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:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Jan 21 18:49:02 2020

@author: dennis
"""

import atexit
import io
import sys
import math

_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())

def find(n, x):
    for c in range(x, int(math.sqrt(n))+1):
        if n%c == 0:
            return c
    return 0

for _ in range(int(input())):
    n = int(input())
    a = find(n, 2)
    if a:
        b = find(n//a, a+1)
        if b:
            c = n//(a*b)
    if (a and b and c) and (a != b != c != a) and (a*b*c == n):
        print('YES')
        print(a, b, c)
    else:
        print('NO')