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 
#include <bits/stdc++.h>
using namespace std;
void even_distance(long long dis) {
  long long print = 1;
  for (long long l = 1; l <= (dis / 2); l++) {
    cout << print << " ";
    print++;
  }
  print -= 2;
  for (long long l = 1; l <= dis - (dis / 2); l++) {
    cout << print << " ";
    print--;
  }
}
void odd_distance(long long dis) {
  long long print = 1;
  for (long long l = 1; l <= dis / 2; l++) {
    cout << print << " ";
    print++;
  }
  print--;
  cout << print << " ";
  print--;
  for (long long l = 1; l <= dis / 2; l++) {
    cout << print << " ";
    print--;
  }
}
int main() {
  cout << endl;
  long long len;
  cin >> len;
  vector<long long> cln;
  bool flag = false;
  for (long long x = 1; x <= len; x++) {
    long long val;
    cin >> val;
    if (flag == false && val == 0) {
      cln.push_back(x);
      for (long long l = 1; l <= x; l++) {
        cout << x - l << " ";
      }
      flag = true;
    } else if (flag == true && val == 0) {
      long long dis = x - cln[cln.size() - 1];
      cln.push_back(x);
      if (dis == 1)
        cout << 0 << " ";
      else if (dis % 2 == 0) {
        even_distance(dis);
      } else {
        odd_distance(dis);
      }
    }
  }
  if (len - cln[cln.size() - 1] > 0) {
    long long sz = len - cln[cln.size() - 1];
    for (long long x = 1; x <= sz; x++) {
      cout << x << " ";
    }
  }
  return 0;
}
