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.*;
public class Main{
  public static void main(String[] args)throws IOException{
    Scanner sc = new Scanner(System.in);
    int a,b,c,d,e,f,g,h,i;
    a = sc.nextInt();
    for(b = 0;b < a;b++){
      c = sc.nextInt();
      d = sc.nextInt();
      e = 0;
      f = Math.max(c,d);
      g = Math.min(c,d);
      if(f >= (g*2)){
        System.out.println(g);
      }else{
        h = f-g;
        g = g-h;
        f = g;
        e = e+ h;
        i = f % 3;
        e = e + (f/3)*2;
        if(i == 2){
          e++;
        }
        System.out.println(e);
      }
    }
  }
}