Training Site # Camping Trip

Input: Standard Input (stdin)
Output: Standard Output (stdout)
Memory limit: 256 megabytes
Time limit: 1.0 seconds

Rin loves camping, and is planning to go on a camping trip. However, not all days are good for camping.

Any day with an average temperature between $A$ and $B$ degrees (inclusive) is considered to be a good day. All other days are bad days for camping.

Rin knows what the average temperature will be during each of the next $N$ days, and would like to schedule her trip as an interval $[L,R]$ within this period ($1 \le L \le R \le N$), where her trip starts on day $L$ and ends on day $R$.

She would like to go on the longest trip possible, but she will only consider a trip where the number of good days is strictly greater than the number of bad days on her trip (including days $L$ and $R$).

## Input

The first line contains three space-separated integers, $N$, $A$, and $B$.

The second line contains $N$ space-separated integers, $t_1, t_2, \dots, t_N$, where $t_i$ is the average temperature of day $i$.

## Output

You should output a single integer – the maximum length of any camping trip over the next $N$ days that satisfies Rin's requirement, or $0$ if no such trip exists.

## Constraints

• $1 \le N \le 200\,000$
• $0 \le A \le B \le 50$
• $0 \le t_i \le 50$ for all $i$

• Subtask 1 (15%): $t_i \le t_{i+1}$ for all $i$
• Subtask 2 (20%): $N \le 100$
• Subtask 3 (25%): $N \le 5\,000$
• Subtask 4 (40%): No further constraints apply

## Sample Explanation

In the first sample case, the longest possible camping trip is $[3,7]$ (starting on day 3 and ending on day 7), which is 5 days long. There are 3 good days and 2 bad days on this trip, which meets Rin's requirement.

In the second sample case, there are two possible solutions – $[1,3]$ and $[6,8]$, which are both 3 days long.

Note: Python submissions should use Python 3.6 (PyPy 7.3), as submissions using Python 3.8 may not be fast enough to pass some subtasks.

• ### Sample Input 1

7 21 23
18 18 19 20 21 22 22


### Sample Output 1

5

• ### Sample Input 2

8 21 23
22 24 23 20 20 19 21 22


### Sample Output 2

3