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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 * Accomplished using the EduTools plugin by JetBrains
 * https://plugins.jetbrains.com/plugin/10081-edutools
 */
public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int t = Integer.parseInt(br.readLine());
    while (t-- > 0) {
      String[] temp = br.readLine().split(" ");
      int a = Integer.parseInt(temp[0]);
      int b = Integer.parseInt(temp[1]);
      int count = 0;
      while (a > 0 && b > 0 && a + b > 2) {
        if (a < b) {
          int temp1 = a;
          a = b;
          b = temp1;
        }

        if (a - b < b) {
          a = a - 2 * (b / 2);
          count = count + b / 2;
          b = b - b / 2;
        } else {
           a = a - 2 * b;
           count = count + b;
           b = 0;
        }
      }

      System.out.println(count);
    }
    br.close();
  }
}
