#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int a, b, c;
    cin >> a >> b >> c;
    int res = 0;
    if (a + b > b + c) {
      while (a >= 1 && b >= 2) {
        a--;
        b = b - 2;
        res += 3;
      }
      while (b >= 1 && c >= 2) {
        b--;
        c -= 2;
        res = res + 3;
      }
    } else {
      while (b >= 1 && c >= 2) {
        b--;
        c = c - 2;
        res += 3;
      }
      while (a >= 1 && b >= 2) {
        a--;
        b -= 2;
        res = res + 3;
      }
    }
    cout << res << endl;
  }
}
