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.Text;
using System.Diagnostics;
using System.Numerics;
using System.Collections.Generic;

class Myon

{
    public Myon() { }
    public static int Main()
    {
        cin = new Scanner();
        new Myon().calc();
        return 0;
    }
    static Scanner cin;

    void calc()
    {
        int T = cin.nextInt();
        for (int i = 0; i < T; i++)
        {
            Console.WriteLine(calc2());
        }
    }

    int calc2()
    {
        int N = cin.nextInt();
        long[] A = cin.ArrayLong(N);
        string S = cin.next();
        int cnt = S.Length - 1;

        long all = 0;
        List<long> allL = new List<long>();

        while(cnt >= 0)
        {
            List<long> LA = new List<long>();
            List<long> LB = new List<long>();

            while(cnt >= 0 && S[cnt] == '0') { allL.Add(A[cnt]); LA.Add(A[cnt--]); }
            while(cnt >= 0 && S[cnt] == '1') { LB.Add(A[cnt--]); }

            LA.Sort();
            LA.Reverse();
            for (int i = 0; i < LA.Count; i++)
            {
                for (int j = i + 1; j < LA.Count; j++)
                {
                    long next = LA[i] ^ LA[j];
                    if (next < LA[j]) LA[j] = next;
                }
                LA.Sort();
                LA.Reverse();
            }

            long last = -1;

            foreach (var b in LB)
            {
                long now = b;
                foreach (var a in LA)
                {
                    if (now > (now ^ a)) now ^= a;
                }
                if (last == -1) last = now;
                else if (now != last) return 1;
            }

            if (last != -1) all ^= last;
        }

        allL.Sort();
        allL.Reverse();
        for (int i = 0; i < allL.Count; i++)
        {
            for (int j = i + 1; j < allL.Count; j++)
            {
                long next = allL[i] ^ allL[j];
                if (next < allL[j]) allL[j] = next;
            }
            allL.Sort();
            allL.Reverse();
        }


        foreach (var a in allL)
        {
            if (all > (all ^ a)) all ^= a;
        }
        if (all != 0) return 1;
        return 0;
    }
}


class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}