Problem: Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3. Let x_{i,j} defined as follows:

* x_{1,j} := a_j \quad (1 \leq j \leq N)
* x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)



Find x_{N,1}.

Constraints

* 2 \leq N \leq 10^6
* a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:


N
a_1a_2\ldotsa_N


Output

Print x_{N,1}.

Examples

Input

4
1231


Output

1


Input

10
2311312312


Output

0

Solution (in JAVA):

Solution:

public class Main {

  private static void solve() {
    int n = ni();
    char[] s = ns();

    System.out.println(solve(s));


    // int d = 10;
    // for (int i = 0; i < Math.pow(3, d); i++) {
    // char[] s = new char[d];
    // int v = i;
    // for (int j = 0; j < d; j++) {
    // s[j] = (char) (v % 3 + 1 + '0');
    // v /= 3;
    // }
    //
    // int ret = solve(s);
    // int ret3 = solve3(s);
    // if (ret != ret3) {
    // System.out.println(new String(s) + " " + ret + " " + ret3 + "NG");
    // }
    // }

  }



  private static int solve(char[] s) {

    int odd = 0;
    int n = s.length;
    for (int i = 0; i < n; i++) {
      int d = s[i] - '0';
      int m = n - 1;
      int r = i;
      int f = (r | (m - r)) == m ? 1 : 0;
      odd += d * f;
      odd %= 2;
    }

    int[] cnt = new int[4];
    for (char c : s) {
      cnt[c - '0']++;
    }
    if (cnt[1] > 0 && cnt[3] > 0 && cnt[2] == 0) {
      char[] to = new char[n - 1];
      for (int i = 0; i < n - 1; i++) {
        int d = Math.abs(s[i] - s[i + 1]);
        to[i] = (char) ((d == 2 ? 1 : 0) + '0');
      }
      return solve(to) == 1 ? 2 : 0;

    } else {
      return odd;
    }

  }


  private static int solve3(char[] s) {
    int n = s.length;
    int[][] a = new int[n + 1][n];
    for (int i = 0; i < n; i++) {
      a[0][i] = s[i] - '0';
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n - i - 1; j++) {
        a[i + 1][j] = Math.abs(a[i][j] - a[i][j + 1]);
      }
    }
    return a[n - 1][0];
  }



  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}