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 emeralds {
	public static int calc(int s, int d ,int em) {
		if(s <= 1 && d <= 1) {
			return em;
		}
		if(s >=3 && d>= 3) {
			return calc(s-3,d-3,em+2);
		}
		if(s == 1 && d == 2 ) {
			return calc(s-1,d-2,em+1);
		}
		if(s == 2 && d == 1 ) {
			return calc(s-2,d-1,em+1);
		}
		return em;
	}
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s =new Scanner(System.in);
		int t = s.nextInt();
		while(t-->0) {
			int sticks = s.nextInt();
			int diamonds = s.nextInt();
			System.out.println(calc(sticks,diamonds,0));
		}
	}

}
