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 int long long
template<typename T>
void chmin(T &a,T b){
  if(a>b)a=b;
}
void add(set<int> &now,int a){
  for(int p:now)chmin(a,a^(-p));
  if(a)now.insert(-a);
}
bool out(set<int> &now,int a){
  for(int p:now)chmin(a,a^(-p));
  return a;
}

signed main(){
  int t;cin>>t;
  while(t--){
    int n,ans=0;cin>>n;
    vector<int>v(n);
    for(int i=0;i<n;i++)cin>>v[i];
    string s;cin>>s;
    if(s.back()=='1')ans=1;
    set<int> now;
    for(int i=n-1;i>=0;i--){
      if(s[i]=='0')add(now,v[i]);
      else if(out(now,v[i]))ans=1;
    }
    cout<<ans<<endl;
  }
}