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 
import sys
from math import sqrt


def solution(n):
    for i in range(2, int(sqrt(n))+1):
        if n % i == 0:
            a = i
            n_a = n // i
            for j in range(2, int(sqrt(n_a))+1):
                if n_a % j == 0 and j != a:
                    ra, rb, rc = a, j, n // (a * j)
                    if ra != rb and rb != rc and rc != ra:
                        return f"YES\n{ra} {rb} {rc}"

    return "NO"


for line in sys.stdin:
    t = int(line)
    break


for line in sys.stdin:
    n = int(line)
    print(solution(n))
    
