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 CodeChef {
    static FastReader sc;
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;
    static long INF = Integer.MAX_VALUE;

    static class Point {
        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

    }

    static class FastReader {

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();

                }

            }
            return st.nextToken();
        }


    }

    public static void main(String args[]) throws java.lang.Exception {
        sc = new FastReader();
       int t = sc.nextInt();
        while (t-- > 0)
            solve();

    }

    public static void solve() throws IOException {
            long a=sc.nextLong();
            long b=sc.nextLong();long count=0L;
            if(a==0 || b==0)
                System.out.println(0);
            else
            System.out.println((a+b)/3);
            //System.out.println(count);
    }



}
