Toll Gates

AtCoder

IDabc094_b

Time2000ms

Memory256MB

Difficulty—

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: $N$ $M$ $X$ $A_1$ $A_2$ $...$ $A_M$ [samples]

Samples

Input #1

5 3 3
1 2 4

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 $1$.

Input #2

7 3 2
4 5 6

Output #2

0

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

Input #3

10 7 5
1 2 3 4 6 8 9

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Toll Gates",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc094_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N + 1$ squares arranged in a row, numbered $0, 1, ..., N$ from left to right.\nInitially, you are in Square $X$. You can freely travel between adjacent squares. Your goal is to reach Square ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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