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:
for _ in range(int(input())):
    num = int(input())
    done = False
    for i in range(2, int(num ** (1/3)) + 8):
        if num % i != 0:
            continue
        new_num = num // i
        for j in range(i + 1, int(num ** .5) + 8):
            if new_num % j == 0 and new_num // j not in [i, j, 1]:
                print('YES')
                print(f'{i} {j} {new_num // j}')
                done = True
                break
        if done:
            break
    if not done:
        print('NO')