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 collections

def findDistinctTree(n):
    queue = collections.deque()
    queue.append(2)
    i = 2
    while True:
        if queue:
            i = queue.popleft()
        else:
            i += 1
        if i >= n // i:
            print('NO')
            return
        if n % i != 0:
            continue
        m = n // i
        for j in range(i + 1, m):
            if n % j == 0:
                queue.append(j)
            if j >= m / j:
                break
            if m % j != 0:
                continue
            print('YES')
            print('{} {} {}'.format(i, j, m//j))
            return
            
    print('NO')
    return

if __name__ == '__main__':
    N = int(input())
    cases = []
    for _ in range(N):
        n = int(input())
        cases.append(n)
    for case in cases:
        findDistinctTree(case)