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.PrintWriter;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) throws IOException {
        Scanner s = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String[] input;
//        int t = Integer.parseInt(reader.readLine());
        int t = s.nextInt();
        while(t-->0) {
        	int a = s.nextInt(), b = s.nextInt();
        	if(a > b) {
        		int te = a;
        		a = b;
        		b = te;
        	}
        	int temp = b - a;
        	if(temp > a) {
        		temp = a;
        	}
        	a -= temp;
        	b -= 2 * temp;
        	if(a == 0) {
        		out.println(temp);
        	} else {
        		int ans = temp + (a / 3) * 2;
        		a %= 3;
        		b %= 3;
        		if(a == 2) {
        			ans++;
        		}
        		out.println(ans);
        	}
        }
        out.flush();
    }
}
