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.*;
import java.lang.*;
import java.io.*;
 
public class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int num = scan.nextInt();
        while (num > 0){
            int result = 0;
            int sticks = scan.nextInt();
            int dia = scan.nextInt();
            while (sticks >= 1 && dia >= 2 || sticks >= 2 && dia >= 1){
                if (sticks == dia){
                    result += 2*(sticks/3);
                    sticks %= 3;
                    dia %= 3;
                } else if (sticks > dia){
                    if (sticks - dia == 1){
                        sticks -= 2;
                        dia--;
                        result++;
                    } else {
                        int difference = sticks - dia;
                        dia -= difference;
                        sticks -= 2*difference;
                        result += difference;
                    }
                    
                } else {
                    if (dia - sticks == 1){
                        dia -= 2;
                        sticks--;
                        result++;
                    } else {
                        int difference = dia - sticks;
                        sticks -= difference;
                        dia -= 2*difference;
                        result += difference;
                    }
                }
            }
            
            System.out.println(result);
            num--;
        }
    }
}