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
t= int(input())
while t:
   n= int(input())
   r=n
   a=[]
   for i in range(2,int(sqrt(n))):

       if n%i==0:
           a.append(i)
           n=int(n/i)
       if len(a)==2:
           break

   if len(a)==2 and a[0]!=a[1] and a[1]!=n and a[0]!=n and n>=2:
       print("YES",a[0],a[1],n)
   else:
       print("NO")


   t=t-1