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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<string>
#include<iomanip>
#include<cmath>
#include<vector>
#include<algorithm>
#include<utility>
#include<bitset>
#include<set>
#include<map>

using namespace std;

#define int long long
#define endl "\n"

constexpr long long INF = (long long)1e18;
constexpr long long MOD = 1'000'000'007; 

struct fast_io {
	fast_io(){
		std::cin.tie(nullptr);
		std::ios::sync_with_stdio(false);
	};
} fio;


int solve3(vector<int> &A, string &S, map<pair<int,int>,int> &mp, int depth = 0, int x = 0){
	if(depth == A.size()) {
		return !!x;
	}
	
	if(mp[{depth,x}]) return mp[{depth,x}]-1;
	
	
	if(S[depth] == '0') {
		if(solve3(A, S, mp, depth+1, x ^ A[depth]) == 0){
			mp[{depth,x}] = 1;
			return 0;
		}
		if(solve3(A, S,mp, depth+1, x) == 0) {
			mp[{depth,x}] = 1;
			return 0;
		}
		mp[{depth,x}] = 2;
		return 1;
	} else {
		if(solve3(A, S, mp, depth+1, x ^ A[depth]) == 1) {
			mp[{depth,x}] = 2;
			return 1;
		}
		
		if(solve3(A, S, mp, depth+1, x) == 1) {
			mp[{depth,x}] = 2;
			return 1;
		}
		mp[{depth,x}] = 1;
		return 0;
	}
}


signed main(){
	cout<<fixed<<setprecision(10);
	
	int T;
	
	cin>>T;
	
	for(int _ = 0; _ < T; _++){
		int N;
		vector<int> A;
		map<pair<int,int>,int> mp;
		string S;
		
		cin>>N;
		
		A.resize(N);
		
		for(int i = 0; i < N; i++){
			cin>>A[i];
		}
		
		cin>>S;
		
		if(S.back() == '1') {
			cout<<1<<endl;
			continue;
		}
		
		cout<<solve3(A, S, mp, max(0ll, N-25))<<endl;
		
	}
	
	
	return 0;
}