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     LL              long long int
#define     FOR(I,A,B)      for( int I = A; I < B; ++I )
#define     SFI(X)          scanf("%d",&X)
#define     SFL(X)          scanf("%lld",&X)
#define     CIN()           ios_base::sync_with_stdio(false), cin.tie(NULL)


int main() {

    int T;

    cin >> T;

    while(T--) {

        int N;

        SFI(N);

        vector<LL>V(N);

        for(auto &I:V) cin >> I;

        string S;

        cin >> S;

        vector<LL>B;

        bool Ans = false;

        for(int I = N - 1; I >= 0; --I) {

            for(auto It:B) if(V[I] > (V[I] ^ It)) V[I] ^= It;

            if(V[I]) {

                if(S[I] == '1') {
                    Ans = true;
                    break;
                } else {
                    B.emplace_back(V[I]);
                }
            }
        }

        cout << Ans << endl;

    }
}