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: Accepted)

#define _USE_MATH_DEFINES

#include <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <cmath>
#include <bitset>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef tuple<ll, ll, ll> tl3;



const int BIG_NUM = 1e9;
const ll INF = 1000000000000000000;
const ll MOD = 1e9 + 7;
//const ll MOD = 998244353;


int main() {
	int t;
	cin >> t;
	for (int i = 0; i < t; i++) {
		int n;
		cin >> n;
		vector<ll> a(n);
		for (int i = 0; i < n; i++) {
			cin >> a[i];
		}
		string s;
		cin >> s;

		vector<ll> b;
		bool canConsist = true;
		for (int i = n - 1; i >= 0; i--) {
			for (auto x : b) {
				a[i] = min(a[i], a[i]^x);
			}

			if (a[i] > 0) {
				if (s[i] == '1') {
					cout << 1 << endl;
					canConsist = false;
					break;
				}

				b.emplace_back(a[i]);
			}

			
			
		}
		if (!canConsist) {
			continue;
		}
		

		
		cout << 0 << endl;
		
		
	}
}