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.*;
 

public class A
{
	public static void main (final String[] args) throws java.lang.Exception {
        final Scanner sc = new Scanner(System.in);
        final int t = sc.nextInt();
        for(int i=0; i<t; i++){
            int lo = sc.nextInt();
            int hi = sc.nextInt();
            int tools = 0;
            if(lo > hi){
                int temp = hi;
                hi = lo;
                lo = temp;
            }
            while(lo != hi && lo != 0){
                int diff = hi-lo;
                if((diff*2) > hi){
                    diff = hi/2;
                }
                if(diff > lo){
                    diff = Math.min(diff, lo);
                }
                hi -= diff*2;
                lo -= diff;
                tools += diff;

                if(lo > hi){
                    int temp = hi;
                    hi = lo;
                    lo = temp;
                }
            }
            int triples =  (lo/3);
            if(lo - triples*3 > 0 && hi-triples*3 > 1){
                tools ++;
            }
            tools += triples*2;
            System.out.println(tools);
        }
    }

}