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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author MaxHeap
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            ArrayList<Integer> zeros = new ArrayList<>();
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = in.nextInt();
                if (arr[i] == 0) {
                    zeros.add(i);
                }
            }
            for (int i = 0; i < n; i++) {
                if (arr[i] == 0) {
                    out.print("0 ");
                } else {

                    int index = Collections.binarySearch(zeros, i);
                    index = index < 0 ? -(index + 1) : index;
                    if (index == zeros.size()) index -= 1;
                    int can1 = index >= 1 ? index - 1 : index;
                    int can2 = index < zeros.size() - 1 ? index + 1 : index;
                    int ans = Math.min(Math.abs(zeros.get(index) - i), Math.min(Math.abs(zeros.get(can1) - i), Math.abs(zeros.get(can2) - i)));
                    out.print(ans + " ");
                }
            }
        }

    }

    static class FastReader {
        BufferedReader reader;
        StringTokenizer st;

        public FastReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            st = null;
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String line = reader.readLine();
                    if (line == null) {
                        return null;
                    }
                    st = new StringTokenizer(line);
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

