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
def run():
    num = int(input())
    if num < 24:
        print("NO")
        return
    else:
        used = set()
        i = 2
        while i * i <= num:
            if num % i == 0 and i not in used:
                used.add(i)
                num //= i
                break
            i += 1
        while i * i <= num:
            if num % i == 0 and i not in used:
                used.add(i)
                num //= i
                break
            i += 1
        if len(used) < 2 or num in used or num == 1:
            print("NO")
        else:
            print("YES")
            print(used.pop(), used.pop(), num)

n = int(input())
for i in range(n):
    run()