Problem:
Score : 200 points

Problem Statement

There are N + 1 squares arranged in a row, numbered 0, 1, ..., N from left to right.

Initially, you are in Square X.
You can freely travel between adjacent squares. Your goal is to reach Square 0 or Square N.
However, for each i = 1, 2, ..., M, there is a toll gate in Square A_i, and traveling to Square A_i incurs a cost of 1.
It is guaranteed that there is no toll gate in Square 0, Square X and Square N.

Find the minimum cost incurred before reaching the goal.

Constraints

1 \leq N \leq 100

1 \leq M \leq 100

1 \leq X \leq N - 1

1 \leq A_1 < A_2 < ... < A_M \leq N

A_i \neq X

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M X
A_1 A_2 ... A_M

Output

Print the minimum cost incurred before reaching the goal.

Sample Input 1

5 3 3
1 2 4

Sample Output 1

1

The optimal solution is as follows:

First, travel from Square 3 to Square 4. Here, there is a toll gate in Square 4, so the cost of 1 is incurred.

Then, travel from Square 4 to Square 5. This time, no cost is incurred.

Now, we are in Square 5 and we have reached the goal.

In this case, the total cost incurred is 1.

Sample Input 2

7 3 2
4 5 6

Sample Output 2

0

We may be able to reach the goal at no cost.

Sample Input 3

10 7 5
1 2 3 4 6 8 9

Sample Output 3

3

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Scanner;

public class Main {
    public static PrintWriter out;

    public static void main(String[] args) {
        Main.run();
    }

    private static void run() {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next()); // マス目の数
        int m = Integer.parseInt(sc.next()); // 料金所の数
        int x = Integer.parseInt(sc.next()); // 初期地点
        // 料金所マス
        HashSet<Integer> a = new HashSet<>(m);
        for (int i = 0; i < m; i++) {
            a.add(Integer.parseInt(sc.next()));
        }
        // 全てのマス
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n + 1; i++) {
            // 料金所マスは1、それ以外は0とする
            if (a.contains(i)) {
                sb.append(1);
            } else {
                sb.append(0);
            }
        }
        // 初期地点から左右の料金所マスの数を計算
        String left = Main.deleteZero(sb.substring(0, x));
        String right = Main.deleteZero(sb.substring(x + 1));
        int answer = Math.min(left.length(), right.length());
        out.println(answer);
        out.close();
        sc.close();
    }

    /**
     * 引数の文字列から"0"を削除した値を返却
     * @param pstr
     * @return
     */
    private static String deleteZero(String pstr) {
        String str = pstr.replaceAll("0", "_");
        return str.replaceAll("_", "");
    }
}