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.lang.reflect.Array;
import java.util.*;

public class Main {


    public static void main(String[] args) throws IOException {
//        BufferedReader br = new BufferedReader(
//                new InputStreamReader(System.in));
//        BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
//        log.flush();
        Scanner sc = new Scanner(System.in);
        int test = sc.nextInt();
        for (int t = 0; t < test; t++) {
            int a = sc.nextInt(), b = sc.nextInt();
            if (a < b){
                a = (a + b) - (b = a);
            }
            int min = Math.min(a - b, b);
//            System.out.println(min);
            int amount = min;

            a -= amount * 2;
            b -= amount;
//            System.out.println(amount + " " + a + " " + b);

            amount += Math.min(a / 3, b / 3) * 2;

            System.out.println(amount);

        }
    }
}