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.io.*;
import java.lang.reflect.Array;
import java.nio.Buffer;
import java.util.*;

public class Pair {

    public static void main(String[] args) throws Exception {

        try {
            Scanner sc = new Scanner(System.in);
            StringBuilder out = new StringBuilder();
            int T = sc.nextInt();
            while(T!=0){
                long a = sc.nextLong();
                long b = sc.nextLong();
                if(a==0 || b==0){
                    System.out.println(0);
                }
                else{
                    System.out.println((a+b)/3);
                }
                
                --T;
            }
            sc.close();
        }
        catch (Exception e) {
        }
    }
}
