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>
#define int long long
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define F first
#define S second

using namespace std;
typedef pair<int,int> P;
typedef vector<int> ivec;

const int MOD=1000000007;
int INF=100100100100100;

void solve(){
  int n;cin>>n;
  ivec a(n);rep(i,n)cin>>a[i];
  string s;cin>>s;
  
  ivec basis;
  for(int i=n-1;i>=0;i--){
    for(int x:basis)a[i]=min(a[i],a[i]^x);
    if(a[i]){
      if(s[i]=='1'){
        cout<<1<<endl;
        return;
      }
      basis.pb(a[i]);
    }
  }
  cout<<0<<endl;
}
  
signed main(){
  int t;cin>>t;
  rep(i,t)solve();
  return 0;
}