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 final class prog_1
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[][]=new int[n][2];
        for(int i=0;i<n;i++)
        {
            a[i][0]=sc.nextInt();
            a[i][1]=sc.nextInt();
            
        }
        for(int i=0;i<n;i++)
        {
            int c=(a[i][0]+a[i][1])/3;
            int  a1=a[i][0];
            int a2=a[i][1];
            if(c<a1 && c <a2)
            System.out.println(c);
            else if(a1<c && a1<a2 )
            System.out.println(a1);
            else if(a2<c && a2<a1)
            System.out.println(a2);
        }
    }
}