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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <vector>

int main() {
  int N, M, X;
  std::cin >> N;
  std::cin >> M;
  std::cin >> X;

  std::vector<int> A;
  A.resize(M);

  for(auto&& Ai : A)
    std::cin >> Ai;
    
  std::vector<bool> B;
  for(int i = 0; i < N+1; i++)
    B.push_back(std::find(std::cbegin(A), std::cend(A), i) != std::cend(A));
  
  const int sum1 = std::count_if(std::cbegin(B) + X, std::cend(B), [](auto x){ return x; });
  const int sum2 = std::count_if(std::cbegin(B), std::cbegin(B) + X, [](auto x){ return x; });
  
  std::cout << (sum1 < sum2 ? sum1 : sum2) << std::endl;
}