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 math

t = int(input())
for _ in range(t):
    n = int(input())
    factors = []
    for factor in range (2, int(math.sqrt(n))):
        if n <= factor:
            break
        if n % factor == 0:
            if n // factor <= factor:
                break
            factors.append(factor)
            n = n // factor
            if len(factors) == 2:
                break
    if len(factors) == 2:
        factors.append(n)
        print('YES')
        print(' '.join(map(str, factors)))
    else:
        print('NO')