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 os
import math


def f(n):
    result = []
    now = 2
    while len(result) < 2 and now < math.sqrt(n):
        if n % now == 0:
            result.append(now)
            n //= now
        now += 1

    if len(result) == 2 and n not in result:
        return f"YES\n{result[0]} {result[1]} {n}"
    else:
        return "NO"


if os.environ.get('DEBUG', False):
    print(f"{f(64)} = 2 4 8 ")
    print(f"{f(32)} = NO")
    print(f"{f(97)} = NO")
    print(f"{f(2)} = NO")
    print(f"{f(12345)} = 3 5 823")
else:
    for _ in range(int(input())):
        print(f(int(input())))
