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 long long mod = 1e9 + 7;
const long long MX = 2e5 + 5;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tc;
  cin >> tc;
  while (tc--) {
    int n;
    cin >> n;
    vector<int> v;
    for (int i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        v.push_back(i);
        n = n / i;
        break;
      }
    }
    for (int i = 2; i * i <= n; i++) {
      if (n % i == 0 && i != v[0] && i != n / i) {
        v.push_back(i);
        v.push_back(n / i);
        break;
      }
    }
    if (v.size() == 3)
      cout << "YES\n" << v[0] << ' ' << v[1] << ' ' << v[2] << endl;
    else
      cout << "NO\n";
  }
  cerr << "\ntime taken : " << (float)clock() / CLOCKS_PER_SEC << " secs\n";
  return 0;
}