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.util.Scanner;
import java.util.ArrayList;

public class ShovelsandSwords {

  public static void main(String[] args){
    Scanner scan = new Scanner (System.in);
    int test = scan.nextInt();
    int [] s = new int [test];
    int [] d = new int [test];
    for(int i = 0; i < test; i ++){
      s[i] = scan.nextInt();
      d[i] = scan.nextInt();
    }
    int count = 0;
    for(int i = 0; i < test; i ++){
      count = 0;
      if(s[i] == 0 || d[i] == 0){
        System.out.println(0);
      }
      else{
        if(s[i] >= 2 * d[i]){
          count = d[i];
        }
        else if(d[i] >= 2 * s[i]){
          count = s[i];
        }
        else{
          count = 2 * Math.min(s[i]/3, d[i]/3);
          s[i] = s[i] - 3 * count/2;
          d[i] = d[i] - 3 * count/2;
          int remainderMin = Math.min(s[i], d[i]);
          if(s[i] >= 2 * d[i]){
            count += d[i];
          }
          else if(d[i] >= 2 * s[i]){
            count += s[i];
          }
          else if(remainderMin > 0){
            count++;
          }
          
        }
        System.out.println(count);
      }
      
    }

  
  }

}