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.*;
import java.math.*;

public class Main {

    static final int MAX = 200000 + 10;

    static int[] a = new int[MAX];
    static int[] left = new int[MAX];
    static int[] right = new int[MAX];

    // WRITE CODE HERE
    static void solve() throws IOException {
        int n = in.nextInt();
        for (int i = 1; i <= n; i++) {
            a[i] = in.nextInt();
        }
        left[0] = -MAX * 10;
        for (int i = 1; i <= n; i++) {
            if (a[i] == 0) {
                left[i] = i;
            } else {
                left[i] = left[i - 1];
            }
        }

        right[n + 1] = MAX * 10;
        for (int i = n; i >= 1; i--) {
            if (a[i] == 0) {
                right[i] = i;
            } else {
                right[i] = right[i + 1];
            }
        }

        for (int i = 1; i <= n; i++) {
            out.print(Math.min(i - left[i], right[i] - i) + " ");
        }
    }

    static Scanner inp;
    static InputReader in;
    static PrintWriter out;

    public static void main(String[] args) throws IOException {
        inp = new Scanner(System.in);
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    static class InputReader {

        BufferedReader br;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public int nextInt() throws IOException {
            int c = br.read();
            while (c <= 32) {
                c = br.read();
            }
            boolean negative = false;
            if (c == '-') {
                negative = true;
                c = br.read();
            }
            int x = 0;
            while (c > 32) {
                x = x * 10 + c - '0';
                c = br.read();
            }
            return negative ? -x : x;
        }

        public long nextLong() throws IOException {
            int c = br.read();
            while (c <= 32) {
                c = br.read();
            }
            boolean negative = false;
            if (c == '-') {
                negative = true;
                c = br.read();
            }
            long x = 0;
            while (c > 32) {
                x = x * 10 + c - '0';
                c = br.read();
            }
            return negative ? -x : x;
        }

        public String next() throws IOException {
            int c = br.read();
            while (c <= 32) {
                c = br.read();
            }
            StringBuilder sb = new StringBuilder();
            while (c > 32) {
                sb.append((char) c);
                c = br.read();
            }
            return sb.toString();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }

}
