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 sys import stdin,stdout
def main():    
    t = int(input())    
    for z in range(t):
        n = int( input() )
        i = 2
        sw = 1
        while i*i<n and sw:
            if n%i==0:
                j = 2
                tmp = n // i
                while j*j < tmp and sw:
                    if tmp%j==0 and j!=i and (tmp//j)!=i:
                        print("YES")
                        print(i,j,tmp//j)
                        sw = 0 
                    j += 1
            i += 1
        if sw:
            print("NO")

if __name__ == "__main__":
    main()