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.
      
 
/* package codechef; // don't place package name! */
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;






public class HelloWorld{

    public static void main(String[] args) throws IOException 
    { 
  
        Scanner input = new Scanner(System.in);
        input.nextInt();
        while(input.hasNext()){
            int a=input.nextInt();
            int b=input.nextInt();
            int t=0;
            t+=Math.min(Math.max(a, b)-Math.min(a, b), Math.min(a, b));
            boolean done=false;
            if(a>b){
                a-=2*t;
                b-=t;
                done=true;
            }
            if(!done && b>a){
                b-=2*t;
                a-=t;
            }
            if(a==0 || b==0){
                System.out.println(0+t);
                continue;
            }
            
            if(a==b){
                if(a<=1){
                    System.out.println(0+t);
                    continue;
                }
                if(a==2){
                    System.out.println(1+t);
                    continue;
                }
                if(a%3==2){
                    System.out.println(((2*a)/3)+1+t);
                    continue;
                }
                System.out.println(((2*a)/3)+t);
            }
            
        }
        }
 
    
 
}