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.math.*;
import java.util.*;
import java.lang.*;
import java.io.*;

public class Codechef {
	

	

	public static void main(String[] args) throws IOException {
		
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int l = Integer.parseInt(br.readLine());
		while (l-- > 0)
		{
      			String[] sr=br.readLine().split(" ");
      			
      			int a=Integer.parseInt(sr[0]);
      			int b=Integer.parseInt(sr[1]);
      			
      			
      			
      			if((a==0)||(b==0))
      				System.out.println("0");
      			else
      			{
      			int 	x=a<b?a:b;
      			int y=a>b?a:b;
      			if(y>2*x)
      				System.out.println(x);
      			else
      				System.out.println(y/2);
      			
      			
      			}
      			
			
			
		
		
}}}