Solution

#include <iostream>
using namespace std;

static int find_largest_interior_gap(string s, int& gap_start)
{
    int biggest_gap = 0, current_start = -1, N = s.length();
    for (int i = 0; i < N; i++)
        if (s[i] == '1') {
            if (current_start != -1 && i - current_start > biggest_gap) {
                biggest_gap = i - current_start;
                gap_start = current_start;
            }
            current_start = i;
        }
    return biggest_gap;
}

static int find_smallest_interior_gap(string s)
{
    int smallest_gap = 1000000000, current_start = -1, N = s.length();
    for (int i = 0; i < N; i++)
        if (s[i] == '1') {
            if (current_start != -1 && i - current_start < smallest_gap) smallest_gap = i - current_start;
            current_start = i;
        }
    return smallest_gap;
}

static int try_cow_in_largest_gap(string s)
{
    int gap_start, largest_gap = find_largest_interior_gap(s, gap_start);
    if (largest_gap >= 2) {
        s[static_cast<std::basic_string<char, std::char_traits<char>, std::allocator<char>>::size_type>(gap_start) + largest_gap / 2] = '1';
        return find_smallest_interior_gap(s);
    }
    return -1;
}

int main()
{
    int N;
    string s, temp_s;
    cin >> N >> s;
    int answer = 0;

    int gap_start, largest_gap = find_largest_interior_gap(s, gap_start);
    if (largest_gap >= 3) {
        temp_s = s;
        temp_s[gap_start + largest_gap / 3] = '1';
        temp_s[gap_start + largest_gap * 2 / 3] = '1';
        answer = max(answer, find_smallest_interior_gap(temp_s));
    }

    if (s[0] == '0' && s[N - 1] == '0') {
        temp_s = s; temp_s[0] = temp_s[static_cast<std::basic_string<char, std::char_traits<char>, std::allocator<char>>::size_type>(N) - 1] = '1';
        answer = max(answer, find_smallest_interior_gap(temp_s));
    }

    if (s[0] == '0') {
        temp_s = s; temp_s[0] = '1';
        answer = max(answer, try_cow_in_largest_gap(temp_s));
    }

    if (s[N - 1] == '0') {
        temp_s = s; temp_s[static_cast<std::basic_string<char, std::char_traits<char>, std::allocator<char>>::size_type>(N) - 1] = '1';
        answer = max(answer, try_cow_in_largest_gap(temp_s));
    }
    if (largest_gap >= 2) {
        temp_s = s; temp_s[static_cast<std::basic_string<char, std::char_traits<char>, std::allocator<char>>::size_type>(gap_start) + largest_gap / 2] = '1';
        answer = max(answer, try_cow_in_largest_gap(temp_s));
    }

    cout << answer << "\n";
    return 0;
}