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:
for _ in range(int(input())):
     n=int(input())
     s=set()
     for i in range(2,int(pow(n,0.5))+1):
          if(n%i==0):
               s.add(i)
               s.add(n//i)
     l1=list(s)
     n1=len(l1)
     if(n1<3):
          print("NO")
     else:
          flag=0
          for i in range(n1-2):
               if(flag==1):
                    break
               for j in range(i+1,n1-1):
                    if(flag==1):
                         break
                    for k in range(j+1,n1):
                         v=l1[i]*l1[j]*l1[k]
                         if(n==v):
                              flag=1
                              print("YES")
                              print(l1[i],l1[j],l1[k])
                              break
          if(flag==0):
               print("NO")