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


class Read:
    @staticmethod
    def string():
        return input()

    @staticmethod
    def int():
        return int(input())

    @staticmethod
    def list(sep=' '):
        return input().split(sep)

    @staticmethod
    def list_int(sep=' '):
        return list(map(int, input().split(sep)))


def solve():
    n = Read.int()
    for i in range(2, math.ceil(math.sqrt(n))):
        if n % i == 0:
            t = n / i
            for j in range(2, math.ceil(math.sqrt(t))):
                if t % j == 0:
                    res = math.ceil(t / j)
                    if res == i or i == j or j == res:
                        continue
                    print('YES')
                    print('{} {} {}'.format(i, j, res))
                    return
    print('NO')


# query_count = 1
query_count = Read.int()
while query_count:
    query_count -= 1
    solve()