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:
from bisect import *
from collections import *


def factorize(n):  # o(sqr(n))
    c, ans = 2, []
    while (c * c < n):
        if n % c == 0:
            ans.append(c)
            ans.append(n // c)
        c += 1

    if c * c == n:
        ans.append(c)
    return sorted(ans)


for i in range(int(input())):
    n = int(input())
    a = factorize(n)
    c, l, ans = defaultdict(int, Counter(a)), len(a), 'NO'
    for i in range(l):
        for j in range(i+1, l):
            num = n / (a[i] * a[j])
            if c[num] and num not in [a[i], a[j]]:
                print('YES')
                print(*[a[i], a[j], int(num)])
                ans = 'YES'
                break
        if ans == 'YES':
            break

    if ans == 'NO':
        print('NO')