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.*;
import java.io.*;
public class Main{
    public static void main(String[] args)throws IOException
    {
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    int t=Integer.parseInt(br.readLine());
    while(t-->0){
    String ab[]=br.readLine().split(" ");
    long a=Long.parseLong(ab[0]);
    long b=Long.parseLong(ab[1]);
    System.out.println(findEm(a,b));
     }
  }
  static long findEm(long a,long b){
    if(a>=2*b||b>=2*a||a==0||b==0)
        return Math.min(a,b);
    if(a==b){
    if(a%3==0||(a-1)%3==0)
        return 2*(a/3);
    else 
        return 2*((a-2)/3)+1;
    }
    else
    {
    long dif=Math.abs(a-b);
    long val=a<b?a-dif:b-dif;
    return (dif+findEm(val,val));
    }
    }
}
