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.IOException;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    public static void main(String[] args){

        FastReader fastReader = new FastReader();

        long n = fastReader.nextLong();
        ArrayList<Long> array = new ArrayList<>();
        TreeSet<Long> set= new TreeSet<>();
        long zeroes = 0;
        for(long i=0 ; i< n ; i++){
            long element = fastReader.nextLong();
            array.add(element);
            if(element==0){
                zeroes++ ;
                set.add(i);
            }
        }

        ArrayList<Long> setArray = new ArrayList<>();
        for(long index : set){
            setArray.add(index);
        }

//        System.out.println("Set array: " + setArray);

        if(zeroes==1){
            long index = array.indexOf(0L);
            for(long i=0 ; i< array.size() ; i++){
                System.out.print(Math.abs(index-i) + " ");
            }
            System.out.println();
        }
        else {
            StringBuilder stringBuilder = new StringBuilder();
            long first = array.indexOf(0L);
            long last = array.lastIndexOf(0L);
            for(long i=0 ; i< array.size() ; i++){
                if(i <= first){
                    stringBuilder.append(Math.abs(i-first) + " ");
                }

                else if(i>=last){
                    stringBuilder.append(Math.abs(i-last) + " ");
                }

                else {
                    long element = array.get((int) i);
                    long index = i;
                    if(element==0){
                        stringBuilder.append(0 + " ");
                    }

                    else {

                        Long p1 = set.ceiling(index);
                        Long p2 = set.floor(index);

                        long ans = Math.min(Math.abs(p1-index) , Math.abs(p2-index));

                        stringBuilder.append(ans+ " ");



//                        ArrayList<Long> firstArray = new ArrayList<>();
//                        ArrayList<Long> secondArray = new ArrayList<>();
//
//                        firstArray.addAll(array.subList((int) first , (int) index+1));
//                        secondArray.addAll(array.subList((int) index , (int) last+1));
//
////                        System.out.println(firstArray);
////                        System.out.println(secondArray);
//
//                        long p1 = Math.abs(firstArray.indexOf(element) - firstArray.lastIndexOf(0L));
//                        long p2 = Math.abs(secondArray.indexOf(element) - secondArray.indexOf(0L));
//
//                        long ans = Math.min(p1 , p2);
//                        stringBuilder.append(ans + " ");


                    }


                }

            }

            System.out.println(stringBuilder.toString());
        }

    }

































































































            static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }



    }

