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:

import java.io.*;
import java.util.*;

public class Main {
    private int cal(String s, char c) {
        int n = s.length();
        int m = n - 1;
        int ans = 0;
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == c && (m & i) == i) {
                ans ^= 1;
            }
        }
        return ans;
    }

    private void solve() {
        int n = sc.nextInt();
        String s = sc.next();
        StringBuilder sb = new StringBuilder();
        for (int i = 1; i < n; i++) {
            sb.append(Math.abs(s.charAt(i) - s.charAt(i - 1)));
        }

        if (n == 2) {
            out.println(sb.charAt(0));
            return;
        }

        s = sb.toString();
        if (s.contains("1")) {
            out.println(cal(s, '1'));
        } else {
            out.println(cal(s, '2') * 2);
        }
    }

    private static PrintWriter out;
    private static MyScanner sc;

    private static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        private 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());
        }
    }

    public static void main(String[] args) {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        sc = new MyScanner();
        new Main().solve();
        out.close();
    }
}