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:
'''input
5
64
32
97
2
12345
'''
from collections import defaultdict as dd
from collections import Counter as ccd
from itertools import  permutations as pp
from itertools import combinations as cc
from random import randint as rd
from bisect import bisect_left as bl
from bisect import bisect_right as br
import heapq as hq
from math import gcd
'''
Author : dhanyaabhirami
Hardwork beats talent if talent doesn't work hard
'''
'''
Stuck?
See github resources
Derive Formula
Kmcode blog
CP Algorithms Emaxx
'''
mod=pow(10,9) +7
def inp(flag=0):
    if flag==0:
        return list(map(int,input().strip().split(' ')))
    else:
        return int(input())

# Code credits
# assert(debug()==true)
# for _ in range(int(input())):

t=inp(1)
while t:
    t-=1
    n=inp(1)
    a=b=c=0
    i=2
    while i*i<n:
        if n%i==0:
            a=i
            n//=a
            break
        i+=1
    if n!=1 and a!=0:
        i=a+1
        while i*i<n:
            if n%i==0:
                b=i
                n//=b
                break
            i+=1
        if n!=1 and b!=0:
            c=n
            print("YES")
            print(a,b,c)
        else:
            print("NO")
    else:
        print("NO")