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 codeforces {

        public static void main(String[] args) {
            int i,t,a=0,b=0,e = 0;
            t=0;
            Scanner scan = new Scanner(System.in);
            if(scan.hasNextInt()) {
                t = scan.nextInt();
            }
            for ( i = 1; i<=t; i++) {
                String c,d;
                if(scan.hasNext()) {
                    d = scan.next();
                    a = d.equals("") ? 0 : Integer.parseInt(d);
                }
                if(scan.hasNext()) {
                    c = scan.next();
                    b = c.equals("") ? 0 : Integer.parseInt(c);
                }
                if(a==0 || b==0) {
                    e=0;
                    System.out.println(e);
                }
                else {
                    e = (a + b) / 3;
                    System.out.println(e);
                }

            }
        }
    }
