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.*;
import java.io.*;
public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.valueOf(reader.readLine());
        
        while((t--) != 0) {
            String[] info = reader.readLine().split(" ");
            int a = Integer.valueOf(info[0]);
            int b = Integer.valueOf(info[1]);
            
            if(a >= 2 * b || b >= 2 * a) {
                System.out.println(Math.min(a, b));
                continue;
            }
            
            int res = Math.min(a / 3, b / 3);
            a -= 3 * res;
            b -= 3 * res;
            res *= 2;
            int tmp1 = Math.min(a, b / 2);
            int tmp2 = Math.min(a / 2, b);
            res += Math.max(tmp1, tmp2);
            System.out.println(res);
        }
    }
}