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

def solve(n):
    for a in range(2, math.ceil(n ** (1 / 3))):
        if n % a == 0:
            for b in range(a + 1, math.ceil(math.sqrt(n // a))):
                c = n // a // b
                if c * a * b == n:
                    print('YES')
                    print('%d %d %d' % (a, b, c))
                    return False
    return True


t = int(input())
for i in range(t):
    n = int(input())
    if solve(n):
        print("NO")