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 final class code
// public class Main
// class code
// public class Solution
{
    static void solve()throws IOException
    {
        int n=nextInt();
        String s=nextLine();
        int i=0;
        while(i<n && s.charAt(i)!='1')
            i++;
        int diff=-1,trail=0;
        for(i=i+1;i<n;i++)
        {
            if(s.charAt(i)=='0')
                trail++;
            else
            {
                if(diff==-1)
                    diff=trail;
                else if(diff!=trail)
                {
                    out.println("NO");
                    return;
                }
                trail=0;
            }
        }
        out.println("YES");
    }

     
    ///////////////////////////////////////////////////////////

    static final long mod=(long)(1e9+7);
    static final int inf=(int)(1e9+1);
    static final int maxn=(int)(1e6);
    static final long lim=(long)(1e18);

    public static void main(String args[])throws IOException
    {
        br=new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
        out=new PrintWriter(new BufferedOutputStream(new FileOutputStream("output.txt")));
        
        solve();
         
        // int t=nextInt();
        // for(int i=1;i<=t;i++)
        // {
        //    // out.print("Case #"+i+": ");
        //     solve();
        // }
         
        out.close();
    }
    
    static int max(int ... a)
    {
    int ret=a[0];
    for(int i=1;i<a.length;i++)
    ret=Math.max(ret,a[i]);
    return ret;
    }
    static int min(int ... a)
    {
    int ret=a[0];
    for(int i=1;i<a.length;i++)
    ret=Math.min(ret,a[i]);
    return ret;
    }
    static void debug(Object ... a)
    {
    System.out.print("> ");
    for(int i=0;i<a.length;i++)
    System.out.print(a[i]+" ");
    System.out.println();
    }
    static void debug(int a[]){debuga(Arrays.stream(a).boxed().toArray());}
    static void debug(long a[]){debuga(Arrays.stream(a).boxed().toArray());}
    static void debuga(Object a[])
    {
    System.out.print("> ");
    for(int i=0;i<a.length;i++)
    System.out.print(a[i]+" ");
    System.out.println();
    }
    static Random random;
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;
    static String nextToken()throws IOException
    {
    while(st==null || !st.hasMoreTokens())
    st=new StringTokenizer(br.readLine());
    return st.nextToken();
    }
    static String nextLine()throws IOException
    {
    return br.readLine();
    }
    static int nextInt()throws IOException
    {
    return Integer.parseInt(nextToken());
    }
    static long nextLong()throws IOException
    {
    return Long.parseLong(nextToken());
    }
    static double nextDouble()throws IOException
    {
    return Double.parseDouble(nextToken());
    }
}