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 maxn = 1e5 + 100;
int main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    vector<long long> v;
    for (long long i = 2; i * i <= n; i++) {
      if (v.size() == 2) {
        break;
      } else if (n % i == 0) {
        n = n / i;
        v.push_back(i);
      }
    }
    if (v.size() == 2 && n > 1 && v[0] != n && v[1] != n) v.push_back(n);
    if (v.size() == 3)
      cout << "YES" << endl << v[0] << " " << v[1] << " " << v[2] << endl;
    else
      cout << "NO" << endl;
  }
}