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 CodechefJ1 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
  Scanner s=new Scanner(System.in);
  int tc=s.nextInt();
  while(tc>0)
  {
	  tc--;
	  int a=s.nextInt();
	  int b=s.nextInt();
	   if(a*2<=b)
		  System.out.println(a);
	  else if(b*2<=a)
		  System.out.println(b);
	  else
		  System.out.println((a+b)/3);
        
  }
	}
}