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 -*-
"""
Created on Wed Feb 12 15:07:02 2020

@author: Milán
"""

import math

t = int(input())
L = []
for i in range(t):
    L += [int(input())]
    
    
def multiples(n):
    i = 2
    while i <= math.floor(n ** (1./3.)):
        if n%i == 0:
            j = i + 1
            k = n/i
            while j <= math.sqrt(k):
                if k%j == 0 and j != math.sqrt(k):
                    return "\n" + "YES" + "\n" + str(i) + " " + str(j) + " " + str(int(k/j))
                j += 1
        i += 1
    return "\n" + "NO"
        
for l in L:
    print(multiples(l))