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 
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int q, n;
  cin >> q;
  while (q--) {
    cin >> n;
    set<int> A;
    for (int i = 2; i * i < n; i++) {
      if (n % i == 0) {
        A.insert(i);
        n /= i;
        break;
      }
    }
    for (int i = 2; i * i < n; i++) {
      if (n % i == 0) {
        if (A.count(i)) continue;
        A.insert(i);
        n /= i;
        break;
      }
    }
    if (A.count(n) || n == 1 || A.size() < 2) {
      cout << "NO\n";
    } else {
      cout << "YES\n";
      A.insert(n);
      for (int a : A) cout << a << " ";
      cout << "\n";
    }
  }
}
