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:
def main():    
    t = int(input())
    for z in range (t):
        n = int(input())
        arr = []
        i=2;
        while i*i <= n:
            while n%i==0:
                arr.append(i)
                n //= i
            i += 1
        if n>1:arr.append(n)
        a,b,c = 1,1,1
        for x in arr:
            if a==1: a *= x
            elif b==1 or a==b: b *= x
            else: c *= x
        arr = set([a,b,c])
        if a!=1 and b!=1 and c!=1 and len(arr)==3:
            print("YES")
            print(a,b,c) 
        else:
            print("NO")

if __name__ == "__main__":
    main()