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<bits/stdc++.h>
#define rep(i,n) for(int i=0;i<n;++i)
using namespace std;
using ll=long long;
constexpr ll mod=998244353;
constexpr int inf=1000000000;
constexpr ll linf=1000000000000000000;

template<int COL=60>
struct bitmat{
private:
    vector<bitset<COL>> mat;
    int rank;
public:
    int addRow(bitset<COL> &aRow){
        mat.push_back(aRow);
        return eliminate();
    }
    int eliminate(){
        rank=0;
        for(int col=0;col<COL;++col){
            int pivot=-1;
            for(int row=rank;row<mat.size();++row){
                if(mat[row][col]){
                    pivot=row;
                    break;
                }
            }
            if(pivot==-1)continue;
            swap(mat[pivot],mat[rank]);
            for(int row=rank+1;row<mat.size();++row){
                if(mat[row][col]){
                    mat[row]^=mat[rank];
                }
            }
            ++rank;
        }
        return rank;
    }
    int getRank(){
        return rank;
    }
};


int main(){
    int t;
    cin>>t;
    rep(loop,t){
        int n;
        cin>>n;
        vector<bitset<60>> a;
        a.reserve(n);
        rep(i,n){
            int val;
            cin>>val;
            a[i]=bitset<60>(val);
        }
        string s;
        cin>>s;
        bitmat<60> mat;
        int win=0;
        for(int i=n-1;i>=0;--i){
            if(s[i]=='0'){
                mat.addRow(a[i]);
            }
            else{
                int oldrank=mat.getRank();
                int newrank=mat.addRow(a[i]);
                if(oldrank!=newrank){
                    win=1;
                    break;
                }
            }
        }
        cout<<win<<endl;
    }
}