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:
def helper(n):
    upper = int(n**0.5) + 1
    for i in range(2, upper):
        if n % i == 0:
            curr = n //i
            for j in range(i + 1, upper):
                if curr % j == 0:
                    new_curr = curr //j
                    if i < j < new_curr: return [i, j, new_curr]
    return []
        
     

count = int(input())
for _ in range(count):
    ans = helper(int(input()))
    if len(ans) != 3:
        print('NO')
    else:
        print('YES')
        for val in ans:
            print(val, end = ' ')
        print()