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 math


def primeFactors(n):
    d = {}

    while n % 2 == 0:
        try:
            d[2]+=1
        except:
            d[2]=1

        n = n // 2

    for i in range(3, int(math.sqrt(n))+1, 2):

        while n % i == 0:
            try:
                d[i]+=1
            except:
                d[i]=1
            n = n // i

    if n > 2:
        try:
            d[n]+=1
        except:
            d[n]=1
    
    return d


t=int(input())
while t:
    t-=1
    n=int(input())

    d=primeFactors(n)
    # print(d)
    flag=0
    s=0
    toprint=[]


    if len(d)==1:
        for i in d:
            if d[i]>=6:
                flag=1
                toprint=[i,i**2,i**(d[i]-3)]


    elif len(d)>=3:
        flag=1
        cnt=0
        mul=1
        for i in d:
            if cnt==0:
                toprint.append(i**d[i])
            elif cnt==1:
                toprint.append(i**d[i])
            else:
                mul*=(i**d[i])
            cnt+=1
        toprint.append(mul)



    elif len(d)==2:
        keys=list(d.keys())
        if d[keys[0]]+d[keys[1]]>3:
            flag=1
            toprint=[keys[0],keys[1],(keys[0]**(d[keys[0]]-1))*(keys[1]**(d[keys[1]]-1))]

    if len(set(toprint))<3:
        flag=0
    if flag:
        print('YES')
        for i in toprint:
            print(i,end=' ')
        print()
    else:
        print('NO')