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.Scanner;

public class CodeForces2 {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(); int a,b,count=0;
        for (int i = 0; i < n; i++) {
            a = sc.nextInt();   b = sc.nextInt(); 
            count = 0;
            if(a == 0 || b == 0){
                System.out.println("0"); 
                continue;
            }else if(a == b){
                System.out.println(a/2);
                continue;
            }else{
                if(a*2 <= b) System.out.println(a); 
                else if(b*2 <= a)  System.out.println(b);
                else System.out.println((a+b)/3);
            }
        }     
    }
}