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)

// यथा चतुर्भिः कनकं परीक्ष्यते निघर्षणच्छेदनतापताडनैः।
// तथा चतुर्भिः पुरुषः परीक्ष्यते त्यागेन शीलेन गुणेन कर्मणा॥
#include <bits/stdc++.h>
using namespace std;
#define lld long long int
#define M 1000000007
#define fors(i,n) for(int i=0;i<n;++i)
#define fore(i,a,b) for(int i=a;i<=b;++i)
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define vv std::vector<int>
#define mapii std::map<int,int>
#define mpaci std::map<char,int>
#define umapii std::unordered_map<int,int>
#define umapci std::unordered_map<char,int>
#define seti std::set<int>
#define useti std::unordered_set<int>
#define qi std::queue<int>
#define qc std::queue<char>
#define sti std::stack<int>
#define stc std::stack<char>
#define endl "\n"
#define test(i) cout<<i<<endl
#define tests(i) cout<<"i: "<<i<<endl;
#define itrt int t; cin>>t; fors(i,t)
#define itr1 int t; cin>>t;
#define ff first
#define ss second
#define pb push_back
#define vmp make_pair
#define ppb pop_back
#define sorta(a,n) sort(arr,arr+n)
#define sortv(x) sort(x.begin(),x.end())
#define all(x) x.begin(),x.end() 
#define printv(v) for(auto x: v){ cout<< x << " ";}
#define pi 3.14159265358979323846
#define setprc(x) setprecision(x)
void file(){
    #ifdef LOCAL
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
}
bool sortdesk(const pair<int,int> &a, const pair<int,int> &b){return a.ff>b.ff;}
bool sortdesv(const pair<int,int> &a, const pair<int,int> &b){return a.ss>b.ss;}
bool sortascv(const pair<int,int> &a, const pair<int,int> &b){return a.ss<b.ss;}
bool sortasck(const pair<int,int> &a, const pair<int,int> &b){return a.ff<b.ff;}
bool is_prime(int n){if(n==1){return false;}int i=2;while(i*i<=n){if(n%i==0){return false;}i+=1;}return true;}
int gcd(int a, int b){if (b == 0){return a;} return gcd(b, a % b);}
int cntdiv(int n){int cnt=0;for(int i=1;i<=sqrt(n);++i){if(n%i==0){if(n/i==i)++cnt;else{cnt = cnt + 2;}}}return cnt;}
lld posnegmod(lld a,lld b){//return (x%mod+mod)%mod;
long long int r = a % b;
    return r < 0 ? r + b : r;
}
// cout<<fixed<<setprecision(20)
// lld fact(lld n);
// lld nCr(lld n,lld r){return fact(n) / (fact(r) * fact(n - r));}
// lld fact(lld n){ lld res = 1; for(lld i = 2; i <= n; i++){res = res * i;}return res;} 
// const int maxi = 1e6+10;
// vector<lld> v[maxi];
// vector<lld> h(maxi);
// vector<long long> a(maxi,0);
// lld res=0;
// void dfs(int x){
//     if(a[x]){
//         return;
//     }
//     a[x]=1;
//     int flag=1;
//     for(int i:v[x]){
//         if(h[x]<=h[i]){
//             flag=0;
//             break;
//         }
//     }
//     if(flag){
//         ++res;
//     }
// }

void test_case(){
    int n;
    cin>>n;
    map<lld,lld> mp;
    vector<lld> v(n);
    fors(i,n){
        int x;
        cin>>x;
        v[i]=x;
        mp[x]=1;
    }
    string s;
    cin>>s;
    lld x=0;
    for(int i=0;i<n;++i){
        if(s[i]=='1'){
            x= x^v[i];
        }
        else{
            int t=x^v[i];
            if(mp[t]){
                cout<<0<<endl;
                return;
            }
            else{
                x=x^v[i];
            }
        }
    }
    if(x==0){
        cout<<0<<endl;
        return;
    }
    cout<<1<<endl;
}

int main(){
    fastio;
    file();
    // int T=1;
    int T;
    cin>>T;
    for(int nr=1;nr<=T;++nr) {
        // cout<<"Case #"<<nr<<": ";
        test_case();
    }
}
// PD?D??P