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 C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int T = sc.nextInt();
        for(int t=0; t<T; ++t){
            int a =sc.nextInt();
            int b = sc.nextInt();

            if(a>=2*b){
                System.out.println(b);
                continue;
            }
            if(b>=2*a){
                System.out.println(a);
                continue;
            }

            if(b>a){
                int temp = a;
                a = b;
                b = temp;
            }

            int t1 = a/3;
            int t2 = b/3;

            int count = 0;
            if(t1<t2){
                count = 2*t1;
                a -= 3*t1;
                b -= 3*t1;
            }
            else{
                count  = 2*t2;
                a -= 3*t2;
                b -= 3*t2;
            }

            if(a>0 && b>1 || a>1 && b>0)
                count++;

            System.out.println(count);
        }
    }
}