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 CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  int x, i, j, k, n, c, m[3];
  scanf("%d", &x);
  while (x--) {
    j = 0;
    c = 0;
    scanf("%d", &n);
    for (i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        k = n / i;
        if (k > i) {
          for (j = 2; j * j <= k; j++) {
            if (k % j == 0 && j != i && j * j != k && k / j != i) {
              m[0] = i;
              m[1] = j;
              m[2] = k / j;
              c++;
              break;
            }
          }
          if (c > 0) break;
        }
      }
    }
    if (c == 0)
      printf("NO\n");
    else {
      printf("YES\n");
      for (i = 0; i < 3; i++) printf("%d ", m[i]);
      printf("\n");
    }
  }
}