Polycarp plays a well-known computer game (we won't mention its name). In this game, he can craft tools of two types — shovels and swords. To craft a shovel, Polycarp spends two sticks and one diamond; to craft a sword, Polycarp spends two diamonds and one stick.

Each tool can be sold for exactly one emerald. How many emeralds can Polycarp earn, if he has a sticks and b diamonds?

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains two integers a and b (0 ≤ a, b ≤ 10^9) — the number of sticks and the number of diamonds, respectively.

Output

For each test case print one integer — the maximum number of emeralds Polycarp can earn.

Example

Input


4
4 4
1000000000 0
7 15
8 7


Output


2
0
7
5

Note

In the first test case Polycarp can earn two emeralds as follows: craft one sword and one shovel.

In the second test case Polycarp does not have any diamonds, so he cannot craft anything.
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n;
  cin >> n;
  while (n--) {
    long long a, b;
    cin >> a >> b;
    long long minima = min(a, b);
    long long maxima = max(a, b);
    long long ans = 0;
    if (maxima >= 2 * minima)
      cout << minima << endl;
    else {
      long long temp = minima / 3;
      ans = 2 * temp;
      long long temp2 = maxima - temp * 3;
      temp = minima % 3;
      if (temp == 0) {
        cout << ans << endl;
      } else if (temp == 1) {
        if (temp2 >= 2) {
          cout << ans + 1 << endl;
        } else
          cout << ans << endl;
      } else {
        if (temp2 == 0)
          cout << ans << endl;
        else if (temp2 == 1 || temp2 == 2 || temp2 == 3)
          cout << ans + 1 << endl;
        else {
          cout << ans + 2 << endl;
        }
      }
    }
  }
}
