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;
long long t, n, z, x, c, s;
int main() {
  cin >> t;
  while (t--) {
    cin >> n;
    long long f = 0;
    for (int i = 2; i * i <= n; i++) {
      for (int j = i + 1; j * j <= (n / i); j++) {
        z = i * j;
        x = n / z;
        s = i * j * x;
        if (s == n) {
          if (i != j && i != x && j != x) {
            f = 1;
            cout << "YES"
                 << "\n";
            cout << i << " " << j << " " << x << "\n";
            break;
          } else
            continue;
        }
      }
      if (f == 1) break;
    }
    if (f == 0)
      cout << "NO"
           << "\n";
  }
}