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 Solution {
    public static void main(String[] args) {
        Scanner input=new Scanner(System.in);
        int t=input.nextInt();
        while (t-->0){
            long a=input.nextLong();
            long b=input.nextLong();
            long tempres=0;
 
            while (Math.max(a,b)-Math.min(a,b)>=2) {
 
 
                if (a > b + 1) {
                    long temp = (a - b) / 2;
                    if (temp <= b) {
                        b = b - temp;
                        a = a - temp * 2;
                        tempres = tempres + temp;
                    } else {
                        tempres = tempres + b;
//                        System.out.println(tempres);
                        break;
                    }
 
 
                } else if (b > a + 1) {
                    long temp = (b - a) / 2;
                    if (temp <= a) {
                        a = a - temp;
                        b = b - temp * 2;
                        tempres = tempres + temp;
                    } else {
                        tempres = tempres + a;
//                        System.out.println(tempres);
                        break
                                ;
                    }
 
 
                }
            }
 
 
            long res=Math.min(a/3,b/3)*2+tempres;
            a=a%3;
            b=b%3;
            if (a==2&&b>=1||b==2&&a>=1){
                res=res+1;
            }
            System.out.println(res);
 
 
        }
    }
}