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 Main {
    public static void main(String args[]) {
        Scanner sc=new Scanner(System.in);
        Main obj=new Main();
        int t=sc.nextInt();
        ArrayList<Long> ans=new ArrayList<Long>();
        for(int i=0;i<t;i++)
        {
            long a = Long.parseLong(sc.next());
            long b = Long.parseLong(sc.next());
            ans.add(obj.abc(a,b));
        }
        for(long i : ans)
            System.out.println(i);
    }
    long abc(long a, long b)
    {
        long c = (long)Math.min(a,Math.min(b,(a+b)/3));
        return c; 
    }
}