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 JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Main {
    static long [] basis; static int sz; static boolean ok;
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = sc.nextInt();
        for (int tt = 0; tt < t; tt++) {
            int n = sc.nextInt();
            long [] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextLong();
            }
            String s = sc.next();
            basis = new long[62]; sz = 0;
            ok = true;
            for (int i = n - 1; i >= 0; i--) {
                if (s.charAt(i) == '0') {
                    insertVector(a[i], false);
                } else {
                    insertVector(a[i], true);
                }
            }
            out.println(ok ? 0 : 1);
        }
        out.close();
    }

    static void insertVector(long x, boolean represent) {
        for (int bit = 0; bit < 62; bit++) {
            if (((x >> bit) & 1) == 0) continue;
            if (basis[bit] == 0) {
                if (represent) {
                    ok = false;
                    return;
                }
                basis[bit] = x;
                ++sz;
                return;
            }
            x ^= basis[bit];
        }
    }



    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}