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 sys
from math import sqrt


def readlines(type=int):
    return list(map(type, sys.stdin.readline().split()))


def read(type=int):
    return type(sys.stdin.readline().strip())


joint = lambda it, sep=" ": sep.join(
    [str(i) if type(i) != list else sep.join(map(str, i)) for i in it])


def solve(num):
    def break_(num, n, already=-1):
        for i in range(n, int(sqrt(num)) + 1):
            if num % i == 0 and i != num // i and i != already and num // i != already and num // i != 1:
                return i, num // i
        return -1, -1
    first, second = break_(num, 2)
    if first == -1:
        return "NO"
    third, fourth = break_(second, first + 1, first)
    if third == -1:
        return "NO"
    return("YES\n{} {} {}".format(first, third, fourth))

    return "NO"


def main():
    print(joint(list(map(solve, [read() for _ in range(read())])), '\n'))


main()