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 main():
    n = int(input())
    different = [0, 0, 0]
    k = 0
    for i in range(2, int(math.sqrt(n)) + 1):
        if k == 2:
            break
        if n % i == 0 and k < 2:
            n = n // i
            different[k] = i
            k += 1
    if n == 1 or n == different[0] or n == different[1] or different[1] == 0:
        print("NO")
        return
    different[2] = n
    print("YES")
    print(different[0], different[1], different[2])

if __name__ == "__main__":
    t = int(input())
    for i in range(t):
        main()