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 NewClass {

    public static void main(String[] args) {
        Scanner Sc = new Scanner(System.in);
        int t = Sc.nextInt();
        for (int i = 0; i < t; i++) {
                        int result=0;

            int a = Sc.nextInt();
            int b = Sc.nextInt();
            int min, max;
            if (a < b) {
                min = a;
                max = b;
            } else {
                min = b;
                max = a;
            }
            int n=max-min;
            if(min>=n)
            {
            max=max-2*n;
            min=min-n;
            
            }
            else n=0;
            int result1 = 0;
            if (min * 2 <= max) {
                result1 = min;
            }
            
            
            
            int min1 = min;
            result += (min1 / 3);
            result *= 2;
            result+=n;
            min = min % 3;
            
            max = max % 3;
                if (max >= min) {
                if (max == 2 && min == 1||max == 2 && min == 2) {
                    result++;
                }
            } else {
                if (max == 1 && min == 2||max == 2 && min == 2) {
                    result++;
                }
            }
            
            
            if (result1 > result) {
                System.out.println(result1 );
              
            } else {
                System.out.println(result);
                

            }
        }
    }
}