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:
import io
import os

from collections import Counter, defaultdict, deque


def solve(N, ):

    ans = []
    while len(ans) < 2:
        for i in range(ans[-1] + 1 if ans else 2, int(N**0.5) + 1):
            if N % i == 0:
                ans.append(i)
                N //= i
                break
        else:
            return 'NO'
    if len(ans) != 2:
        return 'NO'
    if N <= ans[-1]:
        return 'NO'
    ans.append(N)

    return 'YES\n' + ' '.join(map(str, ans))

if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    T = int(input())
    for t in range(T):
        N, = [int(x) for x in input().split()]
        ans = solve(N, )
        print(ans)