Problem:
Score : 700 points

Problem Statement

N cells are arranged in a row.
Some of them may contain tokens.
You are given a string s that consists of 0s and 1s.
If the i-th character of s is 1, the i-th cell (from left) contains a token.
Otherwise, it doesn't contain a token.

Snuke wants to perform the following operation as many times as possible.
In each operation, he chooses three consecutive cells.
Let's call the cells X, Y, Z from left to right.
In order for the operation to be valid, both X and Z must contain tokens and Y must not contain a token.
Then, he removes these two tokens and puts a new token on Y.

How many operations can he perform if he performs operations in the optimal way?

Constraints

1 \leq N \leq 500,000

|s| = N

Each character in s is either 0 or 1.

Input

Input is given from Standard Input in the following format:

N
s

Output

Print the answer.

Sample Input 1

7
1010101

Sample Output 1

2

For example, he can perform two operations in the following way:

Perform an operation on the last three cells. Now the string that represents tokens becomes 1010010.

Perform an operation on the first three cells. Now the string that represents tokens becomes 0100010.

Note that the choice of operations matters.
For example, if he chooses three cells in the middle first, he can perform no more operations.

Sample Input 2

50
10101000010011011110001001111110000101010111100110

Sample Output 2

10

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Collections.Generic;
using System.Diagnostics;
using Enu = System.Linq.Enumerable;

public class Program
{
    public void Solve()
    {
        int N = Reader.Int();
        var S = Reader.String();
        var A = S.Select(c => c - '0').ToArray();
        var Left = new List<long>();
        var Right = new List<long>();

        for (int i = 0; i + 2 < N; i++)
            if (A[i] == 1 && A[i + 1] == 0 && A[i + 2] == 1)
            {
                int L = i - 1, R = i + 3;
                while (L >= 0 && A[L] == 1) L--;
                while (R < N && A[R] == 1) R++;
                Right.Add(((long)(L + 1) << 32) + (i + 3));
                Left.Add(((long)i << 32) + R);
            }
        Left.Sort();
        Right.Sort();
        var dp = new int[N + 1];
        int nextRight = 0, Li = 0, Ri = 0;
        for (int i = 0; i < N; i++)
        {
            CheckMax(ref dp[i + 1], dp[i]);
            if (Ri < Right.Count && (int)(Right[Ri] >> 32) == i)
                nextRight = (int)Right[Ri++];
            if (nextRight >= i + 3)
                CheckMax(ref dp[nextRight], dp[i] + nextRight - i - 2);
            if (Li < Left.Count && (int)(Left[Li] >> 32) == i)
            {
                int R = (int)Left[Li++];
                for (int next = i + 3; next <= R; next++)
                    CheckMax(ref dp[next], dp[i] + (next - i - 2));
            }
        }

        Console.WriteLine(dp[N]);
    }

    bool CheckMax(ref int a, int b) { if (b > a) { a = b; return true; } return false; }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { Dispose(); A = new string[0]; }
    public static void Set(TextReader r) { Init(); reader = r; }
    public static void Set(string file) { Init(); reader = new StreamReader(file); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    public static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    public static void Dispose() { reader.Dispose(); }
    static string[] Split(string s) { return s.Split(separator, op); }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}