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 string
import math
import collections 


def LeReseauLMD(n):
    orin = n
    a,b,c = 0,0,0
    for a in range(2,math.floor(n**0.5)+1):
        if n%a==0:
            n //=a
            for b in range(2,math.floor((n)**0.5)+1):
                if n%b == 0 and b != a:
                    """for c in range(2,math.floor(n**0.5)+1):
                        if n%c == 0 and c != b and c != a:
                            break"""
                    c = n//b
                    if c == a or c == b:
                        c = 0
                    break
            break
    if a*b*c == orin:
        return f"{a} {b} {c}"
    else:
        return "NO"

def main():
    q = int(input())
    for _ in range(q):
        n = int(input())
        rep = LeReseauLMD(n)
        if rep != "NO":
            print("YES")
        print(rep)
    
    
             
main()