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 math import sqrt

N = int(input())

for i in range(N):
    n = int(input())
    res = []
    is_good = False

    for i in range(2, n//6 + 1):
        if i > sqrt(n):
            break

        if n % i == 0:
            res.append(i)
            n /= i
            if len(res) == 2:
                if n > i:
                    is_good = True
                break

    if is_good:
        print(f'YES\n{res[0]} {res[1]} {int(n)}')
    else:
        print('NO')