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 PYTHON):

Solution:
import sys
import math
Z = sys.stdin.readline
def main():
    for t in range(int(Z().strip())):
        n = int(Z().strip())
        c=00
        if n>=24:
            r=[0]
            for i in range(2,roundsqrt(n)):
                if n%i==0:
                    q=n//i
                    r[0]=i 
                    break
            if r[0]!=0:    
                for i in range(r[0]+1,roundsqrt(q)):
                    if q%i==0:
                        r.append(i)
                        c=1
                        break
                if c==1:
                    r.append(n/((r[0])*(r[1])))
                    print("YES")
                    print(" ".join(str(x) for x in r))
                else:
                    print("NO")
            else:
                print("NO")
        else:
            print("NO")
            
def roundsqrt(x):
    return int(math.ceil(math.sqrt(x)))    
    
if __name__=="__main__":
    main()