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:
def find(num):
  a=0
  b=0
  i=2
  while (i*i)<=num:
    
    if num%i==0:
      if a==0:a=i
      elif b==0:b=i
      num=num//i
   
    if a>0 and b>0:
      return [a,b]
    i+=1
  return None
for i in range(int(input())):
    n=int(input())
    A=find(n)
    if not A or n<=2:print("NO")
    else:
     a=A[0]
     b=A[1]
     c=a*b
     if n%a==0 and n//a!=a and n//a!=b and (a*b*(n//a))==n:
        print("YES")
        print(a,b,n//a)
     if n%b==0 and n//b!=a and n//b!=b and (a*b*(n//b))==n:
       print("YES")
       print(a,b,n//b)
     elif n%c==0 and n//c!=a and n//c!=b and (a*b*(n//c))==n:
       print("YES")
       print(a,b,n//c)
     else:print("NO")