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 s = new Scanner(System.in);
	    int t = s.nextInt();
	    while(t-->0){
	        int a = s.nextInt();
	        int b = s.nextInt();
	        if(a==1 && b==1){
                System.out.println(0);
            }
	        else if(a==0 || b==0){
                System.out.println(0);
            }
	        else if(a<3 && b <3){
                System.out.println(1);
            }
	        else if(a<3 && b>=3){
                System.out.println(1);
            }
	        else if(a>=3 && b< 3 ){
                System.out.println(1);
            }
	        else{
	            int val = (a+b)/3;
                System.out.println(val);
            }
        }
    }
}
