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# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		for(;T>0;T--){
			
			N = ri();
			A = rla();
			S = rs();
			
			var l = new List<char>();
			var ll = new List<List<long>>();
			
			l.Add(S[0]);
			ll.Add(new List<long>(){A[0]});
			
			for(int i=1;i<N;i++){
				if(S[i] == l[l.Count - 1]){
					ll[ll.Count - 1].Add(A[i]);
				} else {
					l.Add(S[i]);
					ll.Add(new List<long>(){A[i]});
				}
			}
//foreach(var a in ll) Console.WriteLine(String.Join(" ",a));
			/*
			if(l[l.Count - 1] != '0'){
				Console.WriteLine(1);
				continue;
			}
			*/
			List<List<long>> bs = new List<List<long>>();
			for(int i=0;i<ll.Count;i++){
				bs.Add(Gauss(ll[i]));
			}
			
//foreach(var a in bs) Console.WriteLine(String.Join(" ",a));
			
			
			List<long> a = new List<long>();
			bool chk = true;
			for(int i=l.Count - 1; i>= 0; i--){
				switch(l[i]){
					case '0':{
						foreach(var n in bs[i]) a.Add(n);
						a = Gauss(a);
					} break;
					case '1':{
						var nl = new List<long>();
						var xb = a.ToList();
						xb.Add(0);
						foreach(var n in bs[i]){
							xb[xb.Count - 1] = n;
//Console.WriteLine("xb: {0}",String.Join(" ",xb));
							var g = Gauss(xb);
//Console.WriteLine("g: {0}",String.Join(" ",g));
							if(g.Count == xb.Count){
								chk = false;
							}
						}
					} break;
				
				}
			}
			Console.WriteLine(chk ? 0 : 1);
		}
	}
	
	List<long> Gauss(List<long> _l){
		var l = _l.ToList();
		int row = 0;
		int msb = 63;
		while(true){
			l.Sort();
			l.Reverse();
			if(row >= l.Count || l[row] == 0) break;
			while((l[row] >> msb) % 2 == 0) msb--;
			for(int j=row + 1;j < l.Count; j++){
				if((l[j] >> msb) % 2 == 1) l[j] ^= l[row];
			}
			row++;
		}
		while(l.Count > 0 && l[l.Count - 1] == 0) l.RemoveAt(l.Count - 1);
		return l;
	}
	
	
	
	
	
	int T;
	int N;
	long[] A;
	String S;
	public Sol(){
		T = ri();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}