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:
t=int(input())
li=[]
def p2(m,a):
 for i in range(2,int(m**(0.5))+1):
  if (int(m/i)==m/i)and(i!=m/i!=a)and(i!=a):
   return [int(i),int(m/i)]
 return "no"
for i in range(t):
 li=li+[int(input())]
for k in li:
 if p2(k,1)!="no":
  l=p2(k,1)
  if p2(l[0],l[1])!="no":
   print("YES")
   print(l[1],p2(l[0],l[1])[0],(p2(l[0],l[1])[1]))
  
  elif p2(l[1],l[0])!="no":
   print("YES")
   print(l[0],p2(l[1],l[0])[0],(p2(l[1],l[0])[1]))
  else: 
   print("NO")
 else:
 	print("NO")