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:
import math
t=int(input())
for i in range(t):
   n=int(input())
   f=0
   l=[]
   l1=[]
   for j in range(2,int(math.sqrt(n))+1):
      if n%j==0:
         l.append(j) 
         l.append(n//j)
   l1=list(set(l))
   l1.sort()
   if len(l1)==0:
      print("NO")
   else:
      a=l1[0] 
      n=n//a 
      for j in range(len(l1)):
         if n%l1[j]==0 and l1[j]!=a:
            b=l1[j]
            n=n//b 
            f=1
            break 
      if f==0:
         print("NO") 
      else:
         if n in l1 and n!=a and n!=b:
            print("YES")
            print(a,b,n) 
         else:
            print("NO")