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 Main{

	public static void main(String[] args) {

		Scanner input = new Scanner(System.in);
		
		int num  = input.nextInt();
		
		for(int i = 0; i < num; i++) {
			int a = input.nextInt();
			int b = input.nextInt();
			int max = (a < b) ? b : a;
			int small = (a > b) ? b : a;
			int result = 0;
		
			if(max >= 2 * small)
				result = small;
			else {
				int count;
				count = small / 3;
				int amax = max - (count * 3);
				int bmax = small - (count * 3);
//				System.out.println(amax + " " + bmax);
				result = (small / 3) * 2;
				if(amax >= 4 && bmax == 2)
					result += 2;
				else if(amax >= 2 && bmax >= 1)
					result++;

			}
			System.out.println(result);
		
		
		
		}

	}

}
