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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {

    /**
     * 本処理を実行します。
     */
    public static void execute() {
        Scanner sc = new Scanner(System.in);

        int n = nextInt(sc);
        String s = nextString(sc);

        StringBuilder sb = new StringBuilder(s);
        int count = 0;

        for (int i = 0;i < n - 2; i++) {
            String xyz = sb.substring(i, i + 3);

            if (xyz.equals("101")) {
                sb.replace(i, i + 3, "010");
                count++;
            }
        }

        out(count);
    }

    /**
     * 次の標準入力をintで受け取ります。
     * @return 標準入力値(int)
     */
    public static int nextInt(Scanner sc) {
        return sc.nextInt();
    }

    /**
     * 次の標準入力をStringで受け取ります。
     * @return 標準入力値(String)
     */
    public static String nextString(Scanner sc) {
        return sc.next();
    }

    /**
     * 次の標準入力を指定回数分intで受け取ります。
     * @param n 取得回数
     * @return 取得した標準入力値の配列(int)
     */
    public static int[] nextInts(Scanner sc, int n) {
        int[] arr = new int[n];

        for (int i = 0; i < n; i++) {
            arr[i] = nextInt(sc);
        }

        return arr;
    }

    /**
     * 標準出力にオブジェクトを出力します。
     * @param o 出力対象
     */
    public static void out(Object o) {
        System.out.println(o);
    }

    public static void main(String[] args) {
        execute();
    }
}