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.Globalization;

namespace XorBattle
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] A = new long[200];
            long[] res=new long[200];


            string inD0 = Console.ReadLine();
            int T = int.Parse(inD0);

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


                string inD1 = Console.ReadLine();
                int N = int.Parse(inD1);

                string inD2 = Console.ReadLine();
                string[] cngD3 = inD2.Split(' ');

                for (int j=0;j <= N - 1; j++)
                {
                     A[j] = long.Parse(cngD3[j]);

                }

                string inD4 = Console.ReadLine();
                int S = inD4.Length;
                long restmp;
                restmp = 0;
                for (int k = 0; k <= S - 1; k++)
                {
                     restmp =restmp ^ A[k];

                }
                res[i] = restmp;
                
            }

            for (int k = 0; k <= T - 1; k++)
            {
                if (res[k]!= 0)
                {
                    Console.WriteLine("1");

                }
                else
                {
                    Console.WriteLine("0");

                }
            }
                    
        }
    }
}