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.
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import java.util.Scanner;

public class Main
{
	public static void main(String[] args) {
		int T;
		Scanner sc = new Scanner(System.in);
		T = sc.nextInt();
		while(T!=0){
		    int a = sc.nextInt();
		    int b = sc.nextInt();
		    if(a>(2*b)){
		        System.out.println(b);
		    }
		    else if(b>(2*a)){
		        System.out.println(a);
		    }
		    else{
		        int A = a/3;
		        int B = b/3;
		        int min = Math.min(A,B);
		        int fcnt = min*2;
		        a = a - (min*3);
		        b = b - (min*3);
		        if((a>=1 && b>1) || (a>1 && b>=1)){
    		        fcnt++;
		        }
		        System.out.println(fcnt);
		    }
		    T--;
		}
	}
}
