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:
def R(): return map(int, input().split())
def I(): return int(input())
def S(): return str(input())

def L(): return list(R())

from collections import Counter 

import math
import sys

for _ in range(I()):
    n=I()
    div=[]
    n2=n

    for i in range(2,int(math.sqrt(n))+1):
        if n%i ==0:
            div.append(i)
            n/=i

    if n>1:
        div.append(n)

    if len(div)<3 or n2//(div[0]*div[1])== div[0] or n2//(div[0]*div[1])==div[1]:
        print('NO')
    else:
        print('YES')
        print(div[0],div[1],n2//(div[0]*div[1]))