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.lang.*;
import java.io.*;
public class GFG
 {
	 public static void main (String[] args)throws IOException
	 {
	 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	 int t=Integer.parseInt(br.readLine());
	 while(t-->0)
	 {
	     String[] ab=br.readLine().split(" ");
	     int a=Integer.parseInt(ab[0]);
	     int b=Integer.parseInt(ab[1]);
	     int count=0;
	     while(a!=0 && b!=0 && a==b)
	     {
	         
	         count++;
	         if(a>b)
	         {
	         count++;
	         a=a-2;
	         b=b-1;
	         }
	         else
	         {
	         count++;
	         b=b-2;
	         a=a-1;   
	         }
	         
	     }
	     if(a==b)
	     count=count+(a+b)/2;
	     System.out.println(count);
	     
	 }
	 }
	 
}