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:
t = int(input())
for _ in range(t):
    n = int(input())
    arr = [1] * 3
    i = 0
    p = 2
    while n > 1:
        if n % p != 0:
            p += 1
            if p >= int(n**0.5) + 1:
                break
            continue
        arr[i] *= p
        n //= p
        if i > 0 and arr[1] == arr[0]:
            continue
        i += 1
        if i == 2:
            break
    if i < 2 or n == 1 or n == arr[0] or n == arr[1]:
        print('NO')
    else:
        print('YES')
        print(f'{arr[0]} {arr[1]} {n}')