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;
const int mod = 1e9 + 7;
const long long inf = 5e18;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int t;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    vector<long long> a;
    for (long long i = 2; i <= min(100000ll, n); i++) {
      if (n % i == 0) {
        a.push_back(i);
        n /= i;
        if (a.size() == 2) {
          break;
        }
      }
    }
    if (a.size() < 2) {
      cout << "NO\n";
    } else {
      vector<long long> ans;
      ans = a;
      ans.push_back(n);
      sort(ans.begin(), ans.end());
      if (ans[1] == ans[2] or ans[0] == ans[1] or ans[0] < 2) {
        cout << "NO\n";
      } else {
        cout << "YES\n";
        for (long long i : ans) {
          cout << i << ' ';
        }
        cout << '\n';
      }
    }
  }
}