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<iostream>
#include<vector>
using namespace std;
typedef long long li;
#define rep(i,n) for(int i=0;i<(n);i++)
#define df 0
template<class T> void print(const T& t){ cout << t << "\n"; }
template<class T, class... Ts> void print(const T& t, const Ts&... ts) { cout << t; if (sizeof...(ts)) cout << " "; print(ts...); }
// Container コンテナ型, map以外
template< template<class ...> class Ctn,class T>
std::ostream& operator<<(std::ostream& os,const Ctn<T>& v){
  auto itr=v.begin();
  while(itr!=v.end()){
    if(itr!=v.begin())cout << " ";
    cout << *(itr++);
  }
  return os;
}

int ord(li a){
  li b,i=1;
  while(b=(a>>i)){
    a|=b;
    i*=2;
  }
  return __builtin_popcountl(a);
}

int in(li a,vector<li>& space){
  for(li x:space){
    if(ord(x)==ord(a)) a^=x;
  }
  
  return !a;
}


void add(li a,vector<li>& space){
  if(df)print("add",a);
  for(li& x:space){
    if(ord(x)==ord(a)) a^=x;
    if(x<a) swap(a,x);
  }
  if(a){
    space.push_back(a);
  }
//  normarize(space);
  if(df)print(space);
}

int main(){
  int q;cin >>q;
  if(df)print(q);
  if(df)rep(i,20)print(i,ord(i));
  rep(_,q){
    int n; cin >>n;
    vector<li> a(n);
    rep(i,n) cin >>a[i];
    if(df)print("a",a);
    string s; cin >>s;
    vector<li> space;
    int flag=0;
    rep(j,n){
      int i=n-j-1;
      int c=s[i]-'0'; li h=a[i];
      if(df)print("c,h",c,h);
      if(c){
        if(!in(h,space)){
          flag=1;
          break;
        }
      } else {
        add(h,space);
      }
    }
    print(flag);
    if(df)print("---------------");
  }
}