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.*;
public class one
{
    
    public static int backtrack(int a, int b, int x, int y, int total)
    {
        if((x+y)>=a || (x+y)>=b)
        {
            return total;
        }
        int ax = backtrack(a,b,x+1,y+2,total +1);
        int bx = backtrack(a,b,x+2,y+1,total +1);
        if(ax>bx)
        {
            return ax;
        }
        return bx;
        
    }
    
    
    public static void main(String args[])
{
    Scanner sc = new Scanner(System.in);
 int t = sc.nextInt();
 sc.nextLine();
    for(int x=0;x<t;x++)
    {
    String str[] = sc.nextLine().split(" ");
    int a = Integer.parseInt(str[0]);
    int b = Integer.parseInt(str[1]);
    
    System.out.println(backtrack(a,b,0,0,0));
    
}}
}