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 ShovelsAndSwords {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t, a, b, result;

        t = in.nextInt();

        for (int i=0; i < t; i++) {
            a = in.nextInt();
            b = in.nextInt();
            if (a > 0 && b > 0) {
                if (a > b) {
                    if (a/b > 1) {
                        result = b;
                    }
                    else {
                        result = 2 * (b/3);
                        if (b%3 != 0) {
                            result += 1;
                            if (b%3 == 2 && a%3 == 2) {
                                result += 1;
                            }
                        }
                    }
                    
                }
                else if (a < b) {
                    if (b/a > 1) {
                        result = a;
                    }
                    else {
                        result = 2 * (a/3);
                        if (a%3 != 0) {
                            result += 1;
                            if (b%3 == 2 && a%3 == 2) {
                                result += 1;
                            }
                        }
                    }
                    
                }
                else {
                    result = 2 * (a/3);
                    if ((a%3 == 1 && b%3 == 2) || (a%3 == 2 && b%3 == 1)) {
                        result += 1;
                    }
                }
            }
            else {
                result = 0;
            }

            System.out.println(result);
        }

        in.close();
    }
}