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;
using ll = long long;
template <class T, class U> using Pa = pair<T, U>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vec<T>>;

void solve(){
    int N;
    cin >> N;
    vec<ll> A(N);
    for(auto& x:A) cin >> x;
    string S;
    cin >> S;
    vec<ll> base;
    for(int i=N-1;i>=0;i--){
        ll a = A[i];
        for(auto& b:base) a = min(a,b^a);
        if(S[i]=='1'){
            if(a){
                cout << 1 << "\n";
                return ;
            }
        }else{
            base.push_back(a);
        }
    }
    cout << 0 << "\n";
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int T;
    cin >> T;
    while(T--){
        solve();
    }
}