#! /usr/bin/env pypy def test_miller_rabin(n: int, bases: list): nn = n - 1 e = (nn & -nn).bit_length() - 1 o = n >> e # assert n == (o << e | 1) for b in bases: x = pow(b, o, n) if x == 1: continue for _ in range(e): y = pow(x, 2, n) if y == 1: if x == n - 1: break else: # nontrivial sqrt(1) found return False x = y else: return False return True def is_prime(n: int): if n < 2: return False for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]: if n == p: return True if n % p == 0: return False if n < 41**2: return True if n < 2047: return test_miller_rabin(n, [2]) if n < 90_80191: return test_miller_rabin(n, [31, 73]) if n < 47591_23141: return test_miller_rabin(n, [2, 7, 61]) if n < 112_20046_69633: return test_miller_rabin(n, [2, 13, 23, 16_62803]) if n < 3_77057_95821_54547: return test_miller_rabin(n, [2, 8_80937, 25_70940, 6103_86380, 41307_85767]) return test_miller_rabin(n, [2, 325, 9375, 28178, 450775, 9780504, 17952_65022]) from math import gcd def factorize(n: int): assert n >= 1 if n == 1: return [] if is_prime(n): return [n] ans = [] for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]: while n % p == 0: n //= p ans.append(p) def dfs(nn: int): if nn == 1: return if is_prime(nn): ans.append(nn) return factor_round = 1 << nn.bit_length() // 8 def find_factor(): x0 = 0 def f(x): return (x * x + 1) % nn while True: x0 += 1 x, y = x0, f(x0) d = 1 checkpoint = x, y while d == 1: combined = 1 for _ in range(factor_round): # Floyd's x, y = f(x), f(f(y)) combined = combined * abs(x - y) % nn d = gcd(combined, nn) if d == 1: # この round では見つからなかった checkpoint = x, y elif d != nn: # 非自明な約数 return d # else: d == nn: maybe found, break # 1つずつ進める x, y = checkpoint d = 1 while d == 1: x, y = f(x), f(f(y)) d = gcd(abs(x - y), nn) if d != 1 and d != nn: return d d = find_factor() dfs(d) dfs(nn // d) dfs(n) return ans def solve(): n = int(input()) factorize(n) if __name__ == "__main__": solve()