You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given an integer numberOfUsers representing the total number of users and an array events of size n x 3.
Each events[i] can be either of the following two types:

Message Event: ["MESSAGE", "timestampi", "mentions_stringi"]

This event indicates that a set of users was mentioned in a message at timestampi.
The mentions_stringi string can contain one of the following tokens:

id: where  is an integer in range [0,numberOfUsers - 1]. There can be multiple ids separated by a single whitespace and may contain duplicates. This can mention even the offline users.
ALL: mentions all users.
HERE: mentions all online users.

Offline Event: ["OFFLINE", "timestampi", "idi"]

This event indicates that the user idi had become offline at timestampi for 60 time units. The user will automatically be online again at time timestampi + 60.

Return an array mentions where mentions[i] represents the number of mentions the user with id i has across all MESSAGE events.
All users are initially online, and if a user goes offline or comes back online, their status change is processed before handling any message event that occurs at the same timestamp.
Note that a user can be mentioned multiple times in a single message event, and each mention should be counted separately.

Example 1:

Input: numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","71","HERE"]]
Output: [2,2]
Explanation:
Initially, all users are online.
At timestamp 10, id1 and id0 are mentioned. mentions = [1,1]
At timestamp 11, id0 goes offline.
At timestamp 71, id0 comes back online and "HERE" is mentioned. mentions = [2,2]

Example 2:

Input: numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","12","ALL"]]
Output: [2,2]
Explanation:
Initially, all users are online.
At timestamp 10, id1 and id0 are mentioned. mentions = [1,1]
At timestamp 11, id0 goes offline.
At timestamp 12, "ALL" is mentioned. This includes offline users, so both id0 and id1 are mentioned. mentions = [2,2]

Example 3:

Input: numberOfUsers = 2, events = [["OFFLINE","10","0"],["MESSAGE","12","HERE"]]
Output: [0,1]
Explanation:
Initially, all users are online.
At timestamp 10, id0 goes offline.
At timestamp 12, "HERE" is mentioned. Because id0 is still offline, they will not be mentioned. mentions = [0,1]

Constraints:

1 <= numberOfUsers <= 100
1 <= events.length <= 100
events[i].length == 3
events[i][0] will be one of MESSAGE or OFFLINE.
1 <= int(events[i][1]) <= 105
The number of id mentions in any "MESSAGE" event is between 1 and 100.
0 <=  <= numberOfUsers - 1
It is guaranteed that the user id referenced in the OFFLINE event is online at the time the event occurs.

Your solution to the problem should be a method of the class Solution called countMentions and should pass all tests. Use the following starter code:
```python
class Solution:
    def countMentions(self, numberOfUsers: int, events: List[List[str]]) -> List[int]:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given an integer numberOfUsers representing the total number of users and an array events of size n x 3.
Each events[i] can be either of the following two types:

Message Event: ["MESSAGE", "timestampi", "mentions_stringi"]

This event indicates that a set of users was mentioned in a message at timestampi.
The mentions_stringi string can contain one of the following tokens:

id: where  is an integer in range [0,numberOfUsers - 1]. There can be multiple ids separated by a single whitespace and may contain duplicates. This can mention even the offline users.
ALL: mentions all users.
HERE: mentions all online users.

Offline Event: ["OFFLINE", "timestampi", "idi"]

This event indicates that the user idi had become offline at timestampi for 60 time units. The user will automatically be online again at time timestampi + 60.

Return an array mentions where mentions[i] represents the number of mentions the user with id i has across all MESSAGE events.
All users are initially online, and if a user goes offline or comes back online, their status change is processed before handling any message event that occurs at the same timestamp.
Note that a user can be mentioned multiple times in a single message event, and each mention should be counted separately.

Example 1:

Input: numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","71","HERE"]]
Output: [2,2]
Explanation:
Initially, all users are online.
At timestamp 10, id1 and id0 are mentioned. mentions = [1,1]
At timestamp 11, id0 goes offline.
At timestamp 71, id0 comes back online and "HERE" is mentioned. mentions = [2,2]

Example 2:

Input: numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","12","ALL"]]
Output: [2,2]
Explanation:
Initially, all users are online.
At timestamp 10, id1 and id0 are mentioned. mentions = [1,1]
At timestamp 11, id0 goes offline.
At timestamp 12, "ALL" is mentioned. This includes offline users, so both id0 and id1 are mentioned. mentions = [2,2]

Example 3:

Input: numberOfUsers = 2, events = [["OFFLINE","10","0"],["MESSAGE","12","HERE"]]
Output: [0,1]
Explanation:
Initially, all users are online.
At timestamp 10, id0 goes offline.
At timestamp 12, "HERE" is mentioned. Because id0 is still offline, they will not be mentioned. mentions = [0,1]

Constraints:

1 <= numberOfUsers <= 100
1 <= events.length <= 100
events[i].length == 3
events[i][0] will be one of MESSAGE or OFFLINE.
1 <= int(events[i][1]) <= 105
The number of id mentions in any "MESSAGE" event is between 1 and 100.
0 <=  <= numberOfUsers - 1
It is guaranteed that the user id referenced in the OFFLINE event is online at the time the event occurs.

Your solution to the problem should be a method of the class Solution called countMentions and should pass all tests. Use the following starter code:
```python
class Solution:
    def countMentions(self, numberOfUsers: int, events: List[List[str]]) -> List[int]:
        # Add your code here
```

SOLUTION:

assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","1","id0"],["MESSAGE","1","HERE"],["MESSAGE","1","ALL"]]) == [3]

assert Solution().countMentions(numberOfUsers = 2, events = [["OFFLINE","10","0"],["MESSAGE","12","HERE"]]) == [0, 1]

assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","1"],["MESSAGE","20","HERE"],["MESSAGE","60","ALL"]]) == [3, 2, 3]

assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","5","ALL"],["OFFLINE","10","0"],["MESSAGE","20","HERE"]]) == [1]

assert Solution().countMentions(numberOfUsers = 4, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","ALL"],["MESSAGE","25","id0 id2"]]) == [2, 1, 3, 2]

assert Solution().countMentions(numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","12","ALL"]]) == [2, 2]

assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","5","id0 id1 id2 id3 id4"],["OFFLINE","10","0"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","id2 id3 id4"],["MESSAGE","25","ALL"]]) == [2, 2, 4, 4, 4]

assert Solution().countMentions(numberOfUsers = 4, events = [["MESSAGE","1","id0 id1"],["OFFLINE","2","0"],["MESSAGE","3","HERE"],["MESSAGE","65","id0"],["OFFLINE","70","1"],["MESSAGE","75","ALL"]]) == [3, 3, 2, 2]

assert Solution().countMentions(numberOfUsers = 3, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["MESSAGE","15","id0 id1 id2"],["MESSAGE","20","HERE"],["MESSAGE","25","ALL"]]) == [2, 2, 3]

assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","ALL"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["OFFLINE","20","2"],["MESSAGE","25","id0 id1 id2"]]) == [3, 2, 3]

assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","1","id0"],["OFFLINE","10","0"],["MESSAGE","20","HERE"]]) == [1]

assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","1","ALL"],["OFFLINE","61","0"],["MESSAGE","120","HERE"]]) == [1]

assert Solution().countMentions(numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","71","HERE"]]) == [2, 2]

assert Solution().countMentions(numberOfUsers = 4, events = [["OFFLINE","20","0"],["MESSAGE","25","HERE"],["OFFLINE","30","1"],["MESSAGE","35","ALL"]]) == [1, 2, 2, 2]

assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","1"],["MESSAGE","20","HERE"],["MESSAGE","30","ALL"]]) == [3, 2, 3]

assert Solution().countMentions(numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","71","HERE"]] ) == [2, 2]

assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","ALL"]]) == [3, 2, 3]

assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","5","id0 id1 id2 id3 id4"],["OFFLINE","10","0"],["MESSAGE","20","HERE"],["OFFLINE","25","1"],["MESSAGE","30","ALL"]]) == [2, 3, 3, 3, 3]

Answer: assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","1","id0"],["MESSAGE","1","HERE"],["MESSAGE","1","ALL"]]) == [3]

Answer: assert Solution().countMentions(numberOfUsers = 2, events = [["OFFLINE","10","0"],["MESSAGE","12","HERE"]]) == [0, 1]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","1"],["MESSAGE","20","HERE"],["MESSAGE","60","ALL"]]) == [3, 2, 3]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","1","id0 id1 id2 id3 id4"],["OFFLINE","2","0"],["OFFLINE","3","1"],["MESSAGE","4","HERE"],["MESSAGE","65","id0 id1"],["OFFLINE","70","2"],["MESSAGE","75","ALL"]]) == [3, 3, 3, 3, 3]

Answer: assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","5","ALL"],["OFFLINE","10","0"],["MESSAGE","20","HERE"]]) == [1]

Answer: assert Solution().countMentions(numberOfUsers = 4, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","ALL"],["MESSAGE","25","id0 id2"]]) == [2, 1, 3, 2]

Answer: assert Solution().countMentions(numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","12","ALL"]]) == [2, 2]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","5","id0 id1 id2 id3 id4"],["OFFLINE","10","0"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","id2 id3 id4"],["MESSAGE","25","ALL"]]) == [2, 2, 4, 4, 4]

Answer: assert Solution().countMentions(numberOfUsers = 4, events = [["MESSAGE","1","id0 id1"],["OFFLINE","2","0"],["MESSAGE","3","HERE"],["MESSAGE","65","id0"],["OFFLINE","70","1"],["MESSAGE","75","ALL"]]) == [3, 3, 2, 2]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["MESSAGE","15","id0 id1 id2"],["MESSAGE","20","HERE"],["MESSAGE","25","ALL"]]) == [2, 2, 3]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","ALL"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["OFFLINE","20","2"],["MESSAGE","25","id0 id1 id2"]]) == [3, 2, 3]

Answer: assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","1","id0"],["OFFLINE","10","0"],["MESSAGE","20","HERE"]]) == [1]

Answer: assert Solution().countMentions(numberOfUsers = 1, events = [["MESSAGE","1","ALL"],["OFFLINE","61","0"],["MESSAGE","120","HERE"]]) == [1]

Answer: assert Solution().countMentions(numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","71","HERE"]]) == [2, 2]

Answer: assert Solution().countMentions(numberOfUsers = 4, events = [["OFFLINE","20","0"],["MESSAGE","25","HERE"],["OFFLINE","30","1"],["MESSAGE","35","ALL"]]) == [1, 2, 2, 2]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","1"],["MESSAGE","20","HERE"],["MESSAGE","30","ALL"]]) == [3, 2, 3]

Answer: assert Solution().countMentions(numberOfUsers = 2, events = [["MESSAGE","10","id1 id0"],["OFFLINE","11","0"],["MESSAGE","71","HERE"]] ) == [2, 2]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","ALL"]]) == [3, 2, 3]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","5","id0 id1 id2 id3 id4"],["OFFLINE","10","0"],["MESSAGE","20","HERE"],["OFFLINE","25","1"],["MESSAGE","30","ALL"]]) == [2, 3, 3, 3, 3]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","1","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","10","0"],["OFFLINE","20","1"],["MESSAGE","30","HERE"],["OFFLINE","40","2"],["OFFLINE","50","3"],["OFFLINE","60","4"],["MESSAGE","70","HERE"],["OFFLINE","80","5"],["OFFLINE","90","6"],["MESSAGE","100","HERE"],["OFFLINE","110","7"],["OFFLINE","120","8"],["MESSAGE","130","HERE"],["OFFLINE","140","9"],["MESSAGE","150","ALL"]]) == [5, 4, 5, 4, 4, 4, 4, 5, 5, 6]

Answer: assert Solution().countMentions(numberOfUsers = 7, events = [["MESSAGE","1","id0 id0 id1 id1 id2 id2 id3 id3 id4 id4 id5 id5 id6 id6"],["OFFLINE","2","0"],["MESSAGE","3","HERE"],["OFFLINE","4","1"],["MESSAGE","5","ALL"],["OFFLINE","6","2"],["MESSAGE","10","id0 id2"],["OFFLINE","11","3"],["MESSAGE","15","HERE"],["OFFLINE","16","4"],["MESSAGE","20","ALL"],["MESSAGE","25","id0 id1 id2 id3 id4 id5 id6 id0 id1 id2 id3 id4 id5 id6"],["OFFLINE","26","0"],["MESSAGE","30","HERE"],["OFFLINE","31","1"],["MESSAGE","35","ALL"],["OFFLINE","36","2"],["MESSAGE","40","id0 id1 id2 id3 id4 id5 id6 id0 id1 id2 id3 id4 id5 id6"],["OFFLINE","41","3"],["MESSAGE","45","HERE"],["OFFLINE","46","4"],["MESSAGE","50","ALL"],["OFFLINE","51","5"],["MESSAGE","55","id0 id1 id2 id3 id4 id5 id6 id0 id1 id2 id3 id4 id5 id6"],["OFFLINE","56","6"],["MESSAGE","60","HERE"],["MESSAGE","65","ALL"]]) == [14, 14, 15, 14, 15, 17, 17]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","1","id0 id1"],["OFFLINE","2","0"],["OFFLINE","3","1"],["MESSAGE","4","HERE"],["OFFLINE","5","2"],["OFFLINE","6","3"],["MESSAGE","7","HERE"],["OFFLINE","8","4"],["MESSAGE","9","HERE"],["MESSAGE","61","id0 id1 id2 id3 id4"],["MESSAGE","62","HERE"],["MESSAGE","121","ALL"],["MESSAGE","122","HERE"]]) == [5, 4, 4, 4, 5]

Answer: assert Solution().countMentions(numberOfUsers = 7, events = [["MESSAGE","10","id0 id1"],["OFFLINE","15","0"],["MESSAGE","20","id0 id1 id2"],["OFFLINE","25","1"],["MESSAGE","30","HERE"],["OFFLINE","35","2"],["MESSAGE","40","id0 id1 id2 id3 id4"],["OFFLINE","45","3"],["MESSAGE","50","id0 id1 id2 id3 id4 id5 id6"],["MESSAGE","90","HERE"],["OFFLINE","95","4"],["MESSAGE","100","ALL"]]) == [6, 6, 5, 4, 5, 4, 4]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","5","id1 id2"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["OFFLINE","20","2"],["MESSAGE","25","HERE"],["OFFLINE","30","3"],["MESSAGE","35","HERE"],["OFFLINE","40","4"],["MESSAGE","45","HERE"],["OFFLINE","50","5"],["MESSAGE","55","HERE"],["OFFLINE","60","6"],["MESSAGE","65","HERE"],["OFFLINE","70","7"],["MESSAGE","75","HERE"],["OFFLINE","80","8"],["MESSAGE","85","HERE"],["OFFLINE","90","9"],["MESSAGE","95","HERE"],["MESSAGE","100","ALL"],["MESSAGE","110","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","115","0"],["MESSAGE","120","HERE"],["MESSAGE","130","ALL"],["OFFLINE","135","1"],["MESSAGE","140","HERE"],["MESSAGE","150","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","155","2"],["MESSAGE","160","HERE"],["MESSAGE","170","ALL"]]) == [8, 16, 11, 11, 11, 12, 13, 13, 14, 14]

Answer: assert Solution().countMentions(numberOfUsers = 8, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["OFFLINE","15","2"],["MESSAGE","20","HERE"],["OFFLINE","25","3"],["MESSAGE","30","id0 id1 id2 id3"],["OFFLINE","35","4"],["OFFLINE","40","5"],["MESSAGE","45","id0 id1 id2 id3 id4 id5"],["OFFLINE","50","6"],["MESSAGE","55","HERE"],["OFFLINE","60","7"],["MESSAGE","65","ALL"],["MESSAGE","70","HERE"],["MESSAGE","75","id0 id1 id2 id3 id4 id5 id6 id7"]]) == [5, 5, 4, 5, 4, 4, 3, 4]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","1","ALL"],["OFFLINE","2","0"],["OFFLINE","3","1"],["MESSAGE","4","HERE"],["OFFLINE","5","2"],["MESSAGE","6","HERE"],["MESSAGE","61","id0 id1 id2"],["MESSAGE","62","HERE"],["MESSAGE","121","ALL"],["MESSAGE","122","HERE"]]) == [5, 4, 5]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","5","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","15","0"],["MESSAGE","20","HERE"],["OFFLINE","25","1"],["MESSAGE","30","ALL"],["OFFLINE","35","2"],["MESSAGE","45","HERE"],["OFFLINE","50","3"],["MESSAGE","55","ALL"],["OFFLINE","65","4"],["MESSAGE","70","HERE"],["OFFLINE","75","5"],["MESSAGE","80","ALL"],["OFFLINE","85","6"],["MESSAGE","90","HERE"],["OFFLINE","95","7"],["MESSAGE","100","ALL"],["OFFLINE","105","8"],["MESSAGE","110","HERE"],["OFFLINE","115","9"],["MESSAGE","120","ALL"]]) == [8, 9, 8, 9, 8, 9, 9, 10, 10, 11]

Answer: assert Solution().countMentions(numberOfUsers = 15, events = [["MESSAGE","1","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14"],["OFFLINE","2","0"],["MESSAGE","3","HERE"],["OFFLINE","4","1"],["MESSAGE","5","ALL"],["OFFLINE","6","2"],["MESSAGE","10","id0 id2"],["OFFLINE","11","3"],["MESSAGE","15","HERE"],["OFFLINE","16","4"],["MESSAGE","20","ALL"],["OFFLINE","21","5"],["MESSAGE","25","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14"],["OFFLINE","26","6"],["MESSAGE","30","HERE"],["OFFLINE","31","7"],["MESSAGE","35","ALL"],["OFFLINE","36","8"],["MESSAGE","40","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14"],["OFFLINE","41","9"],["MESSAGE","45","HERE"],["OFFLINE","46","10"],["MESSAGE","50","ALL"],["OFFLINE","51","11"],["MESSAGE","55","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14"],["OFFLINE","56","12"],["MESSAGE","60","HERE"],["OFFLINE","61","13"],["MESSAGE","65","ALL"],["OFFLINE","66","14"],["MESSAGE","70","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14"]]) == [11, 11, 12, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15]

Answer: assert Solution().countMentions(numberOfUsers = 8, events = [["OFFLINE","10","0"],["MESSAGE","20","HERE"],["OFFLINE","30","1"],["MESSAGE","40","HERE"],["OFFLINE","50","2"],["MESSAGE","60","HERE"],["OFFLINE","70","3"],["MESSAGE","80","HERE"],["OFFLINE","90","4"],["MESSAGE","100","HERE"],["OFFLINE","110","5"],["MESSAGE","120","HERE"],["OFFLINE","130","6"],["MESSAGE","140","HERE"],["OFFLINE","150","7"],["MESSAGE","160","HERE"],["MESSAGE","200","ALL"]]) == [6, 6, 6, 6, 6, 6, 7, 8]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["MESSAGE","1","id0 id1 id2 id3 id4 id5"],["OFFLINE","10","0"],["MESSAGE","20","HERE"],["OFFLINE","30","1"],["MESSAGE","40","ALL"],["OFFLINE","50","2"],["MESSAGE","60","HERE"],["OFFLINE","70","3"],["MESSAGE","80","ALL"],["OFFLINE","90","4"],["MESSAGE","100","HERE"],["OFFLINE","110","5"],["MESSAGE","120","ALL"],["MESSAGE","130","HERE"],["MESSAGE","140","ALL"]]) == [7, 8, 7, 8, 7, 8]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","10","id0 id1"],["OFFLINE","15","0"],["MESSAGE","20","HERE"],["OFFLINE","25","1"],["MESSAGE","30","ALL"],["MESSAGE","40","id0 id1"],["MESSAGE","50","HERE"],["OFFLINE","55","2"],["MESSAGE","60","ALL"],["MESSAGE","70","id0 id1 id2"],["MESSAGE","80","HERE"],["MESSAGE","90","ALL"]]) == [7, 7, 6]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["OFFLINE","15","2"],["MESSAGE","20","ALL"],["MESSAGE","25","HERE"],["OFFLINE","30","3"],["OFFLINE","35","4"],["MESSAGE","40","id0 id1 id2 id3 id4"],["MESSAGE","80","HERE"],["MESSAGE","100","ALL"]]) == [4, 4, 4, 4, 4]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["OFFLINE","10","0"],["MESSAGE","12","HERE"],["OFFLINE","20","1"],["MESSAGE","25","HERE"],["OFFLINE","30","2"],["MESSAGE","35","HERE"],["OFFLINE","40","3"],["MESSAGE","45","HERE"],["OFFLINE","50","4"],["MESSAGE","55","HERE"],["OFFLINE","60","5"],["MESSAGE","65","HERE"],["MESSAGE","70","ALL"],["MESSAGE","75","id0 id1 id2 id3 id4 id5"],["OFFLINE","80","0"],["MESSAGE","85","HERE"],["MESSAGE","90","id0 id1 id2 id3 id4 id5"],["OFFLINE","95","1"],["MESSAGE","100","HERE"],["MESSAGE","110","ALL"]]) == [4, 6, 7, 8, 8, 9]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["MESSAGE","10","id0 id1 id2"],["OFFLINE","15","0"],["OFFLINE","20","1"],["OFFLINE","25","2"],["MESSAGE","30","HERE"],["OFFLINE","35","3"],["MESSAGE","40","id3 id4"],["OFFLINE","45","4"],["MESSAGE","50","HERE"],["OFFLINE","55","5"],["MESSAGE","60","ALL"],["MESSAGE","100","id0 id1 id2 id3 id4 id5"],["MESSAGE","150","HERE"],["MESSAGE","200","ALL"]]) == [5, 5, 5, 6, 6, 6]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","10","id0 id1 id2 id3 id4"],["OFFLINE","20","0"],["MESSAGE","30","HERE"],["MESSAGE","40","ALL"],["OFFLINE","50","1"],["MESSAGE","60","HERE"],["MESSAGE","70","ALL"],["OFFLINE","80","2"],["MESSAGE","90","HERE"],["MESSAGE","100","ALL"],["OFFLINE","110","3"],["MESSAGE","120","HERE"],["MESSAGE","130","ALL"],["OFFLINE","140","4"],["MESSAGE","150","HERE"],["MESSAGE","160","ALL"]]) == [9, 9, 9, 9, 10]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","1","id0 id1 id2 id3 id4"],["OFFLINE","5","0"],["OFFLINE","10","1"],["OFFLINE","15","2"],["MESSAGE","20","HERE"],["OFFLINE","25","3"],["MESSAGE","30","ALL"],["OFFLINE","35","4"],["MESSAGE","40","id0 id1 id2 id3 id4"],["MESSAGE","80","HERE"]]) == [4, 4, 4, 4, 4, 3, 3, 3, 3, 3]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","5","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","15","0"],["MESSAGE","25","id1 id2 id3 id4"],["OFFLINE","35","1"],["MESSAGE","45","id2 id3 id4 id5"],["OFFLINE","55","2"],["MESSAGE","65","id3 id4 id5 id6"],["OFFLINE","75","3"],["MESSAGE","85","id4 id5 id6 id7"],["OFFLINE","95","4"],["MESSAGE","105","id5 id6 id7 id8"],["OFFLINE","115","5"],["MESSAGE","125","id6 id7 id8 id9"],["OFFLINE","135","6"],["MESSAGE","145","id7 id8 id9"],["OFFLINE","155","7"],["MESSAGE","165","id8 id9"],["OFFLINE","175","8"],["MESSAGE","185","id9"],["OFFLINE","195","9"],["MESSAGE","205","HERE"],["MESSAGE","215","ALL"]]) == [3, 4, 5, 6, 7, 7, 7, 6, 6, 6]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","1","id0"],["OFFLINE","2","0"],["MESSAGE","3","id0"],["OFFLINE","4","1"],["MESSAGE","5","id1"],["OFFLINE","6","2"],["MESSAGE","7","id2"],["OFFLINE","8","3"],["MESSAGE","9","id3"],["OFFLINE","10","4"],["MESSAGE","11","id4"],["MESSAGE","12","HERE"],["MESSAGE","13","ALL"]]) == [3, 2, 2, 2, 2]

Answer: assert Solution().countMentions(numberOfUsers = 15, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["OFFLINE","15","2"],["MESSAGE","20","HERE"],["OFFLINE","25","3"],["MESSAGE","30","id0 id1 id2 id3"],["OFFLINE","35","4"],["OFFLINE","40","5"],["MESSAGE","45","id0 id1 id2 id3 id4 id5"],["OFFLINE","50","6"],["MESSAGE","55","HERE"],["OFFLINE","60","7"],["MESSAGE","65","ALL"],["OFFLINE","70","8"],["MESSAGE","75","HERE"],["OFFLINE","80","9"],["MESSAGE","85","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","90","10"],["MESSAGE","95","HERE"],["OFFLINE","100","11"],["MESSAGE","105","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11"],["OFFLINE","110","12"],["MESSAGE","115","ALL"],["OFFLINE","120","13"],["MESSAGE","125","HERE"],["OFFLINE","130","14"],["MESSAGE","135","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14"]]) == [10, 10, 10, 10, 9, 8, 7, 8, 7, 8, 7, 8, 7, 7, 8]

Answer: assert Solution().countMentions(numberOfUsers = 8, events = [["MESSAGE","5","id1 id2"],["OFFLINE","10","0"],["OFFLINE","20","1"],["MESSAGE","25","HERE"],["OFFLINE","30","2"],["OFFLINE","30","3"],["MESSAGE","40","id0 id1 id2 id3"],["MESSAGE","80","ALL"],["OFFLINE","100","4"],["OFFLINE","100","5"],["MESSAGE","120","HERE"],["MESSAGE","140","id4 id5"],["OFFLINE","150","6"],["MESSAGE","160","ALL"]]) == [4, 5, 6, 5, 4, 4, 4, 4]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["OFFLINE","20","1"],["MESSAGE","25","HERE"],["MESSAGE","70","ALL"],["OFFLINE","80","2"],["MESSAGE","90","HERE"],["MESSAGE","150","ALL"]]) == [4, 5, 5]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["OFFLINE","10","0"],["OFFLINE","20","1"],["MESSAGE","30","HERE"],["OFFLINE","40","2"],["OFFLINE","50","3"],["MESSAGE","60","id0 id1 id2 id3"],["OFFLINE","70","4"],["MESSAGE","80","HERE"],["MESSAGE","90","id4 id5"],["OFFLINE","100","5"],["OFFLINE","110","6"],["MESSAGE","120","id6 id7"],["OFFLINE","130","7"],["MESSAGE","140","HERE"],["MESSAGE","150","id8 id9"],["OFFLINE","160","8"],["OFFLINE","170","9"],["MESSAGE","180","ALL"]]) == [4, 4, 4, 4, 4, 4, 4, 4, 5, 5]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","1","id0 id1 id2 id3 id4"],["OFFLINE","2","0"],["OFFLINE","3","1"],["MESSAGE","4","HERE"],["MESSAGE","5","id5 id6 id7 id8 id9"],["OFFLINE","6","2"],["MESSAGE","65","id0 id1"],["OFFLINE","70","3"],["MESSAGE","75","ALL"],["OFFLINE","120","4"],["MESSAGE","125","HERE"],["OFFLINE","130","5"],["MESSAGE","135","ALL"],["OFFLINE","140","6"],["MESSAGE","145","HERE"],["OFFLINE","150","7"],["MESSAGE","155","ALL"],["OFFLINE","160","8"],["MESSAGE","165","HERE"],["OFFLINE","170","9"],["MESSAGE","175","ALL"]]) == [9, 9, 9, 8, 6, 7, 7, 8, 8, 9]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","1","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","2","0"],["MESSAGE","3","HERE"],["OFFLINE","4","1"],["MESSAGE","5","ALL"],["OFFLINE","6","2"],["MESSAGE","10","id0 id2"],["OFFLINE","11","3"],["MESSAGE","15","HERE"],["OFFLINE","16","4"],["MESSAGE","20","ALL"],["OFFLINE","21","5"],["MESSAGE","25","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","26","6"],["MESSAGE","30","HERE"],["OFFLINE","31","7"],["MESSAGE","35","ALL"],["OFFLINE","36","8"],["MESSAGE","40","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","41","9"],["MESSAGE","45","HERE"],["MESSAGE","50","ALL"]]) == [8, 8, 9, 8, 9, 9, 9, 10, 10, 10]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","10","id0 id1 id2 id3 id4"],["OFFLINE","20","0"],["MESSAGE","30","HERE"],["OFFLINE","40","1"],["MESSAGE","50","HERE"],["OFFLINE","60","2"],["MESSAGE","70","HERE"],["OFFLINE","80","3"],["MESSAGE","90","HERE"],["OFFLINE","100","4"],["MESSAGE","110","HERE"],["MESSAGE","120","ALL"]]) == [4, 4, 4, 5, 6]

Answer: assert Solution().countMentions(numberOfUsers = 7, events = [["OFFLINE","5","0"],["MESSAGE","10","HERE"],["OFFLINE","15","1"],["MESSAGE","20","HERE"],["OFFLINE","25","2"],["MESSAGE","30","HERE"],["OFFLINE","35","3"],["MESSAGE","40","HERE"],["OFFLINE","45","4"],["MESSAGE","50","HERE"],["OFFLINE","55","5"],["MESSAGE","60","HERE"],["OFFLINE","65","6"],["MESSAGE","70","HERE"],["MESSAGE","75","ALL"],["MESSAGE","80","id0 id1 id2 id3 id4 id5 id6 id0 id1 id2 id3 id4 id5 id6"],["MESSAGE","85","HERE"],["MESSAGE","90","ALL"]]) == [6, 6, 7, 7, 8, 9, 10]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["MESSAGE","5","id0 id1 id2 id3 id4 id5"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["OFFLINE","20","1"],["MESSAGE","25","HERE"],["OFFLINE","30","2"],["MESSAGE","35","HERE"],["OFFLINE","40","3"],["MESSAGE","45","HERE"],["OFFLINE","50","4"],["MESSAGE","55","HERE"],["OFFLINE","60","5"],["MESSAGE","65","HERE"],["MESSAGE","70","ALL"],["MESSAGE","75","id0 id1 id2 id3 id4 id5 id0 id1 id2 id3 id4 id5"],["MESSAGE","80","HERE"],["MESSAGE","85","ALL"]]) == [6, 7, 7, 8, 9, 10]

Answer: assert Solution().countMentions(numberOfUsers = 20, events = [["MESSAGE","1","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"],["OFFLINE","2","0"],["MESSAGE","3","HERE"],["OFFLINE","4","1"],["MESSAGE","5","ALL"],["OFFLINE","6","2"],["MESSAGE","10","id0 id2"],["OFFLINE","11","3"],["MESSAGE","15","HERE"],["OFFLINE","16","4"],["MESSAGE","20","ALL"],["OFFLINE","21","5"],["MESSAGE","25","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"],["OFFLINE","26","6"],["MESSAGE","30","HERE"],["OFFLINE","31","7"],["MESSAGE","35","ALL"],["OFFLINE","36","8"],["MESSAGE","40","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"],["OFFLINE","41","9"],["MESSAGE","45","HERE"],["OFFLINE","46","10"],["MESSAGE","50","ALL"],["OFFLINE","51","11"],["MESSAGE","55","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"],["OFFLINE","56","12"],["MESSAGE","60","HERE"],["OFFLINE","61","13"],["MESSAGE","65","ALL"],["OFFLINE","66","14"],["MESSAGE","70","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"],["OFFLINE","71","15"],["MESSAGE","75","HERE"],["OFFLINE","76","16"],["MESSAGE","80","ALL"],["OFFLINE","81","17"],["MESSAGE","85","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"],["OFFLINE","86","18"],["MESSAGE","90","HERE"],["OFFLINE","91","19"],["MESSAGE","95","ALL"]]) == [16, 16, 17, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20]

Answer: assert Solution().countMentions(numberOfUsers = 7, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","id0 id1 id2"],["OFFLINE","25","2"],["OFFLINE","30","3"],["MESSAGE","35","HERE"],["MESSAGE","40","id4 id4 id4"],["OFFLINE","45","4"],["OFFLINE","50","5"],["MESSAGE","55","HERE"],["MESSAGE","60","id5 id5 id5"],["OFFLINE","65","6"],["MESSAGE","70","HERE"],["MESSAGE","75","ALL"]]) == [3, 3, 3, 2, 6, 6, 4]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","10","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","15","0"],["MESSAGE","20","HERE"],["OFFLINE","25","1"],["MESSAGE","30","id2 id3 id4"],["OFFLINE","35","2"],["MESSAGE","40","ALL"],["MESSAGE","45","id0 id1"],["OFFLINE","50","3"],["MESSAGE","55","HERE"],["OFFLINE","60","4"],["MESSAGE","65","id0 id1 id2 id3 id4"],["MESSAGE","75","ALL"]]) == [5, 6, 6, 6, 7, 5, 5, 5, 5, 5]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["OFFLINE","10","0"],["MESSAGE","12","HERE"],["MESSAGE","20","ALL"],["MESSAGE","65","id0"],["OFFLINE","70","2"],["MESSAGE","75","HERE"],["MESSAGE","80","id0 id2"],["OFFLINE","90","1"],["MESSAGE","100","HERE"],["MESSAGE","120","ALL"]]) == [6, 4, 4]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","1","id0 id1"],["OFFLINE","15","0"],["MESSAGE","20","id0 id2"],["OFFLINE","25","1"],["MESSAGE","30","HERE"],["OFFLINE","35","2"],["MESSAGE","40","ALL"],["MESSAGE","45","id0"],["MESSAGE","50","id1"],["MESSAGE","55","id2"],["OFFLINE","60","0"],["OFFLINE","65","1"],["MESSAGE","70","HERE"],["OFFLINE","75","2"],["MESSAGE","80","ALL"]]) == [5, 4, 5]

Answer: assert Solution().countMentions(numberOfUsers = 7, events = [["MESSAGE","1","id1 id2"],["OFFLINE","2","0"],["OFFLINE","3","1"],["MESSAGE","4","HERE"],["OFFLINE","5","2"],["OFFLINE","6","3"],["MESSAGE","7","HERE"],["OFFLINE","8","4"],["MESSAGE","9","HERE"],["MESSAGE","61","id0 id1 id2 id3 id4 id5 id6"],["MESSAGE","62","HERE"],["MESSAGE","121","ALL"],["MESSAGE","122","HERE"]]) == [4, 4, 5, 4, 5, 7, 7]

Answer: assert Solution().countMentions(numberOfUsers = 7, events = [["MESSAGE","1","id0 id1 id2"],["OFFLINE","10","0"],["MESSAGE","20","id3 id4 id5"],["OFFLINE","30","1"],["MESSAGE","40","id0 id1"],["OFFLINE","50","2"],["MESSAGE","60","HERE"],["OFFLINE","70","3"],["MESSAGE","80","ALL"],["OFFLINE","90","4"],["MESSAGE","100","id0 id1 id2"],["OFFLINE","110","5"],["MESSAGE","120","HERE"],["OFFLINE","130","6"],["MESSAGE","140","ALL"],["MESSAGE","150","HERE"],["MESSAGE","160","ALL"]]) == [8, 8, 7, 6, 6, 5, 5]

Answer: assert Solution().countMentions(numberOfUsers = 8, events = [["MESSAGE","1","id0 id1 id2 id3 id4 id5 id6 id7"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["OFFLINE","20","1"],["MESSAGE","25","HERE"],["OFFLINE","30","2"],["MESSAGE","35","HERE"],["OFFLINE","35","3"],["MESSAGE","40","HERE"],["OFFLINE","45","4"],["MESSAGE","50","HERE"],["OFFLINE","55","5"],["MESSAGE","60","HERE"],["OFFLINE","65","6"],["MESSAGE","70","HERE"],["OFFLINE","75","7"],["MESSAGE","80","HERE"],["MESSAGE","85","ALL"],["MESSAGE","90","id0 id1 id2 id3 id4 id5 id6 id7 id0 id1 id2 id3 id4 id5 id6 id7"],["MESSAGE","95","HERE"],["MESSAGE","100","ALL"]]) == [8, 8, 8, 8, 9, 10, 11, 12]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","1","id0"],["MESSAGE","2","id1"],["MESSAGE","3","id2"],["MESSAGE","4","id3"],["MESSAGE","5","id4"],["MESSAGE","6","id5"],["MESSAGE","7","id6"],["MESSAGE","8","id7"],["MESSAGE","9","id8"],["MESSAGE","10","id9"],["OFFLINE","11","0"],["OFFLINE","21","1"],["OFFLINE","31","2"],["OFFLINE","41","3"],["OFFLINE","51","4"],["OFFLINE","61","5"],["OFFLINE","71","6"],["OFFLINE","81","7"],["OFFLINE","91","8"],["OFFLINE","101","9"],["MESSAGE","110","HERE"],["MESSAGE","120","ALL"]]) == [3, 3, 3, 3, 2, 2, 2, 2, 2, 2]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["OFFLINE","20","1"],["MESSAGE","25","ALL"],["OFFLINE","30","2"],["MESSAGE","35","HERE"],["OFFLINE","40","3"],["MESSAGE","45","ALL"],["OFFLINE","50","4"],["MESSAGE","55","HERE"],["OFFLINE","60","5"],["MESSAGE","65","ALL"]]) == [4, 5, 5, 5, 5, 6]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","5","id1 id2"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["OFFLINE","20","2"],["MESSAGE","25","HERE"],["OFFLINE","30","3"],["MESSAGE","35","HERE"],["OFFLINE","40","4"],["MESSAGE","45","HERE"],["MESSAGE","55","ALL"],["OFFLINE","60","1"],["MESSAGE","65","HERE"],["MESSAGE","70","id1 id2 id3 id4"],["OFFLINE","75","0"],["MESSAGE","80","HERE"],["MESSAGE","90","ALL"]]) == [2, 8, 6, 5, 6]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["MESSAGE","5","id1 id2 id3 id4 id5"],["OFFLINE","10","0"],["OFFLINE","10","1"],["MESSAGE","20","HERE"],["MESSAGE","70","id0 id1"],["OFFLINE","80","2"],["OFFLINE","80","3"],["MESSAGE","100","ALL"]]) == [2, 3, 3, 3, 3, 3]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["MESSAGE","5","id1 id1 id2 id2"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["MESSAGE","20","id0 id0 id0 id0"],["OFFLINE","25","2"],["MESSAGE","30","HERE"],["MESSAGE","35","id3 id3 id3"],["OFFLINE","40","3"],["MESSAGE","45","HERE"],["MESSAGE","50","ALL"],["OFFLINE","55","4"],["OFFLINE","60","5"],["MESSAGE","65","HERE"],["MESSAGE","70","ALL"]]) == [10, 4, 5, 7, 5, 5]

Answer: assert Solution().countMentions(numberOfUsers = 8, events = [["OFFLINE","15","0"],["OFFLINE","20","1"],["OFFLINE","25","2"],["MESSAGE","30","HERE"],["MESSAGE","35","ALL"],["OFFLINE","40","3"],["OFFLINE","45","4"],["MESSAGE","50","HERE"],["OFFLINE","55","5"],["MESSAGE","60","ALL"],["OFFLINE","65","6"],["MESSAGE","70","HERE"],["OFFLINE","75","7"],["MESSAGE","80","ALL"]]) == [3, 3, 3, 4, 4, 5, 5, 6]

Answer: assert Solution().countMentions(numberOfUsers = 20, events = [["MESSAGE","5","id0 id1 id2 id3 id4 id5 id6 id7"],["OFFLINE","10","0"],["OFFLINE","15","1"],["OFFLINE","20","2"],["OFFLINE","25","3"],["MESSAGE","30","HERE"],["OFFLINE","35","4"],["OFFLINE","40","5"],["OFFLINE","45","6"],["OFFLINE","50","7"],["MESSAGE","55","ALL"],["OFFLINE","60","8"],["OFFLINE","65","9"],["OFFLINE","70","10"],["MESSAGE","75","HERE"],["OFFLINE","80","11"],["OFFLINE","85","12"],["OFFLINE","90","13"],["MESSAGE","95","ALL"],["OFFLINE","100","14"],["MESSAGE","105","HERE"],["OFFLINE","110","15"],["OFFLINE","115","16"],["MESSAGE","120","ALL"],["OFFLINE","125","17"],["MESSAGE","130","HERE"],["OFFLINE","135","18"],["MESSAGE","140","ALL"],["OFFLINE","145","19"],["MESSAGE","150","HERE"]]) == [9, 9, 8, 8, 9, 9, 9, 8, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 8, 8]

Answer: assert Solution().countMentions(numberOfUsers = 6, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["MESSAGE","15","HERE"],["OFFLINE","20","2"],["MESSAGE","25","id0 id1 id2"],["OFFLINE","30","3"],["MESSAGE","35","HERE"],["OFFLINE","40","4"],["MESSAGE","45","id0 id1 id2 id3 id4"],["OFFLINE","50","5"],["MESSAGE","55","ALL"],["MESSAGE","60","HERE"],["MESSAGE","65","id0 id1 id2 id3 id4 id5"]]) == [4, 4, 5, 4, 5, 4]

Answer: assert Solution().countMentions(numberOfUsers = 20, events = [["OFFLINE","5","0"],["OFFLINE","10","1"],["OFFLINE","15","2"],["MESSAGE","20","HERE"],["OFFLINE","25","3"],["MESSAGE","30","id0 id1 id2 id3"],["OFFLINE","35","4"],["OFFLINE","40","5"],["MESSAGE","45","id0 id1 id2 id3 id4 id5"],["OFFLINE","50","6"],["MESSAGE","55","HERE"],["OFFLINE","60","7"],["MESSAGE","65","ALL"],["OFFLINE","70","8"],["MESSAGE","75","HERE"],["OFFLINE","80","9"],["MESSAGE","85","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9"],["OFFLINE","85","10"],["MESSAGE","90","HERE"],["OFFLINE","95","11"],["MESSAGE","100","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11"],["OFFLINE","105","12"],["MESSAGE","110","ALL"],["OFFLINE","115","13"],["MESSAGE","120","HERE"],["OFFLINE","125","14"],["MESSAGE","130","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14"],["OFFLINE","135","15"],["MESSAGE","140","HERE"],["OFFLINE","145","16"],["MESSAGE","150","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16"],["OFFLINE","155","17"],["MESSAGE","160","ALL"],["OFFLINE","165","18"],["MESSAGE","170","HERE"],["OFFLINE","175","19"],["MESSAGE","180","id0 id1 id2 id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"]]) == [15, 15, 15, 15, 13, 13, 12, 13, 12, 13, 11, 12, 11, 10, 11, 10, 11, 10, 10, 11]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","1","id0 id1"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["MESSAGE","20","id0"],["OFFLINE","25","1"],["MESSAGE","30","HERE"],["MESSAGE","40","ALL"],["OFFLINE","50","2"],["MESSAGE","60","HERE"]]) == [3, 3, 3]

Answer: assert Solution().countMentions(numberOfUsers = 4, events = [["OFFLINE","5","0"],["MESSAGE","10","HERE"],["OFFLINE","15","1"],["MESSAGE","20","HERE"],["OFFLINE","25","2"],["MESSAGE","30","HERE"],["OFFLINE","35","3"],["MESSAGE","40","HERE"],["MESSAGE","50","ALL"],["MESSAGE","60","id0 id1 id2 id3 id0 id1 id2 id3"],["MESSAGE","70","HERE"],["MESSAGE","80","ALL"]]) == [5, 5, 6, 7]

Answer: assert Solution().countMentions(numberOfUsers = 3, events = [["MESSAGE","1","id0 id1 id2"],["OFFLINE","2","0"],["OFFLINE","3","1"],["OFFLINE","4","2"],["MESSAGE","5","HERE"],["MESSAGE","6","ALL"],["MESSAGE","7","id0 id1 id2"],["MESSAGE","8","HERE"],["MESSAGE","9","ALL"],["MESSAGE","10","id0 id1 id2"],["MESSAGE","11","HERE"],["MESSAGE","12","ALL"],["MESSAGE","13","id0 id1 id2"],["MESSAGE","14","HERE"],["MESSAGE","15","ALL"]]) == [8, 8, 8]

Answer: assert Solution().countMentions(numberOfUsers = 15, events = [["MESSAGE","5","id0 id1 id2 id3 id4"],["OFFLINE","10","0"],["OFFLINE","15","1"],["OFFLINE","20","2"],["MESSAGE","25","HERE"],["OFFLINE","30","3"],["OFFLINE","35","4"],["MESSAGE","40","ALL"],["OFFLINE","45","5"],["OFFLINE","50","6"],["MESSAGE","55","HERE"],["OFFLINE","60","7"],["OFFLINE","65","8"],["MESSAGE","70","ALL"],["OFFLINE","75","9"],["OFFLINE","80","10"],["MESSAGE","85","HERE"],["OFFLINE","90","11"],["MESSAGE","95","ALL"],["OFFLINE","100","12"],["MESSAGE","105","HERE"],["OFFLINE","110","13"],["MESSAGE","115","ALL"]]) == [7, 7, 7, 7, 7, 6, 5, 6, 6, 6, 6, 7, 7, 8, 8]

Answer: assert Solution().countMentions(numberOfUsers = 5, events = [["MESSAGE","1","id0 id0 id1 id1 id2 id2 id3 id3 id4 id4"],["OFFLINE","2","0"],["MESSAGE","3","HERE"],["OFFLINE","4","1"],["MESSAGE","5","ALL"],["OFFLINE","6","2"],["MESSAGE","10","id0 id2"],["OFFLINE","11","3"],["MESSAGE","15","HERE"],["OFFLINE","16","4"],["MESSAGE","20","ALL"],["MESSAGE","25","id0 id1 id2 id3 id4 id0 id1 id2 id3 id4"],["OFFLINE","26","0"],["MESSAGE","30","HERE"],["OFFLINE","31","1"],["MESSAGE","35","ALL"],["OFFLINE","36","2"],["MESSAGE","40","id0 id1 id2 id3 id4 id0 id1 id2 id3 id4"],["OFFLINE","41","3"],["MESSAGE","45","HERE"],["OFFLINE","46","4"],["MESSAGE","50","ALL"]]) == [11, 11, 12, 11, 12]

Answer: assert Solution().countMentions(numberOfUsers = 10, events = [["MESSAGE","5","id0 id1 id2"],["OFFLINE","10","0"],["MESSAGE","15","HERE"],["OFFLINE","20","1"],["MESSAGE","25","ALL"],["MESSAGE","30","id3 id4 id5"],["OFFLINE","35","2"],["MESSAGE","40","HERE"],["OFFLINE","45","3"],["MESSAGE","50","ALL"],["OFFLINE","55","4"],["MESSAGE","60","HERE"],["OFFLINE","65","5"],["MESSAGE","70","ALL"]]) == [4, 5, 5, 6, 6, 7, 6, 6, 6, 6]

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def countMentions(self, numberOfUsers: int, events: List[List[str]]) -> List[int]:
        events.sort(key=lambda e: (int(e[1]), e[0][2]))
        ans = [0] * numberOfUsers
        online_t = [0] * numberOfUsers
        lazy = 0
        for etype, ts, s in events:
            cur = int(ts)
            if etype[0] == "O":
                online_t[int(s)] = cur + 60
            elif s[0] == "A":
                lazy += 1
            elif s[0] == "H":
                for i, t in enumerate(online_t):
                    if t <= cur:
                        ans[i] += 1
            else:
                for a in s.split():
                    ans[int(a[2:])] += 1
        if lazy:
            for i in range(numberOfUsers):
                ans[i] += lazy
        return ans


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given an array nums of length n. You are also given an integer k.
You perform the following operation on nums once:

Select a subarray nums[i..j] where 0 <= i <= j <= n - 1.
Select an integer x and add x to all the elements in nums[i..j].

Find the maximum frequency of the value k after the operation.

Example 1:

Input: nums = [1,2,3,4,5,6], k = 1
Output: 2
Explanation:
After adding -5 to nums[2..5], 1 has a frequency of 2 in [1, 2, -2, -1, 0, 1].

Example 2:

Input: nums = [10,2,3,4,5,5,4,3,2,2], k = 10
Output: 4
Explanation:
After adding 8 to nums[1..9], 10 has a frequency of 4 in [10, 10, 11, 12, 13, 13, 12, 11, 10, 10].

Constraints:

1 <= n == nums.length <= 105
1 <= nums[i] <= 50
1 <= k <= 50

Your solution to the problem should be a method of the class Solution called maxFrequency and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxFrequency(self, nums: List[int], k: int) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given an array nums of length n. You are also given an integer k.
You perform the following operation on nums once:

Select a subarray nums[i..j] where 0 <= i <= j <= n - 1.
Select an integer x and add x to all the elements in nums[i..j].

Find the maximum frequency of the value k after the operation.

Example 1:

Input: nums = [1,2,3,4,5,6], k = 1
Output: 2
Explanation:
After adding -5 to nums[2..5], 1 has a frequency of 2 in [1, 2, -2, -1, 0, 1].

Example 2:

Input: nums = [10,2,3,4,5,5,4,3,2,2], k = 10
Output: 4
Explanation:
After adding 8 to nums[1..9], 10 has a frequency of 4 in [10, 10, 11, 12, 13, 13, 12, 11, 10, 10].

Constraints:

1 <= n == nums.length <= 105
1 <= nums[i] <= 50
1 <= k <= 50

Your solution to the problem should be a method of the class Solution called maxFrequency and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxFrequency(self, nums: List[int], k: int) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().maxFrequency(nums = [5,5,5,5,5], k = 5) == 5

assert Solution().maxFrequency(nums = [10,20,30,40,50], k = 50) == 2

assert Solution().maxFrequency(nums = [1,50,1,50,1], k = 50) == 3

assert Solution().maxFrequency(nums = [50,1,50,1,50], k = 50) == 4

assert Solution().maxFrequency(nums = [25,25,25,25,25], k = 1) == 5

assert Solution().maxFrequency(nums = [1,2,3,4,5], k = 5) == 2

assert Solution().maxFrequency(nums = [1,2,3,4,5], k = 3) == 2

assert Solution().maxFrequency(nums = [30,30,30,30,30], k = 20) == 5

assert Solution().maxFrequency(nums = [5,4,3,2,1], k = 1) == 2

assert Solution().maxFrequency(nums = [1,2,3,4,5,6], k = 1) == 2

assert Solution().maxFrequency(nums = [1,1,1,1,1], k = 5) == 5

assert Solution().maxFrequency(nums = [1,1,1,1,1], k = 1) == 5

assert Solution().maxFrequency(nums = [1,100,1,100,1,100], k = 1) == 3

assert Solution().maxFrequency(nums = [25,25,25,25,25], k = 25) == 5

assert Solution().maxFrequency(nums = [48,48,48,48,48], k = 50) == 5

assert Solution().maxFrequency(nums = [1,2,3,4,5], k = 50) == 1

assert Solution().maxFrequency(nums = [50,49,48,47,46], k = 50) == 2

assert Solution().maxFrequency(nums = [50,50,50,50,50], k = 50) == 5

assert Solution().maxFrequency(nums = [5,4,3,2,1], k = 3) == 2

Answer: assert Solution().maxFrequency(nums = [5,5,5,5,5], k = 5) == 5

Answer: assert Solution().maxFrequency(nums = [10,20,30,40,50], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [1,50,1,50,1], k = 50) == 3

Answer: assert Solution().maxFrequency(nums = [25,25,25,25,25,25,25,25,25,25], k = 25) == 10

Answer: assert Solution().maxFrequency(nums = [50,1,50,1,50], k = 50) == 4

Answer: assert Solution().maxFrequency(nums = [25,25,25,25,25], k = 1) == 5

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5], k = 5) == 2

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5], k = 3) == 2

Answer: assert Solution().maxFrequency(nums = [30,30,30,30,30], k = 20) == 5

Answer: assert Solution().maxFrequency(nums = [1,2,2,3,3,3,4,4,4,4], k = 4) == 7

Answer: assert Solution().maxFrequency(nums = [5,4,3,2,1], k = 1) == 2

Answer: assert Solution().maxFrequency(nums = [10,2,3,4,5,5,4,3,2,2], k = 10) == 4

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5,6], k = 1) == 2

Answer: assert Solution().maxFrequency(nums = [1,2,2,3,3,3,4,4,4,4], k = 3) == 7

Answer: assert Solution().maxFrequency(nums = [30,30,30,30,30,30,30,30,30,30], k = 50) == 10

Answer: assert Solution().maxFrequency(nums = [1,1,1,1,1], k = 5) == 5

Answer: assert Solution().maxFrequency(nums = [1,1,1,1,1], k = 1) == 5

Answer: assert Solution().maxFrequency(nums = [30,30,30,30,30,30,30,30,30,30], k = 10) == 10

Answer: assert Solution().maxFrequency(nums = [1,100,1,100,1,100], k = 1) == 3

Answer: assert Solution().maxFrequency(nums = [25,25,25,25,25], k = 25) == 5

Answer: assert Solution().maxFrequency(nums = [48,48,48,48,48], k = 50) == 5

Answer: assert Solution().maxFrequency(nums = [1,10,100,1000,10000], k = 10) == 2

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5], k = 50) == 1

Answer: assert Solution().maxFrequency(nums = [50,49,48,47,46], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [50,50,50,50,50], k = 50) == 5

Answer: assert Solution().maxFrequency(nums = [1,1,2,2,3,3,4,4,5,5], k = 2) == 4

Answer: assert Solution().maxFrequency(nums = [5,4,3,2,1], k = 3) == 2

Answer: assert Solution().maxFrequency(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42], k = 50) == 15

Answer: assert Solution().maxFrequency(nums = [50,49,48,47,46,45,44,43,42,41,40,39,38,37,36], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10], k = 5) == 6

Answer: assert Solution().maxFrequency(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40], k = 20) == 2

Answer: assert Solution().maxFrequency(nums = [1, 50, 1, 50, 1, 50, 1, 50, 1, 50], k = 49) == 5

Answer: assert Solution().maxFrequency(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], k = 5) == 2

Answer: assert Solution().maxFrequency(nums = [1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5], k = 4) == 7

Answer: assert Solution().maxFrequency(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], k = 10) == 1

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5,6,7,8,9,10], k = 5) == 2

Answer: assert Solution().maxFrequency(nums = [5,4,3,2,1,1,2,3,4,5,5,4,3,2,1], k = 3) == 5

Answer: assert Solution().maxFrequency(nums = [1, 50, 1, 50, 1, 50, 1, 50, 1, 50], k = 50) == 6

Answer: assert Solution().maxFrequency(nums = [45, 45, 45, 45, 45, 50, 50, 50, 50, 50], k = 50) == 10

Answer: assert Solution().maxFrequency(nums = [30, 20, 10, 40, 50, 60, 70, 80, 90, 100], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50], k = 5) == 2

Answer: assert Solution().maxFrequency(nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], k = 1) == 30

Answer: assert Solution().maxFrequency(nums = [50, 50, 49, 49, 48, 48, 47, 47, 46, 46], k = 50) == 4

Answer: assert Solution().maxFrequency(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42], k = 42) == 20

Answer: assert Solution().maxFrequency(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25], k = 24) == 10

Answer: assert Solution().maxFrequency(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 1) == 20

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], k = 20) == 1

Answer: assert Solution().maxFrequency(nums = [3,3,3,3,3,3,3,3,3,3], k = 3) == 10

Answer: assert Solution().maxFrequency(nums = [10, 20, 30, 40, 50, 40, 30, 20, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], k = 30) == 12

Answer: assert Solution().maxFrequency(nums = [40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 20) == 4

Answer: assert Solution().maxFrequency(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40], k = 10) == 2

Answer: assert Solution().maxFrequency(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 1) == 10

Answer: assert Solution().maxFrequency(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50], k = 1) == 15

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], k = 150) == 1

Answer: assert Solution().maxFrequency(nums = [10,10,10,10,10,10,10,10,10,10], k = 10) == 10

Answer: assert Solution().maxFrequency(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41], k = 40) == 1

Answer: assert Solution().maxFrequency(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39], k = 20) == 1

Answer: assert Solution().maxFrequency(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 10) == 2

Answer: assert Solution().maxFrequency(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29], k = 50) == 1

Answer: assert Solution().maxFrequency(nums = [25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25], k = 50) == 52

Answer: assert Solution().maxFrequency(nums = [30, 1, 30, 2, 30, 3, 30, 4, 30, 5], k = 30) == 6

Answer: assert Solution().maxFrequency(nums = [10,20,30,40,50,60,70,80,90,100], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], k = 3) == 20

Answer: assert Solution().maxFrequency(nums = [49,49,49,49,49,49,49,49,49,49], k = 49) == 10

Answer: assert Solution().maxFrequency(nums = [1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10], k = 25) == 2

Answer: assert Solution().maxFrequency(nums = [5, 4, 5, 4, 5, 4, 5, 4, 5, 4], k = 5) == 6

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], k = 15) == 2

Answer: assert Solution().maxFrequency(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], k = 20) == 2

Answer: assert Solution().maxFrequency(nums = [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], k = 40) == 2

Answer: assert Solution().maxFrequency(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25], k = 25) == 20

Answer: assert Solution().maxFrequency(nums = [1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15], k = 15) == 4

Answer: assert Solution().maxFrequency(nums = [2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5], k = 10) == 5

Answer: assert Solution().maxFrequency(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4], k = 3) == 7

Answer: assert Solution().maxFrequency(nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50, 10, 20, 30, 40, 50], k = 50) == 4

Answer: assert Solution().maxFrequency(nums = [5,10,15,20,25,30,35,40,45,50], k = 5) == 2

Answer: assert Solution().maxFrequency(nums = [30, 30, 30, 30, 30, 30, 30, 30, 30, 30], k = 50) == 10

Answer: assert Solution().maxFrequency(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], k = 1) == 10

Answer: assert Solution().maxFrequency(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25], k = 25) == 15

Answer: assert Solution().maxFrequency(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 1) == 2

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 25) == 1

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], k = 20) == 2

Answer: assert Solution().maxFrequency(nums = [30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1], k = 30) == 2

Answer: assert Solution().maxFrequency(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], k = 3) == 6

Answer: assert Solution().maxFrequency(nums = [1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1], k = 2) == 11

Answer: assert Solution().maxFrequency(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], k = 15) == 1

Answer: assert Solution().maxFrequency(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1], k = 1) == 9

Answer: assert Solution().maxFrequency(nums = [30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30], k = 30) == 20

Answer: assert Solution().maxFrequency(nums = [10,20,30,40,50,60,70,80,90,100], k = 100) == 2

Answer: assert Solution().maxFrequency(nums = [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,50], k = 5) == 2

Answer: assert Solution().maxFrequency(nums = [1, 3, 5, 7, 9, 11, 13, 15], k = 10) == 1

Answer: assert Solution().maxFrequency(nums = [50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1], k = 25) == 2

Answer: assert Solution().maxFrequency(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5], k = 3) == 6

Answer: assert Solution().maxFrequency(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150], k = 100) == 2

Answer: assert Solution().maxFrequency(nums = [49, 48, 47, 46, 45, 44, 43, 42, 41, 40], k = 40) == 2

Answer: assert Solution().maxFrequency(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 100) == 2

Answer: assert Solution().maxFrequency(nums = [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15], k = 15) == 15

Answer: assert Solution().maxFrequency(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25], k = 50) == 20

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], k = 50) == 1

Answer: assert Solution().maxFrequency(nums = [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5], k = 5) == 54

Answer: assert Solution().maxFrequency(nums = [25, 24, 23, 22, 21, 20, 19, 18, 17, 16], k = 40) == 1

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], k = 10) == 2

Answer: assert Solution().maxFrequency(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], k = 30) == 1

Answer: assert Solution().maxFrequency(nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], k = 50) == 20

Answer: assert Solution().maxFrequency(nums = [1,1,1,2,2,2,3,3,3,4,4,4], k = 1) == 6

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 5) == 2

Answer: assert Solution().maxFrequency(nums = [40, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 50) == 3

Answer: assert Solution().maxFrequency(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 50) == 15

Answer: assert Solution().maxFrequency(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42], k = 42) == 10

Answer: assert Solution().maxFrequency(nums = [30, 20, 10, 40, 50, 30, 20, 10], k = 30) == 3

Answer: assert Solution().maxFrequency(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 90) == 2

Answer: assert Solution().maxFrequency(nums = [50,50,50,50,50,50,50,50,50,50], k = 1) == 10

Answer: assert Solution().maxFrequency(nums = [49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30], k = 49) == 2

Answer: assert Solution().maxFrequency(nums = [10, 10, 10, 20, 20, 20, 30, 30, 30, 40, 40, 40, 50, 50, 50], k = 30) == 6

Answer: assert Solution().maxFrequency(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10], k = 9) == 5

Answer: assert Solution().maxFrequency(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41], k = 25) == 1

Answer: assert Solution().maxFrequency(nums = [50, 40, 30, 20, 10, 50, 40, 30, 20, 10], k = 25) == 2

Answer: assert Solution().maxFrequency(nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], k = 25) == 2

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], k = 10) == 2

Answer: assert Solution().maxFrequency(nums = [1,2,2,3,3,3,4,4,4,4,5,5,5,5,5], k = 3) == 8

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], k = 10) == 2

Answer: assert Solution().maxFrequency(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], k = 3) == 4

Answer: assert Solution().maxFrequency(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25], k = 10) == 10

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], k = 15) == 2

Answer: assert Solution().maxFrequency(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], k = 40) == 2

Answer: assert Solution().maxFrequency(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36], k = 50) == 2

Answer: assert Solution().maxFrequency(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], k = 3) == 57

Answer: assert Solution().maxFrequency(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], k = 100) == 1

Answer: assert Solution().maxFrequency(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25], k = 25) == 31

Answer: assert Solution().maxFrequency(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], k = 10) == 1

Answer: assert Solution().maxFrequency(nums = [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21], k = 15) == 2

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
  def maxFrequency(self, nums: list[int], k: int) -> int:
    return nums.count(k) + max(self._kadane(nums, target, k)
                               for target in range(1, 51)
                               if target != k)

  def _kadane(self, nums: list[int], target: int, k: int) -> int:
    """
    Returns the maximum achievable frequency of `k` by Kakane's algorithm,
    where each `target` in subarrays is transformed to `k`.
    """
    maxSum = 0
    sum = 0
    for num in nums:
      if num == target:
        sum += 1
      elif num == k:
        sum -= 1
      if sum < 0:  # Reset sum if it becomes negative (Kadane's spirit).
        sum = 0
      maxSum = max(maxSum, sum)
    return maxSum


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given an integer eventTime denoting the duration of an event, where the event occurs from time t = 0 to time t = eventTime.
You are also given two integer arrays startTime and endTime, each of length n. These represent the start and end time of n non-overlapping meetings, where the ith meeting occurs during the time [startTime[i], endTime[i]].
You can reschedule at most k meetings by moving their start time while maintaining the same duration, to maximize the longest continuous period of free time during the event.
The relative order of all the meetings should stay the same and they should remain non-overlapping.
Return the maximum amount of free time possible after rearranging the meetings.
Note that the meetings can not be rescheduled to a time outside the event.

Example 1:

Input: eventTime = 5, k = 1, startTime = [1,3], endTime = [2,5]
Output: 2
Explanation:

Reschedule the meeting at [1, 2] to [2, 3], leaving no meetings during the time [0, 2].

Example 2:

Input: eventTime = 10, k = 1, startTime = [0,2,9], endTime = [1,4,10]
Output: 6
Explanation:

Reschedule the meeting at [2, 4] to [1, 3], leaving no meetings during the time [3, 9].

Example 3:

Input: eventTime = 5, k = 2, startTime = [0,1,2,3,4], endTime = [1,2,3,4,5]
Output: 0
Explanation:
There is no time during the event not occupied by meetings.

Constraints:

1 <= eventTime <= 109
n == startTime.length == endTime.length
2 <= n <= 105
1 <= k <= n
0 <= startTime[i] < endTime[i] <= eventTime
endTime[i] <= startTime[i + 1] where i lies in the range [0, n - 2].

Your solution to the problem should be a method of the class Solution called maxFreeTime and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxFreeTime(self, eventTime: int, k: int, startTime: List[int], endTime: List[int]) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given an integer eventTime denoting the duration of an event, where the event occurs from time t = 0 to time t = eventTime.
You are also given two integer arrays startTime and endTime, each of length n. These represent the start and end time of n non-overlapping meetings, where the ith meeting occurs during the time [startTime[i], endTime[i]].
You can reschedule at most k meetings by moving their start time while maintaining the same duration, to maximize the longest continuous period of free time during the event.
The relative order of all the meetings should stay the same and they should remain non-overlapping.
Return the maximum amount of free time possible after rearranging the meetings.
Note that the meetings can not be rescheduled to a time outside the event.

Example 1:

Input: eventTime = 5, k = 1, startTime = [1,3], endTime = [2,5]
Output: 2
Explanation:

Reschedule the meeting at [1, 2] to [2, 3], leaving no meetings during the time [0, 2].

Example 2:

Input: eventTime = 10, k = 1, startTime = [0,2,9], endTime = [1,4,10]
Output: 6
Explanation:

Reschedule the meeting at [2, 4] to [1, 3], leaving no meetings during the time [3, 9].

Example 3:

Input: eventTime = 5, k = 2, startTime = [0,1,2,3,4], endTime = [1,2,3,4,5]
Output: 0
Explanation:
There is no time during the event not occupied by meetings.

Constraints:

1 <= eventTime <= 109
n == startTime.length == endTime.length
2 <= n <= 105
1 <= k <= n
0 <= startTime[i] < endTime[i] <= eventTime
endTime[i] <= startTime[i + 1] where i lies in the range [0, n - 2].

Your solution to the problem should be a method of the class Solution called maxFreeTime and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxFreeTime(self, eventTime: int, k: int, startTime: List[int], endTime: List[int]) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [1,5,9], endTime = [3,7,12]) == 8

assert Solution().maxFreeTime(eventTime = 10, k = 1, startTime = [0,2,9], endTime = [1,4,10]) == 6

assert Solution().maxFreeTime(eventTime = 5, k = 1, startTime = [1,3], endTime = [2,5]) == 2

assert Solution().maxFreeTime(eventTime = 10, k = 2, startTime = [0,3,6], endTime = [2,5,8]) == 4

assert Solution().maxFreeTime(eventTime = 5, k = 2, startTime = [0,1,2,3,4], endTime = [1,2,3,4,5]) == 0

assert Solution().maxFreeTime(eventTime = 8, k = 2, startTime = [0,2,4], endTime = [1,3,5]) == 5

assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,3,6,9,12], endTime = [2,5,8,14,15]) == 5

assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [1,5,9,12], endTime = [3,7,11,14]) == 6

assert Solution().maxFreeTime(eventTime = 8, k = 2, startTime = [1,3,6], endTime = [2,5,7]) == 3

assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [0,3,6,9], endTime = [2,5,8,12]) == 6

assert Solution().maxFreeTime(eventTime = 15, k = 2, startTime = [1,4,7,10], endTime = [2,5,8,12]) == 7

assert Solution().maxFreeTime(eventTime = 20, k = 2, startTime = [0,5,10], endTime = [2,8,15]) == 10

assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [0,4,8,12], endTime = [2,6,10,14]) == 7

assert Solution().maxFreeTime(eventTime = 30, k = 5, startTime = [1,6,11,16,21], endTime = [4,9,14,19,24]) == 15

assert Solution().maxFreeTime(eventTime = 30, k = 5, startTime = [0,6,12,18,24], endTime = [4,10,16,22,28]) == 10

assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,2,5,9,13], endTime = [1,4,6,11,15]) == 11

assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,5,10,15], endTime = [2,7,12,17]) == 12

assert Solution().maxFreeTime(eventTime = 50, k = 5, startTime = [0,10,20,30,40], endTime = [5,15,25,35,45]) == 25

assert Solution().maxFreeTime(eventTime = 100, k = 1, startTime = [0,50], endTime = [10,60]) == 80

assert Solution().maxFreeTime(eventTime = 50, k = 4, startTime = [0,10,20,30,40], endTime = [5,15,25,35,45]) == 25

assert Solution().maxFreeTime(eventTime = 25, k = 4, startTime = [1,6,11,16,21], endTime = [3,8,13,18,23]) == 14

assert Solution().maxFreeTime(eventTime = 50, k = 5, startTime = [0,10,20,30,40], endTime = [5,15,25,35,50]) == 20

assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,5,10,15], endTime = [3,8,13,18]) == 8

assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [1,5,8,12,16], endTime = [3,7,10,15,18]) == 6

assert Solution().maxFreeTime(eventTime = 50, k = 5, startTime = [0,10,15,25,30], endTime = [5,12,20,35,40]) == 18

assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [1,3,5,7,9], endTime = [2,4,6,8,10]) == 13

assert Solution().maxFreeTime(eventTime = 100, k = 5, startTime = [1,20,40,60,80], endTime = [10,30,50,70,90]) == 51

assert Solution().maxFreeTime(eventTime = 25, k = 2, startTime = [0,6,12,18], endTime = [5,11,17,23]) == 4

Answer: assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [1,5,9], endTime = [3,7,12]) == 8

Answer: assert Solution().maxFreeTime(eventTime = 10, k = 1, startTime = [0,2,9], endTime = [1,4,10]) == 6

Answer: assert Solution().maxFreeTime(eventTime = 5, k = 1, startTime = [1,3], endTime = [2,5]) == 2

Answer: assert Solution().maxFreeTime(eventTime = 10, k = 2, startTime = [0,3,6], endTime = [2,5,8]) == 4

Answer: assert Solution().maxFreeTime(eventTime = 5, k = 2, startTime = [0,1,2,3,4], endTime = [1,2,3,4,5]) == 0

Answer: assert Solution().maxFreeTime(eventTime = 8, k = 2, startTime = [0,2,4], endTime = [1,3,5]) == 5

Answer: assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,3,6,9,12], endTime = [2,5,8,14,15]) == 5

Answer: assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [1,5,9,12], endTime = [3,7,11,14]) == 6

Answer: assert Solution().maxFreeTime(eventTime = 8, k = 2, startTime = [1,3,6], endTime = [2,5,7]) == 3

Answer: assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [0,3,6,9], endTime = [2,5,8,12]) == 6

Answer: assert Solution().maxFreeTime(eventTime = 15, k = 2, startTime = [1,4,7,10], endTime = [2,5,8,12]) == 7

Answer: assert Solution().maxFreeTime(eventTime = 20, k = 2, startTime = [0,5,10], endTime = [2,8,15]) == 10

Answer: assert Solution().maxFreeTime(eventTime = 15, k = 3, startTime = [0,4,8,12], endTime = [2,6,10,14]) == 7

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 5, startTime = [0,10,20,30,40,50,60,70,80,90], endTime = [5,15,25,35,45,55,65,75,85,100]) == 30

Answer: assert Solution().maxFreeTime(eventTime = 30, k = 5, startTime = [1,6,11,16,21], endTime = [4,9,14,19,24]) == 15

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 15, startTime = [0,10,20,30,40,50,60,70,80,90,100,110,120,130,140], endTime = [5,15,25,35,45,55,65,75,85,95,105,115,125,135,145]) == 125

Answer: assert Solution().maxFreeTime(eventTime = 750, k = 20, startTime = [0,35,70,105,140,175,210,245,280,315,350,385,420,455,490,525,560,595,630,665], endTime = [25,60,95,130,165,200,235,270,305,340,375,410,445,480,515,550,585,620,655,700]) == 240

Answer: assert Solution().maxFreeTime(eventTime = 1000, k = 20, startTime = [0,50,100,150,200,250,300,350,400,450,500,550,600,650,700,750,800,850,900,950], endTime = [10,60,110,160,210,260,310,360,410,460,510,560,610,660,710,760,810,860,910,960]) == 800

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 3, startTime = [0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190], endTime = [5,15,25,35,45,55,65,75,85,95,105,115,125,135,145,155,165,175,185,200]) == 20

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 7, startTime = [0,15,30,45,60,75,90], endTime = [10,25,40,55,70,85,100]) == 30

Answer: assert Solution().maxFreeTime(eventTime = 1000, k = 50, startTime = [0,20,40,60,80,100,120,140,160,180,200,220,240,260,280,300,320,340,360,380,400,420,440,460,480,500,520,540,560,580,600,620,640,660,680,700,720,740,760,780,800,820,840,860,880,900,920,940,960,980], endTime = [10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350,370,390,410,430,450,470,490,510,530,550,570,590,610,630,650,670,690,710,730,750,770,790,810,830,850,870,890,910,930,950,970,990]) == 500

Answer: assert Solution().maxFreeTime(eventTime = 30, k = 5, startTime = [0,6,12,18,24], endTime = [4,10,16,22,28]) == 10

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 20, startTime = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], endTime = [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]) == 60

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 8, startTime = [10,30,50,70,90,110,130,150], endTime = [20,40,60,80,100,120,140,160]) == 120

Answer: assert Solution().maxFreeTime(eventTime = 400, k = 20, startTime = [10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350,370,390], endTime = [20,40,60,80,100,120,140,160,180,200,220,240,260,280,300,320,340,360,380,400]) == 200

Answer: assert Solution().maxFreeTime(eventTime = 300, k = 10, startTime = [0,15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285], endTime = [15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285,300]) == 0

Answer: assert Solution().maxFreeTime(eventTime = 150, k = 7, startTime = [5,25,45,65,85,105,125], endTime = [15,35,55,75,95,115,135]) == 80

Answer: assert Solution().maxFreeTime(eventTime = 150, k = 5, startTime = [0,30,60,90,120], endTime = [15,45,75,105,150]) == 60

Answer: assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,2,5,9,13], endTime = [1,4,6,11,15]) == 11

Answer: assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,5,10,15], endTime = [2,7,12,17]) == 12

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 5, startTime = [0,20,40,60,80,100,120,140,160,180], endTime = [10,30,50,70,90,110,130,150,170,200]) == 60

Answer: assert Solution().maxFreeTime(eventTime = 120, k = 4, startTime = [0,5,10,20,30,40,50,60,70,80,90,100], endTime = [5,10,15,30,40,50,60,70,80,90,105,110]) == 5

Answer: assert Solution().maxFreeTime(eventTime = 50, k = 5, startTime = [0,10,20,30,40], endTime = [5,15,25,35,45]) == 25

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 1, startTime = [0,50], endTime = [10,60]) == 80

Answer: assert Solution().maxFreeTime(eventTime = 500, k = 25, startTime = [0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290,300,310,320,330,340,350,360,370,380,390,400,410,420,430,440,450,460,470,480,490], endTime = [4,14,24,34,44,54,64,74,84,94,104,114,124,134,144,154,164,174,184,194,204,214,224,234,244,254,264,274,284,294,304,314,324,334,344,354,364,374,384,394,404,414,424,434,444,454,464,474,484,494]) == 156

Answer: assert Solution().maxFreeTime(eventTime = 50, k = 4, startTime = [0,10,20,30,40], endTime = [5,15,25,35,45]) == 25

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 20, startTime = [0,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95], endTime = [2,7,12,17,22,27,32,37,42,47,52,57,62,67,72,77,82,87,92,97]) == 60

Answer: assert Solution().maxFreeTime(eventTime = 1000, k = 30, startTime = [0,30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,540,570,600,630,660,690,720,750,780,810,840,870,900,930,960], endTime = [20,50,80,110,140,170,200,230,260,290,320,350,380,410,440,470,500,530,560,590,620,650,680,710,740,770,800,830,860,890,920,950,980]) == 320

Answer: assert Solution().maxFreeTime(eventTime = 150, k = 7, startTime = [0,25,50,75,100,125], endTime = [10,40,65,90,115,145]) == 60

Answer: assert Solution().maxFreeTime(eventTime = 25, k = 4, startTime = [1,6,11,16,21], endTime = [3,8,13,18,23]) == 14

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 5, startTime = [5,15,25,35,45,55,65,75,85,95,105,115,125,135,145,155,165,175,185,195], endTime = [10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,200]) == 30

Answer: assert Solution().maxFreeTime(eventTime = 50, k = 5, startTime = [0,10,20,30,40], endTime = [5,15,25,35,50]) == 20

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 3, startTime = [0,10,20,30,40,50], endTime = [5,15,25,35,45,60]) == 55

Answer: assert Solution().maxFreeTime(eventTime = 300, k = 15, startTime = [5,25,45,65,85,105,125,145,165,185,205,225,245,265,285], endTime = [15,35,55,75,95,115,135,155,175,195,215,235,255,275,295]) == 150

Answer: assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [0,5,10,15], endTime = [3,8,13,18]) == 8

Answer: assert Solution().maxFreeTime(eventTime = 300, k = 10, startTime = [0,20,40,60,80,100,120,140,160,180,200,220,240,260,280], endTime = [10,30,50,70,90,110,130,150,170,190,210,230,250,270,300]) == 110

Answer: assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [1,5,8,12,16], endTime = [3,7,10,15,18]) == 6

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 8, startTime = [0,15,30,45,60,75,90,105,120,135,150,165,180,195], endTime = [10,25,40,55,70,85,100,115,130,145,160,175,190,200]) == 45

Answer: assert Solution().maxFreeTime(eventTime = 50, k = 5, startTime = [0,10,15,25,30], endTime = [5,12,20,35,40]) == 18

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 10, startTime = [5,15,25,35,45,55,65,75,85,95], endTime = [10,20,30,40,50,60,70,80,90,100]) == 50

Answer: assert Solution().maxFreeTime(eventTime = 150, k = 5, startTime = [0,10,25,40,55,70,85,100,115,130,145], endTime = [10,20,35,50,65,80,95,110,125,140,150]) == 30

Answer: assert Solution().maxFreeTime(eventTime = 20, k = 3, startTime = [1,3,5,7,9], endTime = [2,4,6,8,10]) == 13

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 10, startTime = [1,11,21,31,41,51,61,71,81,91], endTime = [10,20,30,40,50,60,70,80,90,100]) == 10

Answer: assert Solution().maxFreeTime(eventTime = 500, k = 25, startTime = [0,20,40,60,80,100,120,140,160,180,200,220,240,260,280,300,320,340,360,380,400,420,440,460,480], endTime = [10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350,370,390,410,430,450,470,500]) == 240

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 3, startTime = [0,10,20,30,40,50,60,70,80,90], endTime = [5,15,25,35,45,55,65,75,85,95]) == 20

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 10, startTime = [1,5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81,85,89,93,97], endTime = [4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100]) == 11

Answer: assert Solution().maxFreeTime(eventTime = 2000, k = 50, startTime = [0,40,80,120,160,200,240,280,320,360,400,440,480,520,560,600,640,680,720,760,800,840,880,920,960,1000,1040,1080,1120,1160,1200,1240,1280,1320,1360,1400,1440,1480,1520,1560,1600,1640,1680,1720,1760,1800,1840,1880,1920,1960], endTime = [20,60,100,140,180,220,260,300,340,380,420,460,500,540,580,620,660,700,740,780,820,860,900,940,980,1020,1060,1100,1140,1180,1220,1260,1300,1340,1380,1420,1460,1500,1540,1580,1620,1660,1700,1740,1780,1820,1860,1900,1940,1980,2000]) == 980

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 50, startTime = [0,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,160,164,168,172,176,180,184,188,192,196], endTime = [2,6,10,14,18,22,26,30,34,38,42,46,50,54,58,62,66,70,74,78,82,86,90,94,98,102,106,110,114,118,122,126,130,134,138,142,146,150,154,158,162,166,170,174,178,182,186,190,194,198]) == 100

Answer: assert Solution().maxFreeTime(eventTime = 80, k = 3, startTime = [0,10,20,30,40,50,60,70], endTime = [10,20,30,40,50,60,70,80]) == 0

Answer: assert Solution().maxFreeTime(eventTime = 300, k = 30, startTime = [0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290], endTime = [2,12,22,32,42,52,62,72,82,92,102,112,122,132,142,152,162,172,182,192,202,212,222,232,242,252,262,272,282,292]) == 240

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 5, startTime = [5,15,30,45,60,75,90], endTime = [10,20,35,50,65,80,100]) == 55

Answer: assert Solution().maxFreeTime(eventTime = 250, k = 9, startTime = [10,40,70,100,130,160,190,220,230], endTime = [30,60,90,120,150,180,210,240,245]) == 75

Answer: assert Solution().maxFreeTime(eventTime = 30, k = 5, startTime = [0,4,8,12,16,24], endTime = [2,6,10,14,18,28]) == 16

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 20, startTime = [0,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95], endTime = [3,8,13,18,23,28,33,38,43,48,53,58,63,68,73,78,83,88,93,98]) == 40

Answer: assert Solution().maxFreeTime(eventTime = 300, k = 15, startTime = [0,20,40,60,80,100,120,140,160,180,200,220,240,260,280], endTime = [15,35,55,75,95,115,135,155,175,195,215,235,255,275,300]) == 70

Answer: assert Solution().maxFreeTime(eventTime = 75, k = 7, startTime = [5,15,25,35,45,55,65], endTime = [10,20,30,40,50,60,70]) == 40

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 20, startTime = [1,5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77], endTime = [3,7,11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79]) == 60

Answer: assert Solution().maxFreeTime(eventTime = 500, k = 10, startTime = [10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350,370,390,410,430,450,470,490], endTime = [20,40,60,80,100,120,140,160,180,200,220,240,260,280,300,320,340,360,380,400,420,440,460,480,500]) == 110

Answer: assert Solution().maxFreeTime(eventTime = 80, k = 5, startTime = [2,8,14,20,26,32,38,44,50,56], endTime = [6,12,18,24,30,36,42,48,54,60]) == 30

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 2, startTime = [0,20,40,60,80], endTime = [10,30,50,70,100]) == 30

Answer: assert Solution().maxFreeTime(eventTime = 1000, k = 10, startTime = [0,50,100,150,200,250,300,350,400,450,500,550,600,650,700,750,800,850,900,950], endTime = [25,75,125,175,225,275,325,375,425,475,525,575,625,675,725,775,825,875,925,1000]) == 275

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 5, startTime = [0,10,20,30,40,50,60,70,80,90], endTime = [2,12,22,32,42,52,62,72,82,92]) == 48

Answer: assert Solution().maxFreeTime(eventTime = 50, k = 2, startTime = [0,1,2,3,4,5,6,7,8,9], endTime = [5,6,7,8,9,10,11,12,13,14]) == 28

Answer: assert Solution().maxFreeTime(eventTime = 400, k = 15, startTime = [1,9,17,25,33,41,49,57,65,73,81,89,97,105,113,121,129,137,145,153,161,169,177,185,193,201,209,217,225,233,241,249,257,265,273,281,289,297,305,313,321,329,337,345,353,361,369,377,385,393], endTime = [8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144,152,160,168,176,184,192,200,208,216,224,232,240,248,256,264,272,280,288,296,304,312,320,328,336,344,352,360,368,376,384,392,400]) == 16

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 5, startTime = [1,20,40,60,80], endTime = [10,30,50,70,90]) == 51

Answer: assert Solution().maxFreeTime(eventTime = 70, k = 10, startTime = [0,5,10,15,20,25,30,35,40,45,50,55,60,65,70], endTime = [4,9,14,19,24,29,34,39,44,49,54,59,64,69,75]) == 11

Answer: assert Solution().maxFreeTime(eventTime = 5000, k = 10, startTime = [0,1000,2000,3000,4000], endTime = [250,1250,2250,3250,4250]) == 3750

Answer: assert Solution().maxFreeTime(eventTime = 5000, k = 3, startTime = [0,200,400,600,800,1000,1200,1400,1600,1800,2000], endTime = [100,300,500,700,900,1100,1300,1500,1700,1900,2500]) == 2800

Answer: assert Solution().maxFreeTime(eventTime = 25, k = 2, startTime = [0,6,12,18], endTime = [5,11,17,23]) == 4

Answer: assert Solution().maxFreeTime(eventTime = 100, k = 5, startTime = [0,10,20,30,40,50,60,70,80,90], endTime = [5,15,25,35,45,55,65,75,85,95]) == 30

Answer: assert Solution().maxFreeTime(eventTime = 200, k = 10, startTime = [0,20,40,60,80,100,120,140,160,180], endTime = [10,30,50,70,90,110,130,150,170,200]) == 90

Answer: assert Solution().maxFreeTime(eventTime = 50, k = 10, startTime = [0,6,12,18,24,30,36,42,48], endTime = [4,10,16,22,28,34,40,46,50]) == 16

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
  def maxFreeTime(
      self,
      eventTime: int,
      k: int,
      startTime: list[int],
      endTime: list[int]
  ) -> int:
    gaps = ([startTime[0]] +
            [startTime[i] - endTime[i - 1] for i in range(1, len(startTime))] +
            [eventTime - endTime[-1]])
    windowSum = sum(gaps[:k + 1])
    ans = windowSum

    for i in range(k + 1, len(gaps)):
      windowSum += gaps[i] - gaps[i - k - 1]
      ans = max(ans, windowSum)

    return ans