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 Sat Jan 25 10:20:51 2020

@author: Anthony
"""

def abc(num):
    threshold=num**0.5
    myDivisors=[]
    potentialDiv=2
    current=num
    while(potentialDiv<=threshold and current!=1):
        if current//potentialDiv ==  current/potentialDiv:
            myDivisors.append(potentialDiv)
            current/=potentialDiv
        potentialDiv+=1
        if len(myDivisors)>=2 and (current not in myDivisors):
            myDivisors.append(int(current))
            return myDivisors
    if len(myDivisors)>=3 and current==1:
        return myDivisors
    else:
        return False
    

repeat=int(input())
for i in range(0,repeat):
    temp=abc(int(input()))
    if temp:
        for i in range(0,len(temp)):
            for j in range(i+1,len(temp)):
                if (temp[i]*temp[j] not in temp) and len(temp)>3:
                    temp[i]*=temp[j]
                    temp[j]=1
        safiye=[]
        for x in temp:
            if x!=1:
                safiye.append(x)
        if len(safiye)==3:
            print("YES")
            for x in safiye:
                print(x,end=" ")
        else:
            print("NO")
    else:
        print("NO")