Problem: 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.

Example

Input

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000


Output

1
0
0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (long long i = 0; i < (n); ++i)
using ll = long long;
using P = pair<ll,ll>;
using vec = vector<ll>;
using vecp = vector<P>;
using mat = vector<vec>;
using matp = vector<vecp>;
const ll MOD = 1e9+7;
const ll INF = 1e18;
#define all(v) v.begin(), v.end()



int main(){
  ll T;
  cin >> T;
  rep(w,T){
    ll N;
    cin >> N;
    vec A(N);
    rep(i,N){
      cin >> A.at(i);
    }
    string S;
    cin >> S;
    set<ll> B;
    B.insert(0);
    rep(i,N){
      set<ll> C;
      auto b=B.end();
      ll a=A.at(N-1-i);
      rep(j,(ll)B.size()){
        b--;
        a=min(a,a^*b);
      }
      if(S.at(N-1-i)=='0'){
        if(a!=0){
          B.insert(a);
        }
      }else{
        if(a!=0){
          B=C;
          break;
        }
      }
    }
    if(B.size()==0){
      cout << 1 << endl;
    }else{
      cout << 0 << endl;
    }
  }
        
   
}