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.PrintWriter;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int t = in.nextInt();
        while (t-- > 0) {
            int a, b;
            a = in.nextInt();
            b = in.nextInt();

            out.println(ans(a, b));
        }
        out.close();
    }
    private static int ans(int a,int b) {
        if (a == 0 || b == 0) {
            return 0;
        }
        int mx = Math.max(a, b);
        int mn = Math.min(a, b);
        int x = Math.abs(a - b);
        if (x == 0) {
            return (a / 3) * 2;
        }
        int c = Math.min((x + 1) / 2, mn);
        return c + ans(mx - c * 2,  mn - c);
    }
}
