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:
from math import sqrt

def main():
    def solve():

        n = int(input())
        a = 0
        if n%2 == 0:
            a = 2
        else:
            for i in range(3, int(n ** (1./3))+1, 2):
                if n%i == 0:
                    a = i
                    break
        if a == 0:
            print("NO")
            return
        b = 0
        for i in range(a+1, int(sqrt(n//a))+1):
            if (n//a)%i == 0:
                b = i
                break
        if b == 0:
            print("NO")
            return
        c = n//(a*b)
        if b == c:
            print("NO")
            return
        print("YES")
        print(a, b, c)



    q = int(input())
    for _ in range(q):
        solve()


if __name__ == "__main__":
    main()