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 Fri Apr  3 10:55:17 2020

@author: Krishna
"""
import math
t=int(input())
for _ in range(t):
    n=int(input())
    m=n
    d={}
    while n%2==0:
        if 2 not in d:
            d[2]=1
        else:
            d[2] += 1
        n=n/2
    for i in range(3,int(math.sqrt(n))+1,2):
        while n %i == 0:
            if i not in d:
                d[i]=1
            else:
                d[i]+=1
            n=n/i
    if n>2:
        d[int(n)]=1
    l=len(d)
    f=0
    if l==1:
        for key in d.keys():
            if d[key]>=6:
                f=1
                a=key
                b=key**2
                c=int(m/(a*b))
    elif l==2:
        i=0
        k=0
        for key in d.keys():
            k=k+d[key]
            if i==0:
                a=key
            else:
                b=key
            i=i+1
        if k>=4:
            f=1
            c=int(m/(a*b))
    else:
        f=1
        i=0
        for key in d.keys():
            if i==0:
                a=key
            elif i==1:
                b=key
            else:
                break;
            i=i+1
        c=int(m/(a*b))
    
    if f==0:
        print('NO')
    else:
        print('YES')
        print(a,b,c)