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 Question1 {
	static Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		int t = sc.nextInt();
		while(t-->0) {
			solve();
		}
	}
	
	public static void solve() {
		int a = sc.nextInt();
		int b = sc.nextInt();
		
		int ans = 0;
		
		int min = Math.min(a,b);
		int max = Math.max(a, b);
		
		if(max >= 2 * min) {
			System.out.println(min);
			return;
		}
		
		else if(min == max) {
			System.out.println(2 * (min/3));
			return;
		}
		
		int val = min / 3;
		ans = val * 2;
		
		min = min - (val * 3);
		max = max - (val * 3);
		
		if(min > 0 && max > 1)ans++;
		System.out.println(ans);
	}

}
