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() {
  long long t, n;
  cin >> t;
  for (int p = 0; p < t; p++) {
    cin >> n;
    vector<int> ans;
    for (int i = 2; i <= sqrt(n); i++) {
      if (ans.size() == 2) break;
      if (n % i == 0) {
        ans.push_back(i);
        n /= i;
      }
    }
    auto it = find(ans.begin(), ans.end(), n);
    if (it == ans.end() && (n > 1)) ans.push_back(n);
    if (ans.size() < 3)
      cout << "NO\n";
    else {
      printf("YES\n%d %d %d\n", ans[0], ans[1], ans[2]);
    }
  }
}