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 solution{
    public static void main(String args[]){
       Scanner sc=new Scanner(System.in);
       int t;
       t=0;
       if(sc.hasNext())
       t=sc.nextInt();
       while(t>0){
           t--;
           int a,b;
           a=sc.nextInt();
           b=sc.nextInt();
           int c=0;
           while(a>0 && b>0){
               if(a==b){
                   c=a/3;
                   a=a/3;
                   b=b/3;
               }
               else{
                   if(a>b){
                       a-=2;
                       b-=1;
                       c++;
                   }
                   else{
                       b-=2;
                       a-=1;
                       c++;
                   }
               }
           }
           System.out.println(c);
       }
    }
}