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 shovelsandSwords {
	int sh = 0;
	int sw = 0;
	int result = 0;
	public int solver(int stick, int dia) {
		
		while(stick != 0 || dia != 0) {
			
			if(stick == 0 || dia == 0){
				return 0;
			}
			else if(stick <= dia ) {
				stick --;
				dia -= 2;
				sw++;
			} 
			else if(stick > dia ) {
				dia--;
				stick -= 2;
				sh++;
			}
			result = sw + sh;
			break;
		}
		return result;
	}
	public static void  main(String[] args){
		
        Scanner s = new Scanner(System.in);
        int stick = s.nextInt();
		int dia = s.nextInt();
		shovelsandSwords ob = new shovelsandSwords();
		ob.solver(stick, dia);
		s.close();
		}
    }