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.
//package codeforcesa3;
import java.util.*;
public class ShovelsAndSwords {
    public static void main(String[] args) {
        Scanner in=new Scanner (System.in);
        int t=in.nextInt();
        for(int i=0;i<t;i++)
        {
            int a=in.nextInt();
            int b=in.nextInt();
            int min=Math.min(a, b);
            int max=Math.max(a, b);
            int ans=0;
            if(max>=2*min){
                System.out.println(min);
                continue;
            }
            else{
                int diff=max-min;
               
                    min=min-diff;
                    max=max-(2*diff);
                    ans+=diff;
                    ans+=((min/3)*2);
                    if(min%3==2){
                        ans++;
                    }
            }
            System.out.println(ans);
        }
    }
}
