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>
using namespace std;
int main() {
  int t, k = 0;
  cin >> t;
  while (t > 0) {
    k = 0;
    long long n, a, b, c;
    cin >> n;
    for (long long i = 2; i <= sqrt(n); i++) {
      if (n % i == 0) {
        k = 0;
        for (long long j = 2; j <= sqrt(n / i); j++) {
          if (i != j && (n / (i * j)) != i && (n / (i * j)) != j &&
              (n % (i * j)) == 0) {
            cout << "YES\n";
            cout << i << " " << j << " " << n / (i * j) << endl;
            k++;
            break;
          }
        }
        if (k == 1) break;
      }
    }
    if (k == 0) cout << "NO\n";
    t--;
  }
  return 0;
}