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 sys
input = sys.stdin.readline
from collections import *

def factorize(n):
    fct = []
    
    for i in range(2, int(n**0.5)+1):
        c = 0
        
        while n%i==0:
            n //= i
            c += 1
            
        if c>0:
            fct.append((i, c))
    
    if n>1:
        fct.append((n, 1))
    
    return fct

t = int(input())

for _ in range(t):
    n = int(input())
    factors = factorize(n)
    
    if len(factors)==1:
        p, c = factors[0]
        
        if c>=6:
            print('YES')
            print(p, p**2, p**(c-3))
        else:
            print('NO')
    elif len(factors)==2:
        p1, c1 = factors[0]
        p2, c2 = factors[1]
        
        if c1+c2>=4:
            print('YES')
            print(p1, p2, n//p1//p2)
        else:
            print('NO')
    else:
        p1, _ = factors[0]
        p2, _ = factors[1]
        print('YES')
        print(p1, p2, n//p1//p2)