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 {
	static int sh = 0;
	static int sw = 0;
    public static void  main(String[] args){
		int result = 0;
        Scanner s = new Scanner(System.in);
        int tests = s.nextInt();
        int stick = s.nextInt();
		int dia = s.nextInt();
		while(tests != 0) {
			while(stick == 0  || dia == 0){
				if(stick == 0 || dia == 0){
					return;
				}
				else if(stick <= dia ) {
					stick --;
					dia -= 2;
					sw++;
					result++;
				} 
				else if(stick > dia ) {
					dia--;
					stick -= 2;
					sh++;
					result++;
				}
			}
			s.close();
			System.out.println(result);
			tests --;
			}
    	}
	}