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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

import org.omg.CORBA.Principal;

public class Main {
	public static void main(String[] args) throws FileNotFoundException { 
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		FastPrinter out = new FastPrinter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA{
     
	public void solve(int testNumber, FastScanner scan, FastPrinter out) throws FileNotFoundException {
		Scanner sscan = new Scanner(new File("input.txt"));
		PrintStream oout = new PrintStream(new File("output.txt"));
		int n = sscan.nextInt();
		String s = sscan.next();
		int index1 = s.indexOf("1"), index2 = s.indexOf("1", index1 + 1);
		
		int k = index2 - index1;
		boolean p =false;
		for(int i = index2 + 1; i <= s.length() - 1; i++){
			if(s.charAt(i) == '1'){
				if(i - index2 != k){
					p = true; break;
				}else{
					index2 = i;
				}
			}
		}
		
		 if(p){
		 oout.println("NO");
		 }else{
			oout.println("YES");
		 }
		sscan.close();
		oout.close();
	}
}

class FastScanner extends BufferedReader {
	public FastScanner(InputStream is) {
		super(new InputStreamReader(is));
	}
	
	public int read() {
		try{
			int ret = super.read();
			return ret;
		}catch(Exception e){
			throw new InputMismatchException();
		}
	}
	
	public String next() {
        StringBuilder sb = new StringBuilder();
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        if (c < 0) {
            return null;
        }
        while (c >= 0 && !isWhiteSpace(c)) {
            sb.appendCodePoint(c);
            c = read();
        }
        return sb.toString();
    }
	
	static boolean isWhiteSpace(int c) {
        return c >= 0 && c <= 32;
    }
	
	public int nextInt() {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int ret = 0;
        while (c >= 0 && !isWhiteSpace(c)) {
            if (c < '0' || c > '9') {
                throw new NumberFormatException("digit expected " + (char) c
                        + " found");
            }
            ret = ret * 10 + c - '0';
            c = read();
        }
        return ret * sgn;
    }
	
	public long nextLong() {
		return Long.parseLong(next());
	}
	
	public BigInteger nextBigInteger() {
		return new BigInteger(next());
	}
	
	public BigDecimal nextBigDecimal(){
		return new BigDecimal(next());
	}
	
	public String readLine(){
		try{
			return super.readLine();
		}catch(IOException e){
			return null;
		}
	}
}

class FastPrinter extends PrintWriter {
	
	public FastPrinter(OutputStream out) {
		super(out);
	}
	public FastPrinter(Writer out) {
		super(out);
	}
}