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;
public class Main{
  public static void main(String []args){
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    
    
    for(int p=1; p<=n; p++){
    int count=0;  
      int stick=sc.nextInt();
      int diamond=sc.nextInt();
      int mul1=2*diamond;
      int mul2=2*stick;
        
       if(stick==0 || diamond==0){
        System.out.println(0);
        
      }
      else if(2*stick<=diamond){
        System.out.println(stick);
      }
      else if(2*diamond<=stick){
        System.out.println(diamond);
      }
      else if((diamond>stick) || (stick>diamond) || (stick==diamond))
        
      {
        for(;;){  //while(;;) o disilam
          if(diamond==0 || stick==0 || (stick==1 && diamond==1)){ 
            System.out.println(count);
            break;
          }
          
          if(diamond==stick){
           int value=(stick+diamond)/3;
           System.out.println(value);
           break;
          }
          else if(diamond>=stick) {
            diamond=diamond-2;
            stick=stick-1;
            count++;
          }
          else if(diamond<=stick){
            stick=stick-2;
            diamond=diamond-1;
            count++;
        }
      }
    }
  }
  }

}