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 s = new Scanner(System.in);
        int test = s.nextInt();
        for (int i = 0; i < test; i++) {
            int a = s.nextInt();
            int b = s.nextInt();
            System.out.println(calculate(a, b));
        }
    }

    private static int calculate(int a, int b) {
        int count = 0;
        int max = Math.max(a, b);
        int min = Math.min(a, b);
        int diff = max - min;
        max = max - 2 * diff;
        if (max < 0) {
            return min;
        }
        count += diff;
        count += max / 3 * 2;
        max = max % 3;
        if (max == 2) count++;
        return count;
    }
}
