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 Solution {

    public static Scanner sc=new Scanner(System.in);

    public static void main(String[] args) {
        int cas = sc.nextInt();
        while (cas-- > 0){
            int a = sc.nextInt();
            int b = sc.nextInt();
            //awlays a <b
            if (a>b){
                int tmp =a;
                a =b;
                b=tmp;
            }
            if (a >b/2) System.out.println((a+b)/3);
            else System.out.println(Math.min(b/2, a));
        }

    }
}
