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 ii in range(0,t):
  n = int(input())
  a = 0
  b = 0
  c = 0
  if n<24:
    print("NO")
    continue
  ifFind = 0
  for i in range(2,int(math.sqrt(n))+1):
    if ifFind == 1:
      break
    if n%i!=0:
      continue
    n2 = n // i
    for j in range(i+1,int(math.sqrt(n2))+1):
      if n2%j!=0:
        continue
      n3 = n2//j
      if j==n3:
          break
      ifFind = 1
      a=i
      b=j
      c=n3
      break
  if ifFind == 1:
    print("YES")
    print(a,b,c)
  else:
    print("NO")