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 t, n, m, s, s1, i, j, p;
  scanf("%d", &t);
  while (t--) {
    scanf("%d", &n);
    s = pow(n, 1.0 / 3);
    p = 0;
    for (i = 2; i <= s + 1; i++) {
      if (n % i != 0) continue;
      m = n / i;
      s1 = sqrt(m);
      for (j = i + 1; j <= s1; j++)
        if (m % j == 0 && j != m / j) {
          printf("YES\n");
          printf("%d %d %d\n", i, j, m / j);
          p = 1;
          break;
        }
      if (p == 1) break;
    }
    if (p == 0) printf("NO\n");
  }
  return 0;
}