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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 1000000007

ll n;
string s;
ll arr[209];
bool flag ;

map<string, bool> _map;

bool solve(int idx, int curr) {
	// cout<<idx<<" "<<curr<<endl;
	if(idx == n)
		return flag?(curr = 0):(curr != 0);

	string key = to_string(idx) + '_' + to_string(curr);
	if(_map.find(key) != _map.end())
		return _map[key];

	bool ans = false;
		
	if(idx + 1 == n) {

		ans |= (!solve(idx + 1, (curr ^ arr[idx])));
		ans |= (!solve(idx + 1, curr));

	} else {
		if((s[idx + 1] - '0') ^ (s[idx] - '0')){
			ans |= (!solve(idx + 1, (curr ^ arr[idx])));
			ans |= (!solve(idx + 1, curr));
		} else {
			ans |= solve(idx + 1, (curr ^ arr[idx]));
			ans |= solve(idx + 1, curr);
		}
	}
	// cout<<curr<<endl;
	return _map[key] = ans;
}

int main() {
// #ifndef ONLINE_JUDGE
// 	freopen("input.txt", "r", stdin);
// 	freopen("output.txt", "w", stdout);
// #endif

	int t;
	cin>>t;
	while(t--) {
		_map.clear();
		cin>>n;
		for(int i = 0; i < n; i++)  
			cin>>arr[i];
		cin>>s;
		// cout<<"input taken\n"<<endl;
		flag = (s[0] == 0);
		if(!solve(0, 0)) cout<<"0\n";
		else cout<<"1\n";
	}

	
}