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.io.*;
import java.util.*;
import java.math.*;
public class Main{
    public static void main(String[] args) throws IOException {
        try {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            PrintWriter ot=new PrintWriter(System.out);
            int t=Integer.parseInt(br.readLine());
            while(t-->0)
            {
                String s[]=br.readLine().trim().split(" ");
                int a=Integer.parseInt(s[0]);
                int b=Integer.parseInt(s[1]);
                ot.println(find(a,b));
            }
            ot.close();
            br.close();
        } catch (Exception e) {
            //TODO: handle exception
            System.out.println("ERROR");
            return;
        }
    
    }
    public static int find(int a, int b){
        int zero=0;
        if(a==0||b==0)
        return zero;
        if(a>b)
        {
            if(a/2>=b)
            return b;
            else
            {
                return (a+b)/3;
            }
        }
        else
        {
            if(b/2>=a)
            return a;
            else
            {
                return (a+b)/3;
            }
        }
        
    }
}