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:
# cook your dish here
import math
for t in range(int(input())):
    n=int(input())
    flag=False
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            x=i
            yy=n//i
            for j in range(i+1,int(math.sqrt(yy))+1):
                if yy%j==0:
                    y=j
                    z=yy//j
                    if z>=2 and z!=y and z!=x:
                        flag=True
                        l=[x,y,z]
                        print("YES")
                        print(*l)
                        break
            if flag:
                break
    if flag==False:
        print("NO")