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

if __name__ == "__main__":
    t = int(input())
    for _ in range(t):
        n, a, b = int(input()), 0, 0
        i = 1
        for i in range(2, int(math.sqrt(n)) + 1):
            if n % i == 0 and i != n // i:
                n, a = n // i, i
                break
        for j in range(i, int(math.sqrt(n)) + 1):
            if n % j == 0:
                if a != j and a != n // j and j != n // j:
                    n, b = n // j, j
                    break
        if a != 0 and b != 0:
            print("YES")
            print(a, b, n)
        else:
            print("NO")