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:
# Python program to print prime factors 
  
import math 
   
def solution(n):
        a = 0
        b = 0 
        for i in range(2, int(math.sqrt(n))+1):
            if n % i == 0:
                a = i
                n //= i
                break
        if a:
            for j in range(a + 1, int(math.sqrt(n))+1):
                if n % j == 0:
                    b = j
                    n //= j
                    break
        if a and b and b != n:
            print('YES')
            print(f'{a} {b} {n}')
        else:
            print('NO')
t = int(input())
kls = [int(input()) for _ in range(t)]
for k in kls:
   solution(k)