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.*;

public class A {

    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        int t = scn.nextInt();
        while (t-- > 0) {
            long ans = 0;
            long a = scn.nextLong();
            long b = scn.nextLong();
            if(a > b){
                long temp = a;
                a = b;
                b = temp;
            }

            if(a == b){
                System.out.println((a+b) / 3);
            } else {
                if(b >= 2*a){
                    System.out.println(a);
                } else {
                    ans += (b-a);
                    b -= (2*ans);
                    a -= ans;
                    ans += (a+b)/3;
                    System.out.println(ans);
                }
            }
        }
    }
}