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.io.*;
import java.util.*;
public class Main{
	public static void main(String args[]){
		InputStreamReader r = new InputStreamReader(System.in);
		BufferedReader br = new BufferedReader(r);
		try{
			int t = Integer.parseInt(br.readLine());
			for(int i=0;i<t;i++){
				int n = Integer.parseInt(br.readLine());
				String str = br.readLine();
				String value[] = str.split(" ");
				String str1 = br.readLine();
				String type[] = str1.split(" ");
				int count = 1;
				for(int k=0;k<n-1;k++){
					for(int j=0;j<n-k-1;j++){
						if((Integer.parseInt(type[j])!=Integer.parseInt(type[j+1])) && Integer.parseInt(value[j])>Integer.parseInt(value[j+1])){
							String s = value[j];
							value[j] = value[j+1];
							value[j+1] = s;
							String temp = type[j];
							type[j] = type[j+1];
							type[j+1] = temp;
						}
						else if((Integer.parseInt(type[j])==Integer.parseInt(type[j+1])) && Integer.parseInt(value[j])>Integer.parseInt(value[j+1])){
							count = 0;
							break;
						}
						else if((Integer.parseInt(type[j])==Integer.parseInt(type[j+1])) && Integer.parseInt(value[j])<Integer.parseInt(value[j+1])){
							
						}
					}
				}
				if(count==0){
					System.out.println("No");
				}
				else{
					System.out.println("Yes");
				}
			}
		}
		catch(Exception e){
			return;
		}
	}
}