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 sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t--!=0) {
			long a = sc.nextInt();
			long b = sc.nextInt();
			if(a==0 || b==0)
				System.out.println("0");
			else {
				long c = Math.max(a, b);
				long d = Math.min(a, b);
				if(c/d>1)
					System.out.println(d);
				else {
					long count=0;
					count = count+c/3+d/3;
					c = c%3;
					d=d%3;
					if((c>=2 && d>=1) || (c>=1 && d>=2))
						count++;
					System.out.println(count);
				}
			}
		}
	}
}
