime_factorization(INT64_C(87)) == std::vector{INT64_C(3), INT64_C(29)});
assert_that(tools::prime_factorization(INT64_C(88)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(89)) == std::vector{INT64_C(89)});
assert_that(tools::prime_factorization(INT64_C(90)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(91)) == std::vector{INT64_C(7), INT64_C(13)});
assert_that(tools::prime_factorization(INT64_C(92)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(23)});
assert_that(tools::prime_factorization(INT64_C(93)) == std::vector{INT64_C(3), INT64_C(31)});
assert_that(tools::prime_factorization(INT64_C(94)) == std::vector{INT64_C(2), INT64_C(47)});
assert_that(tools::prime_factorization(INT64_C(95)) == std::vector{INT64_C(5), INT64_C(19)});
assert_that(tools::prime_factorization(INT64_C(96)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3)});
assert_that(tools::prime_factorization(INT64_C(97)) == std::vector{INT64_C(97)});
assert_that(tools::prime_factorization(INT64_C(98)) == std::vector{INT64_C(2), INT64_C(7), INT64_C(7)});
assert_that(tools::prime_factorization(INT64_C(99)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(11)});
assert_that(tools::prime_factorization(INT64_C(100)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(5)});
assert_that(tools::prime_factorization(INT64_C(9200527969062830400)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(5), INT64_C(7), INT64_C(7), INT64_C(11), INT64_C(13), INT64_C(17), INT64_C(19), INT64_C(23), INT64_C(29), INT64_C(31), INT64_C(37), INT64_C(41)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775708)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(1319), INT64_C(1748175139661633)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775709)) == std::vector{INT64_C(7), INT64_C(7), INT64_C(13), INT64_C(29), INT64_C(2729), INT64_C(182956886477)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775710)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(131), INT64_C(2699), INT64_C(364289), INT64_C(795659)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775711)) == std::vector{INT64_C(1171), INT64_C(16573), INT64_C(475260479017)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775712)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(11), INT64_C(26202761468337431)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775713)) == std::vector{INT64_C(3), INT64_C(23), INT64_C(133672058505141677)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775714)) == std::vector{INT64_C(2), INT64_C(17), INT64_C(19), INT64_C(215153), INT64_C(66360523403)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775715)) == std::vector{INT64_C(5), INT64_C(1844674407370955143)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775716)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(7), INT64_C(1607), INT64_C(2067431), INT64_C(33049397)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775717)) == std::vector{INT64_C(59), INT64_C(156328339607708063)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775718)) == std::vector{INT64_C(2), INT64_C(41), INT64_C(101), INT64_C(4051), INT64_C(6199), INT64_C(44347651)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775719)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(1024819115206086191)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775720)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(4229), INT64_C(54524545027517)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775721)) == std::vector{INT64_C(53), INT64_C(1791191), INT64_C(97156521827)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775722)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(13), INT64_C(3109), INT64_C(38034210179111)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775723)) == std::vector{INT64_C(7), INT64_C(11), INT64_C(43), INT64_C(27109), INT64_C(234293), INT64_C(438589)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775724)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(124367), INT64_C(18540633843493)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775725)) == std::vector{INT64_C(3), INT64_C(5), INT64_C(5), INT64_C(47), INT64_C(47), INT64_C(55671477512327)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775726)) == std::vector{INT64_C(2), INT64_C(1087), INT64_C(4242581433695849)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775727)) == std::vector{INT64_C(11113), INT64_C(829962389710679)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775728)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(37), INT64_C(34519), INT64_C(83717), INT64_C(199679)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775729)) == std::vector{INT64_C(97), INT64_C(103), INT64_C(2707), INT64_C(32233), INT64_C(10580149)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775730)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(7), INT64_C(89), INT64_C(1480477052464651)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775731)) == std::vector{INT64_C(3), INT64_C(17), INT64_C(319856591), INT64_C(565410991)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775732)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(71), INT64_C(139), INT64_C(1193693), INT64_C(195732949)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775733)) == std::vector{INT64_C(19), INT64_C(239), INT64_C(6197), INT64_C(8209), INT64_C(39926981)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775734)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(11), INT64_C(73), INT64_C(3527), INT64_C(542772044869)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775735)) == std::vector{INT64_C(5), INT64_C(13), INT64_C(141898031336227319)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775736)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(23), INT64_C(46684427), INT64_C(1073741827)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775737)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(7), INT64_C(313), INT64_C(68329), INT64_C(6845414887)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775738)) == std::vector{INT64_C(2), INT64_C(29), INT64_C(31), INT64_C(17597), INT64_C(33289), INT64_C(8757107)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775739)) == std::vector{INT64_C(61), INT64_C(3264649), INT64_C(46315184351)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775740)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(5), INT64_C(153722867280912929)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775741)) == std::vector{INT64_C(75883), INT64_C(299881), INT64_C(405318367)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775742)) == std::vector{INT64_C(2), INT64_C(252449), INT64_C(18267792775679)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775743)) == std::vector{INT64_C(3), INT64_C(79), INT64_C(116533), INT64_C(333958463183)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775744)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(7), INT64_C(32377), INT64_C(524287), INT64_C(1212847)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775745)) == std::vector{INT64_C(5), INT64_C(11), INT64_C(199), INT64_C(11587), INT64_C(72728219243)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775746)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(179), INT64_C(23021), INT64_C(124348343983)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775747)) == std::vector{INT64_C(677), INT64_C(78919), INT64_C(172631277569)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775748)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(13), INT64_C(17), INT64_C(37359691), INT64_C(279276367)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775749)) == std::vector{INT64_C(3), INT64_C(8447), INT64_C(363970326224489)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775750)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(5), INT64_C(5), INT64_C(36893488147419103)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775751)) == std::vector{INT64_C(7), INT64_C(17659), INT64_C(74614903261427)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775752)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(19), INT64_C(93053), INT64_C(217367447189)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775753)) == std::vector{INT64_C(266416229), INT64_C(34620158357)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775754)) == std::vector{INT64_C(2), INT64_C(343242169), INT64_C(13435662733)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775755)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(68321274347072413)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775756)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(11), INT64_C(227), INT64_C(263), INT64_C(18341), INT64_C(191439889)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775757)) == std::vector{INT64_C(149), INT64_C(5987), INT64_C(10339372933139)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775758)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(7), INT64_C(7), INT64_C(43826197), INT64_C(715827881)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775759)) == std::vector{INT64_C(23), INT64_C(41), INT64_C(620441), INT64_C(15764403593)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775760)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(2663), INT64_C(43294085790719)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775761)) == std::vector{INT64_C(3), INT64_C(13), INT64_C(13), INT64_C(619), INT64_C(739), INT64_C(39769184003)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775762)) == std::vector{INT64_C(2), INT64_C(107), INT64_C(1117), INT64_C(38585379884599)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775763)) == std::vector{INT64_C(4481), INT64_C(63601), INT64_C(32363153923)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775764)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(256204778801521549)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775765)) == std::vector{INT64_C(5), INT64_C(7), INT64_C(17), INT64_C(37), INT64_C(418958529950251)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775766)) == std::vector{INT64_C(2), INT64_C(43), INT64_C(67), INT64_C(193), INT64_C(809383), INT64_C(10247197)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775767)) == std::vector{INT64_C(3), INT64_C(11), INT64_C(29), INT64_C(19473149), INT64_C(494927519)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775768)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(409), INT64_C(1793599), INT64_C(1571632781)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775769)) == std::vector{INT64_C(31), INT64_C(10037), INT64_C(29643133428427)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775770)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(5), INT64_C(986507), INT64_C(311650839337)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775771)) == std::vector{INT64_C(19), INT64_C(485440633518672409)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775772)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(7), INT64_C(47), INT64_C(8627903), INT64_C(812322689)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775773)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(1024819115206086197)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775774)) == std::vector{INT64_C(2), INT64_C(13), INT64_C(53), INT64_C(6693303364916383)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775775)) == std::vector{INT64_C(5), INT64_C(5), INT64_C(109), INT64_C(57881), INT64_C(58477284139)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775776)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(59), INT64_C(233), INT64_C(1103), INT64_C(2089), INT64_C(3033169)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775777)) == std::vector{INT64_C(584911), INT64_C(15768846947407)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775778)) == std::vector{INT64_C(2), INT64_C(11), INT64_C(137), INT64_C(547), INT64_C(5594472617641)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775779)) == std::vector{INT64_C(3), INT64_C(7), INT64_C(439208192231179799)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775780)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(5), INT64_C(461168601842738789)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775781)) == std::vector{INT64_C(773), INT64_C(2713), INT64_C(19993), INT64_C(219979633)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775782)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(3), INT64_C(17), INT64_C(23), INT64_C(319279), INT64_C(456065899)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775783)) == std::vector{INT64_C(9223372036854775783)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775784)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(1177067), INT64_C(979486728119)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775785)) == std::vector{INT64_C(3), INT64_C(5), INT64_C(24097), INT64_C(25517345276327)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775786)) == std::vector{INT64_C(2), INT64_C(7), INT64_C(181), INT64_C(229), INT64_C(3697), INT64_C(4299304283)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775787)) == std::vector{INT64_C(13), INT64_C(440303), INT64_C(1611367982233)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775788)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(643), INT64_C(1195356666259043)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775789)) == std::vector{INT64_C(11), INT64_C(3931), INT64_C(213301543369829)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775790)) == std::vector{INT64_C(2), INT64_C(5), INT64_C(19), INT64_C(83), INT64_C(1277), INT64_C(20261), INT64_C(22605091)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775791)) == std::vector{INT64_C(3), INT64_C(3), INT64_C(14737), INT64_C(4837853), INT64_C(14374259)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775792)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(179951), INT64_C(3203431780337)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775793)) == std::vector{INT64_C(7), INT64_C(113), INT64_C(5647), INT64_C(2064883032409)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775794)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(3491), INT64_C(440340496364689)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775795)) == std::vector{INT64_C(5), INT64_C(191), INT64_C(421), INT64_C(90679), INT64_C(252986611)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775796)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(29), INT64_C(79511827903920481)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775797)) == std::vector{INT64_C(3), INT64_C(3074457345618258599)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775798)) == std::vector{INT64_C(2), INT64_C(34421), INT64_C(133978850655919)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775799)) == std::vector{INT64_C(17), INT64_C(17), INT64_C(17), INT64_C(2927), INT64_C(641387128649)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775800)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2), INT64_C(3), INT64_C(3), INT64_C(5), INT64_C(5), INT64_C(7), INT64_C(11), INT64_C(13), INT64_C(31), INT64_C(41), INT64_C(61), INT64_C(151), INT64_C(331), INT64_C(1321)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775801)) == std::vector{INT64_C(157), INT64_C(1973), INT64_C(29775769179641)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775802)) == std::vector{INT64_C(2), INT64_C(37), INT64_C(9902437), INT64_C(12586817029)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775803)) == std::vector{INT64_C(3), INT64_C(71), INT64_C(42013), INT64_C(1030686124187)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775804)) == std::vector{INT64_C(2), INT64_C(2), INT64_C(2305843009213693951)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775805)) == std::vector{INT64_C(5), INT64_C(23), INT64_C(53301701), INT64_C(1504703107)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775806)) == std::vector{INT64_C(2), INT64_C(3), INT64_C(715827883), INT64_C(2147483647)});
assert_that(tools::prime_factorization(INT64_C(9223372036854775807)) == std::vector{INT64_C(7), INT64_C(7), INT64_C(73), INT64_C(127), INT64_C(337), INT64_C(92737), INT64_C(649657)});
assert_that(tools::prime_factorization(UINT64_C(1)) == std::vector<std::uint64_t>{});
assert_that(tools::prime_factorization(UINT64_C(2)) == std::vector{UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(3)) == std::vector{UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(4)) == std::vector{UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(5)) == std::vector{UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(6)) == std::vector{UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(7)) == std::vector{UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(8)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(9)) == std::vector{UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(10)) == std::vector{UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(11)) == std::vector{UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(12)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(13)) == std::vector{UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(14)) == std::vector{UINT64_C(2), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(15)) == std::vector{UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(16)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(17)) == std::vector{UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(18)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(19)) == std::vector{UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(20)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(21)) == std::vector{UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(22)) == std::vector{UINT64_C(2), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(23)) == std::vector{UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(24)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(25)) == std::vector{UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(26)) == std::vector{UINT64_C(2), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(27)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(28)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(29)) == std::vector{UINT64_C(29)});
assert_that(tools::prime_factorization(UINT64_C(30)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(31)) == std::vector{UINT64_C(31)});
assert_that(tools::prime_factorization(UINT64_C(32)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(33)) == std::vector{UINT64_C(3), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(34)) == std::vector{UINT64_C(2), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(35)) == std::vector{UINT64_C(5), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(36)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(37)) == std::vector{UINT64_C(37)});
assert_that(tools::prime_factorization(UINT64_C(38)) == std::vector{UINT64_C(2), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(39)) == std::vector{UINT64_C(3), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(40)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(41)) == std::vector{UINT64_C(41)});
assert_that(tools::prime_factorization(UINT64_C(42)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(43)) == std::vector{UINT64_C(43)});
assert_that(tools::prime_factorization(UINT64_C(44)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(45)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(46)) == std::vector{UINT64_C(2), UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(47)) == std::vector{UINT64_C(47)});
assert_that(tools::prime_factorization(UINT64_C(48)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(49)) == std::vector{UINT64_C(7), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(50)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(51)) == std::vector{UINT64_C(3), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(52)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(53)) == std::vector{UINT64_C(53)});
assert_that(tools::prime_factorization(UINT64_C(54)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(55)) == std::vector{UINT64_C(5), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(56)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(57)) == std::vector{UINT64_C(3), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(58)) == std::vector{UINT64_C(2), UINT64_C(29)});
assert_that(tools::prime_factorization(UINT64_C(59)) == std::vector{UINT64_C(59)});
assert_that(tools::prime_factorization(UINT64_C(60)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(61)) == std::vector{UINT64_C(61)});
assert_that(tools::prime_factorization(UINT64_C(62)) == std::vector{UINT64_C(2), UINT64_C(31)});
assert_that(tools::prime_factorization(UINT64_C(63)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(64)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2)});
assert_that(tools::prime_factorization(UINT64_C(65)) == std::vector{UINT64_C(5), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(66)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(67)) == std::vector{UINT64_C(67)});
assert_that(tools::prime_factorization(UINT64_C(68)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(69)) == std::vector{UINT64_C(3), UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(70)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(71)) == std::vector{UINT64_C(71)});
assert_that(tools::prime_factorization(UINT64_C(72)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(73)) == std::vector{UINT64_C(73)});
assert_that(tools::prime_factorization(UINT64_C(74)) == std::vector{UINT64_C(2), UINT64_C(37)});
assert_that(tools::prime_factorization(UINT64_C(75)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(76)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(77)) == std::vector{UINT64_C(7), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(78)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(79)) == std::vector{UINT64_C(79)});
assert_that(tools::prime_factorization(UINT64_C(80)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(81)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(82)) == std::vector{UINT64_C(2), UINT64_C(41)});
assert_that(tools::prime_factorization(UINT64_C(83)) == std::vector{UINT64_C(83)});
assert_that(tools::prime_factorization(UINT64_C(84)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(85)) == std::vector{UINT64_C(5), UINT64_C(17)});
assert_that(tools::prime_factorization(UINT64_C(86)) == std::vector{UINT64_C(2), UINT64_C(43)});
assert_that(tools::prime_factorization(UINT64_C(87)) == std::vector{UINT64_C(3), UINT64_C(29)});
assert_that(tools::prime_factorization(UINT64_C(88)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(89)) == std::vector{UINT64_C(89)});
assert_that(tools::prime_factorization(UINT64_C(90)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(91)) == std::vector{UINT64_C(7), UINT64_C(13)});
assert_that(tools::prime_factorization(UINT64_C(92)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(23)});
assert_that(tools::prime_factorization(UINT64_C(93)) == std::vector{UINT64_C(3), UINT64_C(31)});
assert_that(tools::prime_factorization(UINT64_C(94)) == std::vector{UINT64_C(2), UINT64_C(47)});
assert_that(tools::prime_factorization(UINT64_C(95)) == std::vector{UINT64_C(5), UINT64_C(19)});
assert_that(tools::prime_factorization(UINT64_C(96)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3)});
assert_that(tools::prime_factorization(UINT64_C(97)) == std::vector{UINT64_C(97)});
assert_that(tools::prime_factorization(UINT64_C(98)) == std::vector{UINT64_C(2), UINT64_C(7), UINT64_C(7)});
assert_that(tools::prime_factorization(UINT64_C(99)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(11)});
assert_that(tools::prime_factorization(UINT64_C(100)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(5)});
assert_that(tools::prime_factorization(UINT64_C(18401055938125660800)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(5), UINT64_C(5), UINT64_C(7), UINT64_C(7), UINT64_C(11), UINT64_C(13), UINT64_C(17), UINT64_C(19), UINT64_C(23), UINT64_C(29), UINT64_C(31), UINT64_C(37), UINT64_C(41)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551516)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(7), UINT64_C(7), UINT64_C(43826197), UINT64_C(715827881)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551517)) == std::vector{UINT64_C(397), UINT64_C(46465350311610961)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551518)) == std::vector{UINT64_C(2), UINT64_C(23), UINT64_C(41), UINT64_C(620441), UINT64_C(15764403593)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551519)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(307), UINT64_C(405029), UINT64_C(16483624697)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551520)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(2663), UINT64_C(43294085790719)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551521)) == std::vector{UINT64_C(18446744073709551521)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551522)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(13), UINT64_C(13), UINT64_C(619), UINT64_C(739), UINT64_C(39769184003)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551523)) == std::vector{UINT64_C(7), UINT64_C(11), UINT64_C(11), UINT64_C(19), UINT64_C(6897409), UINT64_C(166186879)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551524)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(107), UINT64_C(1117), UINT64_C(38585379884599)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551525)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(5), UINT64_C(4441), UINT64_C(55383154165607)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551526)) == std::vector{UINT64_C(2), UINT64_C(4481), UINT64_C(63601), UINT64_C(32363153923)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551527)) == std::vector{UINT64_C(17099), UINT64_C(1078820052266773)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551528)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(256204778801521549)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551529)) == std::vector{UINT64_C(14843), UINT64_C(13973891), UINT64_C(88936633)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551530)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(7), UINT64_C(17), UINT64_C(37), UINT64_C(418958529950251)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551531)) == std::vector{UINT64_C(3), UINT64_C(962165251), UINT64_C(6390705427)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551532)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(43), UINT64_C(67), UINT64_C(193), UINT64_C(809383), UINT64_C(10247197)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551533)) == std::vector{UINT64_C(18446744073709551533)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551534)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(11), UINT64_C(29), UINT64_C(19473149), UINT64_C(494927519)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551535)) == std::vector{UINT64_C(5), UINT64_C(13), UINT64_C(71), UINT64_C(71), UINT64_C(9629), UINT64_C(65539), UINT64_C(89209)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551536)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(409), UINT64_C(1793599), UINT64_C(1571632781)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551537)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(7), UINT64_C(101), UINT64_C(7623919), UINT64_C(126753007)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551538)) == std::vector{UINT64_C(2), UINT64_C(31), UINT64_C(10037), UINT64_C(29643133428427)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551539)) == std::vector{UINT64_C(61), UINT64_C(268909), UINT64_C(1124564966411)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551540)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(5), UINT64_C(986507), UINT64_C(311650839337)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551541)) == std::vector{UINT64_C(23), UINT64_C(73), UINT64_C(7283), UINT64_C(1508546551513)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551542)) == std::vector{UINT64_C(2), UINT64_C(19), UINT64_C(485440633518672409)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551543)) == std::vector{UINT64_C(3), UINT64_C(839), UINT64_C(7328861372153179)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551544)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(7), UINT64_C(47), UINT64_C(8627903), UINT64_C(812322689)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551545)) == std::vector{UINT64_C(5), UINT64_C(11), UINT64_C(3319), UINT64_C(36871), UINT64_C(2740721231)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551546)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(1024819115206086197)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551547)) == std::vector{UINT64_C(17), UINT64_C(211), UINT64_C(251), UINT64_C(1101431), UINT64_C(18601901)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551548)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(13), UINT64_C(53), UINT64_C(6693303364916383)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551549)) == std::vector{UINT64_C(3), UINT64_C(89), UINT64_C(69088929115017047)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551550)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(5), UINT64_C(109), UINT64_C(57881), UINT64_C(58477284139)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551551)) == std::vector{UINT64_C(7), UINT64_C(131), UINT64_C(20116405751046403)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551552)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(59), UINT64_C(233), UINT64_C(1103), UINT64_C(2089), UINT64_C(3033169)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551553)) == std::vector{UINT64_C(401), UINT64_C(119241217), UINT64_C(385788209)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551554)) == std::vector{UINT64_C(2), UINT64_C(584911), UINT64_C(15768846947407)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551555)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(5), UINT64_C(97), UINT64_C(197), UINT64_C(325957), UINT64_C(65812583)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551556)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(11), UINT64_C(137), UINT64_C(547), UINT64_C(5594472617641)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551557)) == std::vector{UINT64_C(18446744073709551557)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551558)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(7), UINT64_C(439208192231179799)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551559)) == std::vector{UINT64_C(41), UINT64_C(163), UINT64_C(269), UINT64_C(8807), UINT64_C(1165112831)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551560)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(461168601842738789)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551561)) == std::vector{UINT64_C(3), UINT64_C(13), UINT64_C(19), UINT64_C(103), UINT64_C(1811), UINT64_C(133458377137)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551562)) == std::vector{UINT64_C(2), UINT64_C(773), UINT64_C(2713), UINT64_C(19993), UINT64_C(219979633)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551563)) == std::vector{UINT64_C(29), UINT64_C(74187931), UINT64_C(8574098437)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551564)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(17), UINT64_C(23), UINT64_C(319279), UINT64_C(456065899)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551565)) == std::vector{UINT64_C(5), UINT64_C(7), UINT64_C(7), UINT64_C(79), UINT64_C(599), UINT64_C(659), UINT64_C(2414428283)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551566)) == std::vector{UINT64_C(2), UINT64_C(9223372036854775783)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551567)) == std::vector{UINT64_C(3), UINT64_C(11), UINT64_C(37), UINT64_C(167), UINT64_C(223), UINT64_C(1039), UINT64_C(6323), UINT64_C(61751)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551568)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(1177067), UINT64_C(979486728119)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551569)) == std::vector{UINT64_C(31), UINT64_C(173), UINT64_C(9419), UINT64_C(439771), UINT64_C(830387)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551570)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(5), UINT64_C(24097), UINT64_C(25517345276327)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551571)) == std::vector{UINT64_C(11071), UINT64_C(844709), UINT64_C(1972539689)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551572)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(7), UINT64_C(181), UINT64_C(229), UINT64_C(3697), UINT64_C(4299304283)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551573)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(31799), UINT64_C(64456059323003)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551574)) == std::vector{UINT64_C(2), UINT64_C(13), UINT64_C(440303), UINT64_C(1611367982233)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551575)) == std::vector{UINT64_C(5), UINT64_C(5), UINT64_C(43), UINT64_C(122099), UINT64_C(140539741759)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551576)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(643), UINT64_C(1195356666259043)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551577)) == std::vector{UINT64_C(139646831), UINT64_C(132095686967)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551578)) == std::vector{UINT64_C(2), UINT64_C(11), UINT64_C(3931), UINT64_C(213301543369829)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551579)) == std::vector{UINT64_C(3), UINT64_C(7), UINT64_C(57906439), UINT64_C(15169580441)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551580)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(5), UINT64_C(19), UINT64_C(83), UINT64_C(1277), UINT64_C(20261), UINT64_C(22605091)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551581)) == std::vector{UINT64_C(17), UINT64_C(72786899), UINT64_C(14907938207)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551582)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(14737), UINT64_C(4837853), UINT64_C(14374259)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551583)) == std::vector{UINT64_C(827), UINT64_C(3894899), UINT64_C(5726879071)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551584)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(179951), UINT64_C(3203431780337)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551585)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(499), UINT64_C(2593), UINT64_C(950441521877)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551586)) == std::vector{UINT64_C(2), UINT64_C(7), UINT64_C(113), UINT64_C(5647), UINT64_C(2064883032409)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551587)) == std::vector{UINT64_C(13), UINT64_C(23), UINT64_C(23), UINT64_C(16561661), UINT64_C(161963371)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551588)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3491), UINT64_C(440340496364689)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551589)) == std::vector{UINT64_C(11), UINT64_C(13177), UINT64_C(127265442359687)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551590)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(191), UINT64_C(421), UINT64_C(90679), UINT64_C(252986611)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551591)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(3), UINT64_C(47), UINT64_C(3384529), UINT64_C(4294967291)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551592)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(29), UINT64_C(79511827903920481)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551593)) == std::vector{UINT64_C(7), UINT64_C(16547), UINT64_C(159258424692517)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551594)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(3074457345618258599)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551595)) == std::vector{UINT64_C(5), UINT64_C(373), UINT64_C(3301), UINT64_C(2996369460503)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551596)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(34421), UINT64_C(133978850655919)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551597)) == std::vector{UINT64_C(3), UINT64_C(6148914691236517199)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551598)) == std::vector{UINT64_C(2), UINT64_C(17), UINT64_C(17), UINT64_C(17), UINT64_C(2927), UINT64_C(641387128649)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551599)) == std::vector{UINT64_C(19), UINT64_C(67), UINT64_C(14490765179661863)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551600)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(3), UINT64_C(5), UINT64_C(5), UINT64_C(7), UINT64_C(11), UINT64_C(13), UINT64_C(31), UINT64_C(41), UINT64_C(61), UINT64_C(151), UINT64_C(331), UINT64_C(1321)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551601)) == std::vector{UINT64_C(53), UINT64_C(348051774975651917)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551602)) == std::vector{UINT64_C(2), UINT64_C(157), UINT64_C(1973), UINT64_C(29775769179641)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551603)) == std::vector{UINT64_C(3), UINT64_C(139), UINT64_C(2306123), UINT64_C(19182323033)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551604)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(37), UINT64_C(9902437), UINT64_C(12586817029)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551605)) == std::vector{UINT64_C(5), UINT64_C(2551), UINT64_C(1446236305269271)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551606)) == std::vector{UINT64_C(2), UINT64_C(3), UINT64_C(71), UINT64_C(42013), UINT64_C(1030686124187)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551607)) == std::vector{UINT64_C(7), UINT64_C(9241), UINT64_C(464773), UINT64_C(613566757)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551608)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(2), UINT64_C(2305843009213693951)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551609)) == std::vector{UINT64_C(3), UINT64_C(3), UINT64_C(818923289), UINT64_C(2502845209)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551610)) == std::vector{UINT64_C(2), UINT64_C(5), UINT64_C(23), UINT64_C(53301701), UINT64_C(1504703107)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551611)) == std::vector{UINT64_C(11), UINT64_C(59), UINT64_C(98818999), UINT64_C(287630261)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551612)) == std::vector{UINT64_C(2), UINT64_C(2), UINT64_C(3), UINT64_C(715827883), UINT64_C(2147483647)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551613)) == std::vector{UINT64_C(13), UINT64_C(3889), UINT64_C(364870227143809)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551614)) == std::vector{UINT64_C(2), UINT64_C(7), UINT64_C(7), UINT64_C(73), UINT64_C(127), UINT64_C(337), UINT64_C(92737), UINT64_C(649657)});
assert_that(tools::prime_factorization(UINT64_C(18446744073709551615)) == std::vector{UINT64_C(3), UINT64_C(5), UINT64_C(17), UINT64_C(257), UINT64_C(641), UINT64_C(65537), UINT64_C(6700417)});
return 0;
}