"""练习 15 进阶版：用 all() 和 math.isqrt() 判断质数。"""
from math import isqrt

n = int(input())
if n < 1:
    raise ValueError("请输入正整数")

is_prime = n > 1 and all(n % divisor != 0 for divisor in range(2, isqrt(n) + 1))
print("prime:", "yes" if is_prime else "no")

remaining = n
prime_factors = []
divisor = 2
while divisor * divisor <= remaining:
    if remaining % divisor == 0:
        prime_factors.append(divisor)
        while remaining % divisor == 0:
            remaining //= divisor
    divisor += 1
if remaining > 1:
    prime_factors.append(remaining)

print("distinct prime factors:", *prime_factors if prime_factors else ["none"])