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
import os


def get_array():
    return list(map(int, input().split(' ')))


def get_divisions(a):
    i = 2
    while i <= math.sqrt(a):
        if a % i == 0:
            yield i
        i += 1
    yield -1


if __name__ == '__main__':
    t = int(input())
    for i in range(t):
        n = int(input())
        divs = get_divisions(n)
        while True:
            a = next(divs)
            f = False
            if a != -1:
                divs_a = get_divisions(n / a)
                while True:
                    b = next(divs_a)
                    if b != -1:
                        c = int(n / a / b)
                        if b != a and c != b:
                            print('YES')
                            print(a, ' ', b, ' ', c)
                            f = True
                            break
                    else:
                        f = False
                        break
                if not f:
                    print('NO')
                break
            else:
                print('NO')
                break