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.InputStreamReader;
import java.io.IOException;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.FileOutputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.FileInputStream;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream;
		try {
			inputStream = new FileInputStream("input.txt");
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
		OutputStream outputStream;
		try {
			outputStream = new FileOutputStream("output.txt");
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
	public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.readInt();
        char[] s = in.readCWord();
        ArrayList<Integer> list = new ArrayList<Integer>();
        for (int i = 0; i < n; i++)
            if (s[i] == '1')
                list.add(i);
        if (list.size() == 0){
            out.println("NO");
            return;
        }
        if (list.size() == 1){
            out.println("YES");
            return;
        }
        int d = list.get(1) - list.get(0);
        for (int i = 1; i < list.size(); i++)
            if (list.get(i) - list.get(i-1) != d){
                out.println("NO");
                return;
            }
        out.println("YES");
	}
}

class InputReader {
    public InputReader(InputStream inputStream){
        in = new BufferedReader(new InputStreamReader(inputStream));
    }

    public String readWord(){
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(readLine());
        return tokenizer.nextToken();
    }

    public char[] readCWord(){
        String s = readWord();
        char[] ans = new char[s.length()];
        for (int i = 0; i < s.length(); i++)
            ans[i] = s.charAt(i);
        return ans;
    }

    public int readInt(){
        return Integer.parseInt(readWord());
    }

    public String readLine(){
        String line = null;
        try{
            line = in.readLine();
        }
        catch (IOException e){
            e.printStackTrace();
        }
        return line;
    }

    private StringTokenizer tokenizer;
    private BufferedReader in;
}

class OutputWriter {
    public OutputWriter(OutputStream outputStream){
        this.out = new PrintWriter(outputStream);
    }

    public OutputWriter(Writer writer){
        this.out = new PrintWriter(writer);
    }

    public void print(Object...a){
        for (int i = 0; i < a.length; i++)
            out.print(a[i]);
    }

    public void println(Object...a){
        print(a);
        out.println();
    }

    public void close(){
        out.close();
    }

    private PrintWriter out;
}