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.io.PrintStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;

public class A {
    static HashMap<Long, Long> combos = new HashMap<>();
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintStream out = System.out;

        int t = Integer.parseInt(br.readLine());

        for (int i = 0; i < t; i++) {
            String[] nm = br.readLine().split(" ");
            int a = Integer.parseInt(nm[0]);
            int b = Integer.parseInt(nm[1]);

            int tot = a+b;
            if (2*a < b) tot = 3*a;
            if (2*b < a) tot = 3*b;
            out.println(tot/3);

        }



        System.out.flush();
    }
}