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) {
	// write your code here
        Scanner sc = new Scanner(System.in);
        int t=sc.nextInt();
        int a, b, i, x, c;
        for (i=0; i<t; i++) {
            a=sc.nextInt();
            b=sc.nextInt();
            if (a>b) c=b; else c=a;
            c-=c%3;
            x=c/3*2;
            a-=c;
            b-=c;
            while (a>1 && b>1) {
                if (a>b) {
                    a-=2;
                    b-=1;
                }
                else {
                    a-=1;
                    b-=2;
                }
                x++;
            }
            if (a*b>1) x++;
            System.out.println(x);
        }
    }
}
