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.*;
public class one {


    


    public static Scanner scn = new Scanner (System.in);
    
    public static void main(String [] args)
    {
        int t = scn.nextInt();
        while (t>0)
        {
            int sticks = scn.nextInt();
            int diamonds = scn.nextInt();
            System.out.println(emerald(sticks,diamonds));
            
            t--;
        }
        
    }
    
    public static int emerald (int sticks , int diamonds)
    {
        int shovel=0;
        int sword =0;
        
        if (sticks==diamonds)
        {
            return sticks/2;
        }
        while (sticks>0 && diamonds >0 && sticks!=diamonds)
        {
            if (sticks>diamonds)
            {
                sticks= sticks-2;
                diamonds=diamonds-1;
                shovel++;
            }
            
            else{
                diamonds = diamonds-2;
                sticks=sticks-1;
                sword++;
            }
            
        }
    
    return shovel+sword;
}
    
}