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;

void solve() {
    int N; cin >> N;
    vector<long long> A(N);
    for (int i = 0; i < N; i++) cin >> A[i];
    string S; cin >> S;
    
    set<long long> B;
    for (int i = N-1; i >= 0; i--) {
        if (S[i] % 2) {
            auto it = B.rbegin();
            while (it != B.rend()) {
                A[i] = min(A[i], A[i] ^ *it);
                it++;
            }
            if (A[i] != 0) {
                cout << 1 << "\n";
                return;
            }
        } else {
            auto it = B.rbegin();
            while (it != B.rend()) {
                A[i] = min(A[i], A[i] ^ *it);
                it++;
            }
            B.emplace(A[i]);
        }
    }
    cout << 0 << "\n";
    return;
}

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