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 program {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int i = input.nextInt();
        for (int j=1;j<=i;j++){
            int a = input.nextInt();
            int b = input.nextInt();
            int count = 0;
            while (a>0 && b>0){
                if (a>b && b>=1){
                    count++;
                    a -= 2;
                    b -= 1;
                }else if (b>a && a>=1){
                    count++;
                    b -= 2;
                    a -= 1;
                }else{
                    break;}
                System.out.println(count);}
        }
    }
}