You are given the array of integer numbers a0, a1, ..., an - 1. For each element find the distance to the nearest zero (to the element which equals to zero). There is at least one zero element in the given array.

Input

The first line contains integer n (1 ≤ n ≤ 2·105) — length of the array a. The second line contains integer elements of the array separated by single spaces ( - 109 ≤ ai ≤ 109).

Output

Print the sequence d0, d1, ..., dn - 1, where di is the difference of indices between i and nearest j such that aj = 0. It is possible that i = j.

Examples

Input

9
2 1 0 3 0 0 3 2 4


Output

2 1 0 1 0 0 1 2 3 

Input

5
0 1 2 3 4


Output

0 1 2 3 4 

Input

7
5 6 0 1 -2 3 4


Output

2 1 0 1 2 3 4 
import java.io.*;
import java.util.StringTokenizer;

public class DistToZeroE20B {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner();
        int l = in.nextInt();
        //int l = 200000;
        int[] arr = new int[l];

        
        for (int i = 0; i < l; i++) arr[i] = in.nextInt();
        //for (int i = 0; i < l; i++) arr[i] = 0;
        
        int[] pre = new int[l];
        int[] post = new int[l];
        int last = -1000000000;
        for (int i = 0; i < l; i++) {
            if (arr[i] == 0) last = i;
            pre[i] = i - last;
        }

        last = 1000000000;
        for (int i = l - 1; i >= 0; i--) {
            if (arr[i] == 0) last = i;
            post[i] = last - i;
        }
        
        
        
        for (int i = 0; i < l; i++) System.out.print(Math.min(pre[i], post[i]) + " ");
        System.out.println();
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return null;
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
