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.Arrays;
import java.util.Scanner;

public class codeforces {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		int at = sc.nextInt();
		for(int it=0;it<at;it++)
		{
				long a=sc.nextLong();
				long b=sc.nextLong();
				long max=a>b?a:b;
				long min=a<b?a:b;
				long ans=min/3;
				if(min*2<=max) {
					System.out.println(min);
				}
				else
				{
				if(min%3==0)
				{
					System.out.println((min/3)*2);
				}
				if(min%3==1)
				{
					ans=max-((min/3)*3);
					if(ans>=2)
					{
						System.out.println(((min/3)*2)+1);
					}
					else
					{
						System.out.println(((min/3)*2));
					}
				}
				if(min%3==2)
				{
					ans=max-((min/3)*3);
					if(ans>=4)
					{
						System.out.println(((min/3)*2)+2);
					}
					else if(ans>0)
					{
						System.out.println(((min/3)*2)+1);
					}
					else
					{
						System.out.println((min/3)*2);
					}
				}}
		}
		sc.close();
	}
}
