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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Submit {
    public static void main(String args[]) throws IOException{
        process();
    }
    public static void process() throws IOException{
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        int T=Integer.parseInt(in.readLine());
        for(int t=0;t<T;t++){
            StringTokenizer st=new StringTokenizer(in.readLine());
            int a=Integer.parseInt(st.nextToken());
            int b=Integer.parseInt(st.nextToken());
            int ans=Math.min((a+b)/3,Math.min(a,b));
            System.out.println(ans);
        }
    }
}
