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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdint.h>
#include <memory.h>

int main(void)
{
    uint32_t N, M, X;
    uint32_t fee[101];
    scanf("%u %u %u", &N, &M, &X);

    /* default: fee is 0 */
    memset(fee, 0, sizeof(fee));

    /* set fee */
    for (uint32_t m = 0; m < M; m++) {
        uint32_t idx;
        scanf("%u", &idx);
        fee[idx] = 1;
    }

    /* to 0 */
    uint32_t costTo0 = 0;
    for (uint32_t idx = 0; idx <= X; idx++) {
        costTo0 += fee[idx];
    }

    /* to N */
    uint32_t costToN = 0;
    for (uint32_t idx = X; idx <= N; idx++) {
        costToN += fee[idx];
    }

    /* answer */
    printf("%u\n", (costTo0 < costToN) ? costTo0 : costToN);

    return 0;
}