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.BufferedWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.InputStreamReader;
import java.io.FileOutputStream;
import java.util.StringTokenizer;
import java.util.Arrays;
public class Polycrap{
	static BufferedWriter out;
	static FastReader sc;
	public static void main(String[] args)throws IOException{
		sc = new FastReader();
		out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out),"ASCII"),512);
		int t = sc.nextInt();
		while(t-- > 0){
			int a = sc.nextInt();
			int b = sc.nextInt();
			int count = Math.min(Math.min(a,b),(a+b)/3);
			out.write(count + "");
			out.write('\n');
			out.flush();
		}
	}
}
class FastReader{
	BufferedReader br;
	StringTokenizer st;
	public FastReader(){ 
		br = new BufferedReader(new InputStreamReader(System.in)); 
	}
	String next(){ 
		while (st == null || !st.hasMoreElements()){ 
			try{ 
				st = new StringTokenizer(br.readLine()); 
			} 
			catch (IOException  e){ 
				e.printStackTrace(); 
			} 
		} 
		return st.nextToken(); 
	}
	int nextInt(){ 
        return Integer.parseInt(next()); 
	}
    long nextLong(){ 
        return Long.parseLong(next()); 
    }
    double nextDouble(){ 
        return Double.parseDouble(next()); 
    }
    String nextLine(){ 
        String str = ""; 
        try{ 
            str = br.readLine(); 
        } 
		catch (IOException e){ 
            e.printStackTrace(); 
        } 
        return str; 
    }
}