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(void) {
  long long t;
  scanf("%lld", &t);
  long long num, sub_num, i, j;
  while (t--) {
    int cnt = 1;
    scanf("%lld", &num);
    for (i = 2; (i * i) <= num; ++i) {
      if (!cnt) {
        break;
      }
      if (!(num % i)) {
        sub_num = (num / i);
        for (j = (i + 1); (j * j) < sub_num; ++j) {
          if (!(sub_num % j)) {
            printf("YES\n%lld %lld %lld\n", i, j, (sub_num / j));
            --cnt;
            break;
          }
        }
      }
    }
    if (cnt) {
      printf("NO\n");
    }
  }
  return 0;
}