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 *

sInt = lambda: int(input())
mInt = lambda: map(int, input().split())
lInt = lambda: list(map(int, input().split()))

def isPrime(n,w):
    for i in range(w,int(sqrt(n))+1):
        if n%i==0:
            return False,i
    return True,0


t = sInt()


for _ in range(t):
    n = sInt()
    q,a = isPrime(n,2)
    if q==True:
        print("NO")
    else:
        n = n//a
        q,b = isPrime(n,a+1)
        if q==True or b==n//b:
            print("NO")
        else:
            print("YES")
            print(a,b,n//b)