Problem:
Score : 400 points

Problem Statement

There are two persons, numbered 0 and 1, and a variable x whose initial value is 0.
The two persons now play a game.
The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):

Person S_i does one of the following:

Replace x with x \oplus A_i, where \oplus represents bitwise XOR.

Do nothing.

Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.

Determine whether x becomes 0 at the end of the game when the two persons play optimally.

Solve T test cases for each input file.

Constraints

1 \leq T \leq 100

1 \leq N \leq 200

1 \leq A_i \leq 10^{18}

S is a string of length N consisting of 0 and 1.

All numbers in input are integers.

Input

Input is given from Standard Input in the following format.
The first line is as follows:

T

Then, T test cases follow.
Each test case is given in the following format:

N
A_1 A_2 \cdots A_N
S

Output

For each test case, print a line containing 0 if x becomes 0 at the end of the game, and 1 otherwise.

Sample Input 1

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000

Sample Output 1

1
0
0

In the first test case, if Person 1 replaces x with 0 \oplus 1=1, we surely have x \neq 0 at the end of the game, regardless of the choice of Person 0.

In the second test case, regardless of the choice of Person 1, Person 0 can make x=0 with a suitable choice.

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net.Sockets;

namespace SandboxForAtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var line1 = Console.In.ReadLine();

            var t = int.Parse(line1);

            for (int iRound = 0; iRound < t; iRound += 1)
            {
                // inputs
                var line2 = Console.In.ReadLine();
                var line3 = Console.In.ReadLine();
                var line4 = Console.In.ReadLine();

                var n = int.Parse(line2);
                decimal[] a = line3.Split(" ").Select(se => decimal.Parse(se)).ToArray();
                char[] s = line4.ToArray();

                decimal x = 0;


                // main

                for (int i = 0; i < n; i += 1)
                {

                    var result = (ulong)x ^ (ulong)a[i];

                    if (s[i] == '0')
                    {
                        if (result == 0)
                        {
                            x = result;
                        }
                    }
                    else if (s[i] == '1')
                    {
                        if (x == 0 && a[i] == 0)
                        {
                        }
                        else
                        {
                            x = result;
                        }
                    }

                }


                Console.WriteLine(x == 0 ? '0' : '1');
            }
        }
    }
}