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.util.*;

public class A_1366{
    static PrintWriter pw = new PrintWriter(System.out);

    public static void main(String arg[]) throws IOException {
        InputStreamReader isr = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(isr);
        StringTokenizer token = new StringTokenizer(" ");

        int n=0;
        int a=0;
        int b=0;
        int j=0;

        n=Integer.parseInt(br.readLine());

        for(j=0;j<=n-1;j++) {
            token=new StringTokenizer(br.readLine());

            a=Integer.parseInt(token.nextToken());
            b=Integer.parseInt(token.nextToken());

            pw.println(getResult(a,b));
        }
        pw.close();

    }

    private static long getResult(int a,int b) {
        int max=a;
        int min=a;
        long count=0;

        if(a==0 || b==0 || (a==1 && b==1))
            return 0;

        if(a>b){
            max=a;
            min=b;
        }
        else{
            min=a;
            max=b;
        }

        int c=max-min;

        if(c>min)
            c=min;

        max=max-2*c;
        min=min-c;
        count=c;

        //max has become equal to min

        count=count+min/3*2;

        if(min%3==2)
            count++;

        return count;

    }
}