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.Scanner;

public class Solution {
    public static void main(String[] args) {
        Scanner input=new Scanner(System.in);
        int t=input.nextInt();
        while (t-->0){
            long a=input.nextLong();
            long b=input.nextLong();
            long max=Math.max(a,b);
            long min=Math.min(a,b);
            long tempres=0;

            if (max>=2*min){
                System.out.println(min);
                continue;
            }

            while ((max-min)>1) {



                    long temp = (max - min) / 2;

                        min = min - temp;
                        max = max - temp * 2;
                        tempres = tempres + temp;


            }




            long k=Math.min(max/3,min/3);
            long res=k*2+tempres;
            max=max-3*k;
            min=min-3*k;


            if (max==2&&min>=1||min==2&&max>=1){
                res=res+1;
            }
            System.out.println(res);


        }
    }
}