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() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int n;
  cin >> n;
  for (long long int i = 0; i < n; i++) {
    long long int a, x;
    cin >> a;
    x = a;
    vector<int> v;
    for (long long int i = 2; i <= sqrt(a); i++) {
      if (a % i == 0) {
        if (a / i == i)
          v.push_back(i);
        else {
          v.push_back(i);
          v.push_back(a / i);
        }
        a = a / i;
      }
    }
    if (v.size() < 2)
      cout << "NO" << '\n';
    else {
      sort(v.begin(), v.end());
      if (x / (v[0] * v[1]) > 1 && x / (v[0] * v[1]) != v[0] &&
          x / (v[0] * v[1]) != v[1]) {
        cout << "YES"
             << "\n";
        cout << v[0] << ' ' << v[1] << ' ' << x / (v[0] * v[1]) << '\n';
      } else
        cout << "NO" << '\n';
    }
  }
}