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 *

for _ in range(int(input())):
    
    n = int(input())
    
    ch1 = 1
    ch2 = 1
    a1 = 0
    a2 = 0
    a3 = 0
    g = 0
    for i in range(2,int(sqrt(n)+1)):
        if(n%i == 0):
            a1 = i
            g = n//i
            break
    else:
        ch1 = 0
    
    if(ch1 == 1):
        for i in range(2,int(sqrt(g)+1)):
            if(g%i == 0 and i!=a1):
                a2 = i
                a3 = g//i
                if(a3 == a1 or a3 == a2):
                    continue
                break
        else:
            ch2 = 0
            
    if(ch1 ==0 or ch2 == 0):
        print("NO")
    else:
        print("YES")
        print(a1,a2,a3)