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.
//package codeforces;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Shovels_and_Swords {

  
		public static void main(String args[]) throws NumberFormatException, IOException
		{
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			int t = Integer.parseInt(br.readLine());
			while(t-- > 0)
			{
				String input[] = br.readLine().split(" ");
				int a = Integer.parseInt(input[0]);
				int b = Integer.parseInt(input[1]);
				int max = Math.max(a, b);
				int min = Math.min(a, b);
				int count = 0;
				if(a == 0 || b == 0)
					count = 0;
//				else if(a == b)
//					count = a/2;
				else if(max/2 >= min)
					count = min;
//				else if(min - (max/2) == 1)
//				{
//					count = max/2;
//				}
				else 
				{
					count =(min + max)/3;
					
				}
				
				System.out.println(count);
					
			}
		}
	}


