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;
typedef pair<int,int> P;
typedef long long ll;
typedef long double ld;
const int inf=1e9+7;
const ll longinf=1LL<<60;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
#define F first
#define S second
constexpr char ln = '\n';

const int mx=100010;
const ll mod=1e9+7;

void solve(){
  int n;
  cin >> n;
  vector<ll> a(n);
  rep(i,n){
    cin >> a[i];
  }
  string s;
  cin >> s;

  vector<ll> t;
  for(int i=n-1; i>=0; i--){
    ll tmp = a[i];
    if(s[i]== '1'){
      for(auto it:t){
        tmp = min(tmp, tmp^it);
      }
      if(tmp!=0){ cout << 1 << ln; return; }
    } else {
      for(auto it:t){
        tmp = min(tmp, tmp^it);
      }
      if(tmp!=0){ t.emplace_back(tmp); }
    }
  }
  cout << 0 << ln;
}

int main(){
  int q; cin >> q;
while(q--){
  solve();
}
  return 0;
}