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:
# -*- encoding: utf-8 -*-
import sys
import math
r_input = sys.stdin.readline

def get_divisor(num):
    divisors = []
    length = int(math.sqrt(num)) + 1

    for i in range(1, length):
        if num % i == 0:
            divisors.append(i)
            divisors.append(num // i)

    return divisors


if __name__ == '__main__':
    T = int(r_input())

    for _ in range(T):
        number = int(r_input())

        f_list = get_divisor(number)
        flag = 0

        for n in f_list:
            tp = number // n
            s_list = get_divisor(tp)

            for m in s_list:
                tmp = sorted([n, m, tp // m])
                if not 1 in tmp:
                    if tmp[0] != tmp[1] and tmp[1] != tmp[2]:
                        print('YES')
                        print(*tmp)
                        flag = 1
                        break

            if flag:
                break

        if not flag:
            print('NO')