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 rebillious {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int p=sc.nextInt();
		sc.nextLine();
		while(p>0) {
		int n=sc.nextInt();
		int m= sc.nextInt();
		int count=0;
		if(m>2*n) {
			System.out.println(n);
		}
		else if(n>2*m) {
			System.out.println(m);
		}
		else {
			if(n!=0&&m!=0) {
				count=(m+n)/3;
			}	
			else
				count=0;
		System.out.println(count);
		}
		p--;
		}
		
		

	}


}
