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)

#include <bits/stdc++.h>

using namespace std;

const int N = 205;

char s[N];
long long A[N];

struct linarBase {
    long long c[64];
    bool insert(long long x) {
        for(int i = 60; ~i; --i) if(x >> i & 1) {
            if(!c[i]) {
                c[i] = x;
                return true;
            } else {
                x ^= c[i];
            }
        }
        return false;
    }
    void init() {
        for(int i = 0; i <= 60; ++i)
            c[i] = 0;
    }
} B;

int main() {
    int Case, n;
    scanf("%d", &Case);
    while(Case--) {
        B.init();
        scanf("%d", &n);
        for(int i = 1; i <= n; ++i)
            scanf("%lld", &A[i]);
        scanf("%s", s + 1);
        bool flag = true;
        for(int i = n; i >= 1; --i) {
            if(B.insert(A[i]) && s[i] == '1') {
                flag = false;
            }
        }
        puts(flag ? "0" : "1");
    }
    return 0;
}