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(int i = 0; i < n; i++)
#define per(i,n) for(int i = n-1; i >= 0; i--)
typedef long long ll;
typedef pair<int, int> P;
typedef pair<long long, long long> Pll;
typedef vector<int> vi;
typedef vector<ll> vll;
const long long mod = 1000000007LL;

void solve() {
  int n;
  cin >> n;
  vll a(n);
  rep(i,n) cin >> a[i];
  string s;
  cin >> s;
  vll basis;
  bool ok = true;
  per(i,n) {
    ll v = a[i];
    for(auto x : basis) v = min(v,v^x);
    if(v) {
      if(s[i]=='1') ok = false;
      basis.push_back(v);
    }
  }
  if(ok) cout << 0 << endl;
  else cout << 1 << endl;
}

int main() {
  int T;
  cin >> T;
  rep(_,T) solve();
  return 0;
}