Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in PYTHON3):

Solution:
# -*- coding: utf-8 -*-
from math import sqrt


def main():
    for _ in range(int(input())):
        n = int(input())
        d = n
        ret = []
        for i in range(2, int(sqrt(n))):
            if d % i == 0:
                d /= i
                ret.append(i)
            if len(ret) == 2:
                break
        if len(ret) < 2:
            print('NO')
            continue
        a, b = ret
        c = n // (a * b)
        if a == c or b == c or (a * b * c) != n:
            print('NO')
            continue
        print('YES')
        print(a, b, c)


if __name__ == '__main__':
    main()