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
from collections import Counter,defaultdict
I =lambda:int(input())
M =lambda:map(int,input().split())
LI=lambda:list(map(int,input().split()))
for _ in range(I()):
    n=I();i=2;a,b,c=-1,-1,-1
    while i*i<=n:
        while n%i==0:
            n//=i
            if a==-1:
                a=i
            elif b==-1 or a==b:
                if b==-1:b=i
                else:b*=i
            else:
                if c==-1:c=i
                else:c*=i
        i+=1
    if n>1:
        if c==-1:c=n
        else:c*=n
    if min(a,b,c)==-1 or b==c or a==b or a==c:
        print("NO")
    else:
        print("YES")
        print(a,b,c)