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 functools import reduce


def factors(n):
    return sorted(list(set(reduce(list.__add__,
                                  ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))))


for _ in range(int(input())):
    N = int(input())
    r = factors(N)
    len_r = len(r)
    tmp = 0
    if len_r - 2 < 3:
        print("NO")
        continue
    for i in range(1, len_r - 1):
        curr_sum = N // r[i]
        for j in range(i + 1, len_r - 1):
            if (curr_sum // r[j]) in r:
                s = {r[i], r[j], curr_sum // r[j]}
                if len(s) == 3 and 1 not in s:
                    print("YES")
                    print(r[i], r[j], curr_sum // r[j])
                    tmp = 1
                    break
        if tmp:
            break
    if not tmp:
        print("NO")