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;
typedef long long LL;

struct Dimension {
    int N;
    vector< LL >basis;
    Dimension(int N) : N(N), basis(N, 0) { }

    bool add(LL x) {
        for (int i = 0; i < N; i++) {
            if (x&(1LL<<i)) {
                if (basis[i]) x ^= basis[i];
                else {
                    basis[i] = x;
                    return true;
                }
            }
        }
        return false;
    }
};

char solve() {
    int n;
    cin >> n;

    vector< LL >A(n);
    for (int i = 0; i < n; i++) cin >> A[i];

    string s;
    cin >> s;

    Dimension d(60);
    for (int i = n-1; i >= 0; i--) {
        if (d.add(A[i])) {
            if (s[i]=='1') return '1';
        }
    }
    return '0';
}


int main() {
    int t;
    cin >> t;

    while (t--) {
        cout << solve() << "\n";
    }


    return 0;
}