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 ejc17v2 {

    public static void main(String[] args) {

        Scanner input = new Scanner(System.in);

        int casos = input.nextInt();

        for(int i =0;i<casos;i++){

            int sticks = input.nextInt();
            int diamonds = input.nextInt();

            if(sticks<diamonds && sticks<(sticks+diamonds)/3){
                System.out.println(sticks);
            } else if(diamonds<sticks && diamonds<(sticks+diamonds)/3){
                System.out.println(diamonds);
            } else {
                System.out.println((sticks+diamonds)/3);
            }
        }

    }
}
