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 
import sys, itertools, math

T = int(sys.stdin.readline())

def solve(n):
  for a in range(2, int(math.sqrt(n))+1):
    if n % a != 0:
      continue
    for b in range(a+1, int(math.sqrt(n))+1):
      r = a * b
      c = n // r
      if n % r == 0 and c != a and c != b:
        print("YES")
        print(a, b, c)
        return
  print("NO")

for _ in range(T):
  n = int(sys.stdin.readline())

  solve(n)