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;

int main(){
    int T;
    cin >> T;
    for (int t = 0; t < T; t++){
        [](){
        int n;
        cin >> n;
        vector<uint64_t> A(n);
        copy_n(istream_iterator<uint64_t>(cin), n, A.begin());
        string S;
        cin >> S;

        vector<uint64_t> base;
        for (int i = n - 1; i >= 0; i--){
            auto a = A[i];
            for (const auto &b: base)
                a = min(a, a ^ b);
            if (a != 0)
                base.push_back(a);
            if (a != 0 and S[i] == '1'){
                puts("1");
                return;
            }
        }
        puts("0");
        }();
    }
}