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.lang.*;
import java.io.*;
import java.math.*;
import java.text.DecimalFormat;
                                        
        public class d1{
          
        public static void main (String[] args) {                        
            PrintWriter pw=new PrintWriter(System.out);
            Scanner sc=new Scanner(System.in);
            int t=1;
            t=sc.nextInt();
            for(int i11=0;i11<t;i11++){
               
               int a=sc.nextInt();
             //  int a1=a;
               int b=sc.nextInt();
              // int b1=b;
               int count=0;
              /* while(a>0&&b>0){
                   if((a==0&&b==0||a==1&&b==1)||(a==0&&b==1||a==1&&b==0))
                      break;
                   if(a>b){
                       a-=2;
                       b--;
                       count++;
                   }
                   else{
                       
                       b-=2;
                       a--;
                       count++;
                   }
               }
             */
             if((a<=b&&a>=b/2)||(b<=a&&b>=a/2))
              pw.println((a+b)/3);
              else
              pw.println(Math.min(a,b));
               
                     }
                       
                       pw.close();
    	}
    }