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 A
{
	public static void main (String[] args) throws IOException
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0)
		{
		    int a=sc.nextInt();
		    int b=sc.nextInt();
		    int Esum=0;
		    if(a==0||b==0)
		    {
		        System.out.println(Esum);
		        continue;
		    }
		    if(a>=b)
		    {
		        if(b>a/2)
		        Esum=(a+b)/3;
		        else
		        Esum=b;
		    }
		    else
		    {
		        if(a>b/2)
		        Esum=(a+b)/3;
		        else
		        Esum=a;
		    }
		    System.out.println(Esum);
		}
	}
}