Distances to Zero

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

inputFormat

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).

outputFormat

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

样例

7
5 6 0 1 -2 3 4

2 1 0 1 2 3 4