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.*;
public class CFE89 
{
	public static void main(String args[])throws IOException
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		while(t-->0)
		{
			String s=br.readLine();
			String st[]=s.split(" ");
			long a=Long.parseLong(st[0]), b=Long.parseLong(st[1]);
			long min=(a<b)?a:b;
			long max=(a>b)?a:b;
			if(min<=max/2)
			{
				System.out.println(min);
				break;
			}
			int c=0;
			while(a>=0 && b>=0)
			{
				if(a>=b && a>=2)
				{
					c++;
					a-=2;
					b-=1;
				}
				else
				{
					c++;
					a-=1;
					b-=2;
				}
			}
			System.out.println(c-1);
		}
	}
}
