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 Wed Jan 22 08:37:17 2020

@author: huynguyen
"""

def findTripple(n):
    res = []
    for i in range(2,int(n**.5)+1):
        if n%i == 0:
            res.append(i)
            n//=i 
        if len(res) ==2:
            break
    if n!=1:
        if res:
            if n not in res:
                res.append(n)
    return res
t = int(input())
for test in range(t):
    n = int(input())
    res = findTripple(n)
    if len(res)==3:
        print("YES")
        print (" ".join([str(item) for item in res]))
    else:
        print ("NO")