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.*;
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;
           int dif=0;
           int val=0;
           while(a>0 && b>0){
               if(a==b && a/3!=0){
		              c+=(a/3)*2;
		              a=a%3;
		              b=b%3;
		           }
		       else if(a==2 && b==2) {
		       		  c++;
		        	  a=0;
		        	}
		       else if(a!=b && ((a>=2 && b>=1) || (a>=1 && b>=2))){
		          if(a>b && a>=2 && b>=1){
		              dif=a-b;
		              val=Math.min(dif,b);
		              a-=(val*2);
		              b-=val;
		              c+=val;
		          }
		          else if(b>a && b>=2 && a>=1){
		              dif=b-a;
		              val=Math.min(dif,a);
		              b-=(val*2);
		              a-=val;
		              c+=val;
		          }
		      }
		           else {
		        	  a=0;
		        	  b=0;
	            }
           }
           System.out.println(c);
       }
    }
}