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 in = new Scanner (System.in);
        int a,b,c;
        int test_cases = in.nextInt();
        for (int i = 0; i < test_cases; i++) {
            a = in.nextInt();
            b = in.nextInt();
            if (2*a<b) {
                c =a;
            }else if (2*b<a){
                c= b;
            }else c = (a+b)/3;
            System.out.println(c);
        }
    }
}