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.*;
import java.lang.*;
 
 
public class Solution{
	
	public static int GetMax(int a,int b) {
		if(a==0||b==0)return 0;
		int l = Math.max(a, b);
		int s = Math.min(a, b);
		if(l>=2*s)return s;
		int diff = l-s;
		l = l - 2*diff;
		s = s - diff;
		if(l==2)return diff+1;
		return diff+2*(l/3);
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		for(int i=0;i<t;i++) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			System.out.println(GetMax(a,b));
		}
	}
}