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() {
  long long int n, t, m, i, a, b, c, k;
  scanf("%lld", &t);
  for (m = 1; m <= t; m++) {
    k = 0;
    scanf("%lld", &n);
    for (i = 2; i <= sqrt(n); i++) {
      if (n % i == 0) {
        a = i;
        n = n / i;
        k++;
        break;
      }
    }
    if (k > 0) {
      for (i = a + 1; i <= sqrt(n); i++) {
        if (n % i == 0) {
          break;
        }
      }
      if (i != n / i && n / i != a && i * (n / i) == n && n / i != 1) {
        b = i;
        c = n / i;
        printf("YES\n");
        printf("%lld %lld %lld\n", a, b, c);
      } else {
        printf("NO\n");
      }
    }
    if (k == 0) {
      printf("NO\n");
    }
  }
  return 0;
}