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 sys
input = lambda:sys.stdin.readline()

int_arr = lambda: list(map(int,input().split()))
str_arr = lambda: list(map(str,input().split()))
get_str = lambda: map(str,input().split())
get_int = lambda: map(int,input().split())
get_flo = lambda: map(float,input().split())

mod = 1000000007

def solve(n):
  ans = []
  i = 2
  while len(ans) < 2 and i*i < n:
    if n % i == 0:
      ans.append(i)
      n //= i
    i += 1

  if len(ans) == 2:
    print("YES")
    print(ans[0],ans[1],n)
  else:
    print("NO")



for _ in range(int(input())):
  n = int(input())
  solve(n)