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.Arrays;
import java.util.Comparator;
import java.util.Scanner;

import javax.lang.model.util.ElementScanner6;

public class Solution {
    static int[] col;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        in.nextLine();
        for (int z = 0; z < t; z++)
        {
            int d = in.nextInt(), s = in.nextInt();
            int ans = 0;
            int diff = Math.abs(d - s);
            if (Math.min(d, s) < diff)
            {
                System.out.println(Math.min(d, s));
            }
            else
            {
                ans = diff;
                if (d > s)
                {
                    d -= 2 * diff;
                    s -= diff;
                }
                else
                {
                    s -= 2 * diff;
                    d -= diff;
                }
                ans += s / 3 * 2;
                if (s % 3 > 1 && d % 3 > 0)
                {
                    ans++;
                }
                else if (s % 3 > 0 && d % 3 > 1)
                {
                    ans++;
                }
                System.out.println(ans);
            }
        }

        in.close();
    }
}
    