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.util.*; 
import java.io.*; 
import java.lang.Math; 
public class Main
{  
    public static void main(String[] args)
{ 
     Scanner in=new Scanner(System.in); 
    int i,t,x,j,c,a,b;
    t=in.nextInt();
    for(i=0;i<t;i++)
    {
        a=in.nextInt();
        b=in.nextInt();
        x=Math.max(a,b);
        j=Math.min(a,b);
        if(a==0||b==0)
        System.out.println(0);
        
        else if(x>=2*j)
        {
            System.out.println(j);
        }
        else
        {
            c=(a+b)/3;
            //System.out.println(a/3);
            //System.out.println(b/3);
            System.out.println(c);
            
        }
        
    }
       
        
}
}