Problem: Recently Vasya got interested in finding extra-terrestrial intelligence. He made a simple extra-terrestrial signals’ receiver and was keeping a record of the signals for n days in a row. Each of those n days Vasya wrote a 1 in his notebook if he had received a signal that day and a 0 if he hadn’t. Vasya thinks that he has found extra-terrestrial intelligence if there is a system in the way the signals has been received, i.e. if all the intervals between successive signals are equal. Otherwise, Vasya thinks that the signals were sent by some stupid aliens no one cares about. Help Vasya to deduce from the information given by the receiver if he has found extra-terrestrial intelligence or not.

Input

The first line contains integer n (3 ≤ n ≤ 100) — amount of days during which Vasya checked if there were any signals. The second line contains n characters 1 or 0 — the record Vasya kept each of those n days. It’s guaranteed that the given record sequence contains at least three 1s.

Output

If Vasya has found extra-terrestrial intelligence, output YES, otherwise output NO.

Examples

Input

8
00111000


Output

YES


Input

7
1001011


Output

NO


Input

7
1010100


Output

YES

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class dd {
    public static void main(String args[]) throws FileNotFoundException,IOException {
        /*InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);*/
        Scanner read = new Scanner(new File("input.txt"));
        int n = read.nextInt();
        String str = read.next();
        int dif = 0, last = -1;
        boolean ans = true;
        for (int i = 0; i < n; i++) {
            if (str.charAt(i) == '1') {
                if (dif != 0 && dif != i - last) {
                    ans = false;
                    break;
                }
                if (last == -1)
                    dif = 0;
                else
                    dif = i - last;
                last = i;
            }
        }
        PrintWriter fout = new PrintWriter(new FileWriter("output.txt"));
        fout.print(ans ? "YES" : "NO");
        fout.close();
    }
    public static void shuffle(long[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }

    public static void shuffle(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }

    public static int gcd(int x, int y) {
        if (y == 0)
            return x;
        return gcd(y, x % y);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

        public long nextLong() {
            return Long.valueOf(next());
        }

        public double nextDouble() {
            return Double.valueOf(next());
        }

        String nextLine() throws IOException {
            return reader.readLine();
        }

    }
}