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.*;



/* Name of the class has to be "Main" only if the class is public. */



public class Main
{
     
     
     
    static PrintWriter out;
    
    
	static class FastReader{
		BufferedReader br;
		StringTokenizer st;
		public FastReader(){
			br=new BufferedReader(new InputStreamReader(System.in));
			out=new PrintWriter(System.out);
		}
		String next(){
			while(st==null || !st.hasMoreElements()){
				try{
					st= new StringTokenizer(br.readLine());
				}
				catch (IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		String nextLine(){
			String str = "";
			try{
				str=br.readLine();
			}
			catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
	}
	

// SHIVAM GUPTA :



// ASCII = 48 + i ;
 
 
    
    
    
public static void main (String[] args) throws java.lang.Exception
{
  FastReader scn = new FastReader() ;
  
  int t = scn.nextInt() ;
  
  for(int k = 1 ; k <= t ; k++)
  {
         int a = scn.nextInt() ; int b = scn.nextInt() ;
         
         if(a ==0 || b==0)out.println(0) ;
         
         
         else if(a ==b)
         {
                if( a % 3 ==0)out.println((a/3)*2 ) ;
                
                else if( a % 3 == 2)
                {
                       out.println((a/3)*2 + 1 ) ;
                       
                }
                
                 else 
                {
                       out.println((a/3)*2 ) ;
                       
                }
                
                
                
         }
         
         else{
                
                int min = (int)Math.min(a,b) ;
                int max =(int)Math.max(a,b) ;
                
                if(max/min >= 2)
                {
                       out.println(min) ;
                }
                else{
                       if( min % 3 == 0)
                       {
                          out.println((min/3 )*2 ) ;    
                       }
                       
                       else if( min % 3 == 1)
                       {
                              if( max - min + 1  >=2 )
                              {
                                    out.println((min/3 )*2+1 ) ;      
                              }
                              else{
                                      out.println((min/3 )*2 ) ;    
                              }
                       }
                       
                       else{
                              
                               if( max - min + 2  >= 4 )
                              {
                                    out.println((min/3 )*2+2 ) ;      
                              }
                              else{
                                      out.println((min/3 )*2  + 1) ;    
                              }
                              
                       }
                       
                       
                }
                
         }
         
  }
  
  out.flush() ;
  
  
}
}
  
