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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.*;

public class Main implements Runnable {
	private boolean _READ_FROM_FILE = true; //System.getSecurityManager() == null; //System.getProperty("ONLINE_JUDGE") == null;
	private boolean _WRITE_TO_FILE = true;
	static final String _IN_FILE = "input.txt";
	static final String _OUT_FILE = "output.txt";
	BufferedReader reader;
	StringTokenizer tokenizer;

	private void core() throws Exception {
		int n = nextInt();
		char[] ch = nextToken().toCharArray();
		
		int last = -1;
		int len = Integer.MAX_VALUE;
		for (int i = 0; i < ch.length; i++) {
			if (ch[i] == '1') {
				if (last != -1) {
					if (len == i - last || len == Integer.MAX_VALUE)
						len = i - last;
					else
						len = -1;
				}
				last = i;
			}
		}
		System.out.println(len != -1 ? "YES" : "NO");
	}
	void debug(Object...os) {
		System.out.println(Arrays.deepToString(os));
	}
//--------------------- IO stuffs ---------------------
    public static void main(String[] args) throws InterruptedException {
        Thread thread = new Thread(new Main());
        thread.start();
        thread.join();
    }
	public void run() {
        try {
        	reader = new BufferedReader(_READ_FROM_FILE ? new FileReader(_IN_FILE) : new InputStreamReader(System.in));
        	System.setOut(new PrintStream(new BufferedOutputStream(_WRITE_TO_FILE ? new FileOutputStream(_OUT_FILE) : System.out)));
            tokenizer = new StringTokenizer("");
            core();
            reader.close();
            System.out.flush();
            System.out.close();
            System.exit(0);
        } catch (Exception e) {
        	System.out.flush();
            e.printStackTrace();
            System.exit(1);
        }
    }
    int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }
    long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
    double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
    String nextToken() throws Exception {
        while (!tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(reader.readLine());
        return tokenizer.nextToken();
    }
    boolean nextIsAvailable() throws Exception {
    	while (!tokenizer.hasMoreElements()) {
    		String line = reader.readLine();
    		if (line == null) return false;
    		tokenizer = new StringTokenizer(line);
    	}
    	return true;
    }
}