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 sys
import math
import heapq
import bisect
import re
from collections import deque
from decimal import *
from fractions import gcd
 
 
def main():
    # [int(i) for i in sys.stdin.readline().split()]
    n = int(sys.stdin.readline())
    q = []
    for i in range(int(n ** 0.5) + 1, 0, -1):
        if n % i == 0:
            q.append(i)
            if n // i != i:
                q.append(n // i)
    q.sort()
    if len(q) <= 3:
        print("NO")
        return 0
    i = 1
    while i < len(q) - 3:
        i += 1
        f = n / q[1] / q[i]
        if f != q[1] and f != q[i] and f >= 2 and f == int(f) and int(f) * q[1] * q[i] == n:
            print("YES")
            print(q[1], q[i], int(f))
            return 0
    print("NO")
        
            
    
        
    
for i in range(int(input())):
    main()