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 k = sc.nextInt();
        while (k-- > 0)
        {
            int a = sc.nextInt();
            int b  = sc.nextInt();
            int max=Math.max(a,b);
            int min=Math.min(a,b);
            if(a==0||b==0)
                System.out.println("0");
else{       if(max%2==0){
                int t1=max/2;
            
                if(t1<=min){
                    int c=t1;
                    int c1=min-t1;
                    if(c1>=2){
if(c1%2==0){
    int c2=c+(c1/2-1);
    System.out.println(c2);
}
else{
    int c2=c+c1/2;
    System.out.println(c2);
}
                }
                else if(c1==0)
                System.out.println(t1);
                    
                   //System.out.println(t1);
                   }
                else
                    System.out.println(min);            }
          else{
                int c=0;
                int t1=max/2;
                if(t1<=min){
                    c=t1;
                int c1=min-t1;
               if(c1==2){
                    int c2 = c + 1;
                System.out.println(c2);
               }
                else if(c1>=2){
if(c1%2==0){
    int c2=c+(c1/2-1)+1;
    System.out.println(c2);
}
else{
    int c2=c+c1/2+1;
    System.out.println(c2);
}
                }
                else if(c1==0)
                System.out.println(t1);
                    
            }else
                    System.out.println(min);
}

}
}
}
}