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.HashSet;
import java.util.Scanner;
public class temp {

	
	
	
	public static void main(String[] args) {
			try (Scanner sc = new Scanner(System.in)) {
			
			int t = sc.nextInt();
			while(t-->0) {
				int a = sc.nextInt(); // sticks 
				int b = sc.nextInt(); // diamonds
				int count=0;
				if(a==0 || b==0) {
					System.out.println("0");
				}else {
					count = (a+b)/3;
					System.out.println(Math.min(count,Math.min(a, b)));
				}
				
			}
			
			
		} catch (Exception e) {
			return;
		}

	}
	
	

}
