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 os import path
if(path.exists('input.txt')):
    sys.stdin = open('input.txt', 'r')
    sys.stdout = open('output.txt', 'w')

get_int = lambda: int(input())
get_ints = lambda: map(int, input().split())
get_ints_list = lambda: list(get_ints())

from math import sqrt

def factorize(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i == 0:
            p = 0
            while n % i == 0:
                n //= i
                p += 1
                factors.append(i)
        i += 1

    if n != 1:
        factors.append(n)
    return factors
t = get_int()



for _ in range(t):
    n = get_int()
    factors = factorize(n)
    l = len(factors)
    if l < 3:
        print("NO")
        continue
    a, b, c = 1, 1, 1
    a = factors[0]

    i = 1
    while i < l:
        b *= factors[i]
        i += 1
        if b != a: break

    while i < l:
        c *= factors[i]
        i += 1


    if a != b and a != c and b != c and a != 1 and b != 1 and c != 1 and a*b*c == n:
        print("YES")
        print(a, b, c)
    else: print("NO")