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:
from math import sqrt

def check(n):
    k=0
    for i in range(2,int(sqrt(n+1))):
        if k==2 and n>=i:
            return a,b,n
        if k==3:
            return a,b,c
        if k<3 and n<i:
            return 'NO'   
               
        if n%i==0:
            k+=1
            n //= i
            
            if k==1:
                a=i
            elif k==2:
                b=i
            elif k==3:
                c=i 
    return 'NO'                   

t = int(input())
for i in range (t):
    n = int(input())
    out = check(n)
    
    if type(out)==str:
        print(out)
    else:
        print('YES')
        for x in list(out):
            print(x,end=" ")
        print()