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 a string word, and an integer numFriends.
Alice is organizing a game for her numFriends friends. There are multiple rounds in the game, where in each round:

word is split into numFriends non-empty strings, such that no previous round has had the exact same split.
All the split words are put into a box.

Find the lexicographically largest string from the box after all the rounds are finished.
A string a is lexicographically smaller than a string b if in the first position where a and b differ, string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
If the first min(a.length, b.length) characters do not differ, then the shorter string is the lexicographically smaller one.

Example 1:

Input: word = "dbca", numFriends = 2
Output: "dbc"
Explanation:
All possible splits are:

"d" and "bca".
"db" and "ca".
"dbc" and "a".

Example 2:

Input: word = "gggg", numFriends = 4
Output: "g"
Explanation:
The only possible split is: "g", "g", "g", and "g".

Constraints:

1 <= word.length <= 2 * 105
word consists only of lowercase English letters.
1 <= numFriends <= word.length

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

SOLUTION:

Question:
PROBLEM:
You are given a string word, and an integer numFriends.
Alice is organizing a game for her numFriends friends. There are multiple rounds in the game, where in each round:

word is split into numFriends non-empty strings, such that no previous round has had the exact same split.
All the split words are put into a box.

Find the lexicographically largest string from the box after all the rounds are finished.
A string a is lexicographically smaller than a string b if in the first position where a and b differ, string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
If the first min(a.length, b.length) characters do not differ, then the shorter string is the lexicographically smaller one.

Example 1:

Input: word = "dbca", numFriends = 2
Output: "dbc"
Explanation:
All possible splits are:

"d" and "bca".
"db" and "ca".
"dbc" and "a".

Example 2:

Input: word = "gggg", numFriends = 4
Output: "g"
Explanation:
The only possible split is: "g", "g", "g", and "g".

Constraints:

1 <= word.length <= 2 * 105
word consists only of lowercase English letters.
1 <= numFriends <= word.length

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

SOLUTION:

assert Solution().answerString(word = "aabbcc", numFriends = 2) == "cc"

assert Solution().answerString(word = "aabbccddeeff", numFriends = 3) == "ff"

assert Solution().answerString(word = "zzzzzzzzz", numFriends = 5) == "zzzzz"

assert Solution().answerString(word = "zyxwvutsrqponmlkjihgfedcba", numFriends = 5) == "zyxwvutsrqponmlkjihgfe"

assert Solution().answerString(word = "abcdefg", numFriends = 3) == "g"

assert Solution().answerString(word = "aabbccddeeff", numFriends = 6) == "ff"

assert Solution().answerString(word = "gggg", numFriends = 4) == "g"

assert Solution().answerString(word = "zyxwvutsrqponmlkjihgfedcba", numFriends = 26) == "z"

assert Solution().answerString(word = "aabbccddeeffgghhiijj", numFriends = 5) == "jj"

assert Solution().answerString(word = "abcdef", numFriends = 3) == "f"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 10) == "zz"

assert Solution().answerString(word = "abcde", numFriends = 3) == "e"

assert Solution().answerString(word = "zxywvutsrqponmlkjihgfedcba", numFriends = 5) == "zxywvutsrqponmlkjihgfe"

assert Solution().answerString(word = "dbca", numFriends = 2) == "dbc"

assert Solution().answerString(word = "mississippi", numFriends = 4) == "ssissipp"

assert Solution().answerString(word = "zzzzyyyxxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaaaa", numFriends = 15) == "zzzzyyyxxxwwvvuuttssrrqqppoonnmmllkkjjiihhgg"

assert Solution().answerString(word = "abcdefghijabcdefghijabcdefghijabcdefghij", numFriends = 20) == "jabcdefghijabcdefghij"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzzzzzzzzzzzzzz", numFriends = 18) == "zzzzzzzzzzzzzzzzzzzz"

assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyzzxywvutsrqponmlkjihgfedcba", numFriends = 20) == "zzxywvutsrqponmlkjihgfedcba"

assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 30) == "dabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdab"

assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 8) == "dabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd"

assert Solution().answerString(word = "zzzzzyyyyyxxxxxwwwwwvvvvvuuuuuttttssssrrrrqqqqppppooooonnnnmmmm", numFriends = 20) == "zzzzzyyyyyxxxxxwwwwwvvvvvuuuuuttttssssrrrrqq"

assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 8) == "dabcdabcdabcdabcdabcdabcd"

assert Solution().answerString(word = "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyx", numFriends = 7) == "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyx"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 25) == "zzzzzzzzzzzzzzzzzzzzzzzzzz"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 20) == "zz"

assert Solution().answerString(word = "aaaaaabbbbbbbbbbccccccccccccdddddddddddddddddd", numFriends = 25) == "dddddddddddddddddd"

assert Solution().answerString(word = "ascendingorder", numFriends = 3) == "scendingorde"

assert Solution().answerString(word = "xyzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxz", numFriends = 30) == "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxz"

assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 10) == "zzzzzzzzzzzzzzzzzzzzzzzzz"

assert Solution().answerString(word = "leetcode", numFriends = 2) == "tcode"

assert Solution().answerString(word = "abcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg", numFriends = 20) == "gabcdefgabcdefgabcdefgabcdefgabcdefga"

assert Solution().answerString(word = "a", numFriends = 1) == "a"

assert Solution().answerString(word = "thisisaverylongwordwithmanycharactersandmultiplesplitcases", numFriends = 12) == "ylongwordwithmanycharactersandmultiplesplitcase"

assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 10) == "zxcvbnm"

assert Solution().answerString(word = "leetcodeleetcodeleetcode", numFriends = 4) == "tcodeleetcodeleetcode"

assert Solution().answerString(word = "pythonprogramming", numFriends = 5) == "ythonprogramm"

assert Solution().answerString(word = "lexicographical", numFriends = 5) == "xicographic"

assert Solution().answerString(word = "descendingorder", numFriends = 3) == "scendingorder"

assert Solution().answerString(word = "abcdefghijabcdefghijabcdefghijabcdefghijabcdefghij", numFriends = 20) == "jabcdefghijabcdefghijabcdefghij"

assert Solution().answerString(word = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", numFriends = 100) == ""

assert Solution().answerString(word = "leetcodeisfun", numFriends = 5) == "un"

assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 12) == "dabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd"

assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 15) == "zxcvbnm"

assert Solution().answerString(word = "abcdefghijabcdefghij", numFriends = 5) == "jabcdefghij"

assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", numFriends = 13) == "zabcdefghijklmnopqrstuvwxyz"

assert Solution().answerString(word = "ababababababababababababab", numFriends = 7) == "babababababababababa"

assert Solution().answerString(word = "aaaaaaaaaabbbbbbbbccccccccddddddddeeeeeeefffffff", numFriends = 6) == "fffffff"

assert Solution().answerString(word = "mmmmmnnnnnooooo", numFriends = 5) == "ooooo"

assert Solution().answerString(word = "abacabadabacaba", numFriends = 4) == "dabacaba"

assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 6) == "zxcvbnm"

assert Solution().answerString(word = "samestartswithsamestart", numFriends = 5) == "withsamestart"

assert Solution().answerString(word = "amazingrace", numFriends = 5) == "zingrac"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 26) == "zz"

assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 20) == "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz"

assert Solution().answerString(word = "aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxxyyyyzzzz", numFriends = 30) == "zzzz"

assert Solution().answerString(word = "banana", numFriends = 3) == "nana"

assert Solution().answerString(word = "racecar", numFriends = 3) == "racec"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 1) == "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz"

assert Solution().answerString(word = "abacabadabacabadabacabad", numFriends = 10) == "dabacabadabacab"

assert Solution().answerString(word = "aabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwwxxxxyyyyzzzz", numFriends = 30) == "zzzz"

assert Solution().answerString(word = "zzzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggeeddbbaa", numFriends = 15) == "zzzyyxxwwvvuuttssrrqqppoonnmmllkkjj"

assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 100) == ""

assert Solution().answerString(word = "abababababababababababab", numFriends = 7) == "bababababababababa"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 15) == "zz"

assert Solution().answerString(word = "uniquecharactersonly", numFriends = 6) == "y"

assert Solution().answerString(word = "ababababababababababababab", numFriends = 12) == "bababababababab"

assert Solution().answerString(word = "abcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcde", numFriends = 10) == "eabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcde"

assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 25) == "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz"

assert Solution().answerString(word = "aaaaabbbbbccccdddddeeeeefffffggggghhhhiiiii", numFriends = 10) == "iiiii"

assert Solution().answerString(word = "repeatedrepeatedrepeated", numFriends = 8) == "tedrepeatedrepeat"

assert Solution().answerString(word = "aaaaaaaaabbbbbbbbcccccccc", numFriends = 9) == "cccccccc"

assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyz", numFriends = 26) == "z"

assert Solution().answerString(word = "leetcodelove", numFriends = 3) == "ve"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 25) == "zz"

assert Solution().answerString(word = "zzzyyyxxxwwvvvuttsrqponmlkjihgfedcba", numFriends = 10) == "zzzyyyxxxwwvvvuttsrqponmlkj"

assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 13) == "zxcvbnm"

assert Solution().answerString(word = "zyxwvutsrqponmlkjihgfedcba", numFriends = 13) == "zyxwvutsrqponm"

assert Solution().answerString(word = "lemonade", numFriends = 2) == "onade"

assert Solution().answerString(word = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", numFriends = 26) == "cabcabcabcabcabcabcabca"

assert Solution().answerString(word = "ppppqqqqrrrrssssttttuuuuvvvvwwwwwxxxxxyyyyyzzzzz", numFriends = 25) == "zzzzz"

assert Solution().answerString(word = "abacabadabacaba", numFriends = 5) == "dabacaba"

assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzzzz", numFriends = 15) == "zzzzzzzzzz"

assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyzyxwvutsrqponmlkjihgfedcba", numFriends = 20) == "zyxwvutsrqponmlkjihgfedcba"

assert Solution().answerString(word = "axbyczdxeyfzgyhzixjykzl", numFriends = 5) == "zl"

Answer: assert Solution().answerString(word = "aabbcc", numFriends = 2) == "cc"

Answer: assert Solution().answerString(word = "aabbccddeeff", numFriends = 3) == "ff"

Answer: assert Solution().answerString(word = "zzzzzzzzz", numFriends = 5) == "zzzzz"

Answer: assert Solution().answerString(word = "zyxwvutsrqponmlkjihgfedcba", numFriends = 5) == "zyxwvutsrqponmlkjihgfe"

Answer: assert Solution().answerString(word = "abcdefg", numFriends = 3) == "g"

Answer: assert Solution().answerString(word = "aabbccddeeff", numFriends = 6) == "ff"

Answer: assert Solution().answerString(word = "gggg", numFriends = 4) == "g"

Answer: assert Solution().answerString(word = "zyxwvutsrqponmlkjihgfedcba", numFriends = 26) == "z"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijj", numFriends = 5) == "jj"

Answer: assert Solution().answerString(word = "abcdef", numFriends = 3) == "f"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 10) == "zz"

Answer: assert Solution().answerString(word = "abcde", numFriends = 3) == "e"

Answer: assert Solution().answerString(word = "zxywvutsrqponmlkjihgfedcba", numFriends = 5) == "zxywvutsrqponmlkjihgfe"

Answer: assert Solution().answerString(word = "dbca", numFriends = 2) == "dbc"

Answer: assert Solution().answerString(word = "mississippi", numFriends = 4) == "ssissipp"

Answer: assert Solution().answerString(word = "zzzzyyyxxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaaaa", numFriends = 15) == "zzzzyyyxxxwwvvuuttssrrqqppoonnmmllkkjjiihhgg"

Answer: assert Solution().answerString(word = "abcdefghijabcdefghijabcdefghijabcdefghij", numFriends = 20) == "jabcdefghijabcdefghij"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzzzzzzzzzzzzzz", numFriends = 18) == "zzzzzzzzzzzzzzzzzzzz"

Answer: assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyzzxywvutsrqponmlkjihgfedcba", numFriends = 20) == "zzxywvutsrqponmlkjihgfedcba"

Answer: assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 30) == "dabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdab"

Answer: assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 8) == "dabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd"

Answer: assert Solution().answerString(word = "zzzzzyyyyyxxxxxwwwwwvvvvvuuuuuttttssssrrrrqqqqppppooooonnnnmmmm", numFriends = 20) == "zzzzzyyyyyxxxxxwwwwwvvvvvuuuuuttttssssrrrrqq"

Answer: assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 8) == "dabcdabcdabcdabcdabcdabcd"

Answer: assert Solution().answerString(word = "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyx", numFriends = 7) == "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyx"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 25) == "zzzzzzzzzzzzzzzzzzzzzzzzzz"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 20) == "zz"

Answer: assert Solution().answerString(word = "aaaaaabbbbbbbbbbccccccccccccdddddddddddddddddd", numFriends = 25) == "dddddddddddddddddd"

Answer: assert Solution().answerString(word = "ascendingorder", numFriends = 3) == "scendingorde"

Answer: assert Solution().answerString(word = "xyzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxz", numFriends = 30) == "zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxz"

Answer: assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 10) == "zzzzzzzzzzzzzzzzzzzzzzzzz"

Answer: assert Solution().answerString(word = "leetcode", numFriends = 2) == "tcode"

Answer: assert Solution().answerString(word = "abcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg", numFriends = 20) == "gabcdefgabcdefgabcdefgabcdefgabcdefga"

Answer: assert Solution().answerString(word = "a", numFriends = 1) == "a"

Answer: assert Solution().answerString(word = "thisisaverylongwordwithmanycharactersandmultiplesplitcases", numFriends = 12) == "ylongwordwithmanycharactersandmultiplesplitcase"

Answer: assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 10) == "zxcvbnm"

Answer: assert Solution().answerString(word = "leetcodeleetcodeleetcode", numFriends = 4) == "tcodeleetcodeleetcode"

Answer: assert Solution().answerString(word = "pythonprogramming", numFriends = 5) == "ythonprogramm"

Answer: assert Solution().answerString(word = "lexicographical", numFriends = 5) == "xicographic"

Answer: assert Solution().answerString(word = "descendingorder", numFriends = 3) == "scendingorder"

Answer: assert Solution().answerString(word = "abcdefghijabcdefghijabcdefghijabcdefghijabcdefghij", numFriends = 20) == "jabcdefghijabcdefghijabcdefghij"

Answer: assert Solution().answerString(word = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", numFriends = 100) == ""

Answer: assert Solution().answerString(word = "leetcodeisfun", numFriends = 5) == "un"

Answer: assert Solution().answerString(word = "abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd", numFriends = 12) == "dabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd"

Answer: assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 15) == "zxcvbnm"

Answer: assert Solution().answerString(word = "abcdefghijabcdefghij", numFriends = 5) == "jabcdefghij"

Answer: assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz", numFriends = 13) == "zabcdefghijklmnopqrstuvwxyz"

Answer: assert Solution().answerString(word = "ababababababababababababab", numFriends = 7) == "babababababababababa"

Answer: assert Solution().answerString(word = "aaaaaaaaaabbbbbbbbccccccccddddddddeeeeeeefffffff", numFriends = 6) == "fffffff"

Answer: assert Solution().answerString(word = "mmmmmnnnnnooooo", numFriends = 5) == "ooooo"

Answer: assert Solution().answerString(word = "abacabadabacaba", numFriends = 4) == "dabacaba"

Answer: assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 6) == "zxcvbnm"

Answer: assert Solution().answerString(word = "samestartswithsamestart", numFriends = 5) == "withsamestart"

Answer: assert Solution().answerString(word = "amazingrace", numFriends = 5) == "zingrac"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 26) == "zz"

Answer: assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 20) == "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz"

Answer: assert Solution().answerString(word = "aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxxyyyyzzzz", numFriends = 30) == "zzzz"

Answer: assert Solution().answerString(word = "banana", numFriends = 3) == "nana"

Answer: assert Solution().answerString(word = "racecar", numFriends = 3) == "racec"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 1) == "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz"

Answer: assert Solution().answerString(word = "abacabadabacabadabacabad", numFriends = 10) == "dabacabadabacab"

Answer: assert Solution().answerString(word = "aabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwwxxxxyyyyzzzz", numFriends = 30) == "zzzz"

Answer: assert Solution().answerString(word = "zzzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggeeddbbaa", numFriends = 15) == "zzzyyxxwwvvuuttssrrqqppoonnmmllkkjj"

Answer: assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 100) == ""

Answer: assert Solution().answerString(word = "abababababababababababab", numFriends = 7) == "bababababababababa"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 15) == "zz"

Answer: assert Solution().answerString(word = "uniquecharactersonly", numFriends = 6) == "y"

Answer: assert Solution().answerString(word = "ababababababababababababab", numFriends = 12) == "bababababababab"

Answer: assert Solution().answerString(word = "abcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcde", numFriends = 10) == "eabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcdeabcde"

Answer: assert Solution().answerString(word = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz", numFriends = 25) == "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz"

Answer: assert Solution().answerString(word = "aaaaabbbbbccccdddddeeeeefffffggggghhhhiiiii", numFriends = 10) == "iiiii"

Answer: assert Solution().answerString(word = "repeatedrepeatedrepeated", numFriends = 8) == "tedrepeatedrepeat"

Answer: assert Solution().answerString(word = "aaaaaaaaabbbbbbbbcccccccc", numFriends = 9) == "cccccccc"

Answer: assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyz", numFriends = 26) == "z"

Answer: assert Solution().answerString(word = "leetcodelove", numFriends = 3) == "ve"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz", numFriends = 25) == "zz"

Answer: assert Solution().answerString(word = "zzzyyyxxxwwvvvuttsrqponmlkjihgfedcba", numFriends = 10) == "zzzyyyxxxwwvvvuttsrqponmlkj"

Answer: assert Solution().answerString(word = "qwertyuiopasdfghjklzxcvbnm", numFriends = 13) == "zxcvbnm"

Answer: assert Solution().answerString(word = "zyxwvutsrqponmlkjihgfedcba", numFriends = 13) == "zyxwvutsrqponm"

Answer: assert Solution().answerString(word = "lemonade", numFriends = 2) == "onade"

Answer: assert Solution().answerString(word = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc", numFriends = 26) == "cabcabcabcabcabcabcabca"

Answer: assert Solution().answerString(word = "ppppqqqqrrrrssssttttuuuuvvvvwwwwwxxxxxyyyyyzzzzz", numFriends = 25) == "zzzzz"

Answer: assert Solution().answerString(word = "abacabadabacaba", numFriends = 5) == "dabacaba"

Answer: assert Solution().answerString(word = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzzzz", numFriends = 15) == "zzzzzzzzzz"

Answer: assert Solution().answerString(word = "abcdefghijklmnopqrstuvwxyzyxwvutsrqponmlkjihgfedcba", numFriends = 20) == "zyxwvutsrqponmlkjihgfedcba"

Answer: assert Solution().answerString(word = "axbyczdxeyfzgyhzixjykzl", numFriends = 5) == "zl"

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 answerString(self, word: str, numFriends: int) -> str:
    if numFriends == 1:
      return word
    s = self._lastSubstring(word)
    sz = len(word) - numFriends + 1
    return s[:min(len(s), sz)]

  # Same as 1163. Last Substring in Lexicographical Order
  def _lastSubstring(self, s: str) -> str:
    i = 0
    j = 1
    k = 0  # the number of the same letters of s[i..n) and s[j..n)

    while j + k < len(s):
      if s[i + k] == s[j + k]:
        k += 1
      elif s[i + k] > s[j + k]:
        # Skip s[j..j + k) and advance to s[j + k + 1] to find a possible
        # lexicographically larger substring since s[i..i + k) == s[j..j + k)
        # and s[i + k] > s[j + k).
        j = j + k + 1
        k = 0
      else:
        # Skip s[i..i + k) and advance to s[i + k + 1] or s[j] to find a
        # possible lexicographically larger substring since
        # s[i..i + k) == s[j..j + k) and s[i + k] < s[j + k).
        # Note that it's unnecessary to explore s[i + k + 1..j) if
        # i + k + 1 < j since they are already explored by j.
        i = max(i + k + 1, j)
        j = i + 1
        k = 0

    return s[i:]


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 of integers nums.
Your task is to find the length of the longest subsequence seq of nums, such that the absolute differences between consecutive elements form a non-increasing sequence of integers. In other words, for a subsequence seq0, seq1, seq2, ..., seqm of nums, |seq1 - seq0| >= |seq2 - seq1| >= ... >= |seqm - seqm - 1|.
Return the length of such a subsequence.

Example 1:

Input: nums = [16,6,3]
Output: 3
Explanation:
The longest subsequence is [16, 6, 3] with the absolute adjacent differences [10, 3].

Example 2:

Input: nums = [6,5,3,4,2,1]
Output: 4
Explanation:
The longest subsequence is [6, 4, 2, 1] with the absolute adjacent differences [2, 2, 1].

Example 3:

Input: nums = [10,20,10,19,10,20]
Output: 5
Explanation:
The longest subsequence is [10, 20, 10, 19, 10] with the absolute adjacent differences [10, 10, 9, 9].

Constraints:

2 <= nums.length <= 104
1 <= nums[i] <= 300

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

SOLUTION:

Question:
PROBLEM:
You are given an array of integers nums.
Your task is to find the length of the longest subsequence seq of nums, such that the absolute differences between consecutive elements form a non-increasing sequence of integers. In other words, for a subsequence seq0, seq1, seq2, ..., seqm of nums, |seq1 - seq0| >= |seq2 - seq1| >= ... >= |seqm - seqm - 1|.
Return the length of such a subsequence.

Example 1:

Input: nums = [16,6,3]
Output: 3
Explanation:
The longest subsequence is [16, 6, 3] with the absolute adjacent differences [10, 3].

Example 2:

Input: nums = [6,5,3,4,2,1]
Output: 4
Explanation:
The longest subsequence is [6, 4, 2, 1] with the absolute adjacent differences [2, 2, 1].

Example 3:

Input: nums = [10,20,10,19,10,20]
Output: 5
Explanation:
The longest subsequence is [10, 20, 10, 19, 10] with the absolute adjacent differences [10, 10, 9, 9].

Constraints:

2 <= nums.length <= 104
1 <= nums[i] <= 300

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

SOLUTION:

assert Solution().longestSubsequence(nums = [1,3,2,4,3,5,4,6,5,7]) == 6

assert Solution().longestSubsequence(nums = [1,10,1,10,1,10,1,10]) == 8

assert Solution().longestSubsequence(nums = [300,1,300,2,300,3,300]) == 7

assert Solution().longestSubsequence(nums = [3,3,3,3,3,3,3,3,3,3]) == 10

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

assert Solution().longestSubsequence(nums = [1,300,2,299,3,298,4,297]) == 8

assert Solution().longestSubsequence(nums = [300,1,300,1,300]) == 5

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

assert Solution().longestSubsequence(nums = [1,100,2,99,3,98,4,97]) == 8

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

assert Solution().longestSubsequence(nums = [100,100,100,100,100]) == 5

assert Solution().longestSubsequence(nums = [1,2,1,2,1,2]) == 6

assert Solution().longestSubsequence(nums = [1,2,3,2,1,2,3,2,1,2]) == 10

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

assert Solution().longestSubsequence(nums = [10,20,10,19,10,20]) == 5

assert Solution().longestSubsequence(nums = [1,2,3,2,1,2,3]) == 7

assert Solution().longestSubsequence(nums = [16,6,3]) == 3

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

assert Solution().longestSubsequence(nums = [1,2,3,4,3,2,1,2,3,4]) == 10

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

assert Solution().longestSubsequence(nums = [300, 250, 200, 150, 100, 50, 0]) == 7

assert Solution().longestSubsequence(nums = [1, 3, 5, 7, 9, 8, 6, 4, 2, 1]) == 7

assert Solution().longestSubsequence(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7]) == 6

assert Solution().longestSubsequence(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10

Answer: assert Solution().longestSubsequence(nums = [1,3,2,4,3,5,4,6,5,7]) == 6

Answer: assert Solution().longestSubsequence(nums = [1,10,1,10,1,10,1,10]) == 8

Answer: assert Solution().longestSubsequence(nums = [300,1,300,2,300,3,300]) == 7

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

Answer: assert Solution().longestSubsequence(nums = [100,150,100,200,100,200,100]) == 5

Answer: assert Solution().longestSubsequence(nums = [300,299,298,297,296,295,294]) == 7

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

Answer: assert Solution().longestSubsequence(nums = [1,300,2,299,3,298,4,297]) == 8

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

Answer: assert Solution().longestSubsequence(nums = [300,1,300,1,300]) == 5

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

Answer: assert Solution().longestSubsequence(nums = [1,100,2,99,3,98,4,97]) == 8

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

Answer: assert Solution().longestSubsequence(nums = [100,100,100,100,100]) == 5

Answer: assert Solution().longestSubsequence(nums = [1,2,1,2,1,2]) == 6

Answer: assert Solution().longestSubsequence(nums = [1,2,3,2,1,2,3,2,1,2]) == 10

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

Answer: assert Solution().longestSubsequence(nums = [10,20,10,19,10,20]) == 5

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

Answer: assert Solution().longestSubsequence(nums = [16,6,3]) == 3

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

Answer: assert Solution().longestSubsequence(nums = [300,299,298,297,296,295,294,293,292,291]) == 10

Answer: assert Solution().longestSubsequence(nums = [100,200,100,150,50,250,150]) == 5

Answer: assert Solution().longestSubsequence(nums = [1,2,3,4,3,2,1,2,3,4]) == 10

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

Answer: assert Solution().longestSubsequence(nums = [150, 100, 150, 200, 100, 150, 200, 250, 150]) == 7

Answer: assert Solution().longestSubsequence(nums = [150, 149, 148, 147, 146, 145, 144, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 131]) == 20

Answer: assert Solution().longestSubsequence(nums = [10, 20, 15, 30, 25, 35, 30, 40, 35, 45, 40, 50, 45, 55, 50, 60, 55, 65, 60, 70, 65, 75, 70, 80, 75, 85, 80, 90, 85, 95]) == 16

Answer: assert Solution().longestSubsequence(nums = [300, 200, 100, 150, 250, 50, 350, 250, 200]) == 6

Answer: assert Solution().longestSubsequence(nums = [300, 1, 299, 2, 298, 3, 297, 4, 296, 5, 295, 6, 294, 7, 293, 8]) == 16

Answer: assert Solution().longestSubsequence(nums = [150, 200, 100, 250, 50, 300, 75, 175, 125, 225, 275, 325, 350, 375, 400, 425, 450, 475, 500]) == 14

Answer: assert Solution().longestSubsequence(nums = [150, 250, 100, 200, 50, 150, 250, 100, 200, 50, 150, 250, 100, 200, 50]) == 8

Answer: assert Solution().longestSubsequence(nums = [300, 1, 299, 2, 298, 3, 297, 4, 296, 5]) == 10

Answer: assert Solution().longestSubsequence(nums = [150, 200, 250, 300, 250, 200, 150, 100, 50, 0, 50, 100, 150, 200, 250]) == 13

Answer: assert Solution().longestSubsequence(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 1, 10, 2, 9, 3, 8, 4, 7, 5, 6]) == 13

Answer: assert Solution().longestSubsequence(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4]) == 20

Answer: assert Solution().longestSubsequence(nums = [10, 20, 30, 25, 40, 50, 60, 55, 70, 80, 75, 90, 100, 95, 110]) == 11

Answer: assert Solution().longestSubsequence(nums = [1, 3, 5, 2, 4, 6, 3, 5, 7, 4, 6, 8, 5, 7, 9, 6, 8, 10]) == 11

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

Answer: assert Solution().longestSubsequence(nums = [10, 20, 30, 40, 50, 40, 30, 20, 10, 20, 30, 40, 50, 40, 30, 20, 10]) == 17

Answer: assert Solution().longestSubsequence(nums = [200, 150, 100, 150, 200, 250, 200, 150, 100, 150, 200]) == 11

Answer: assert Solution().longestSubsequence(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 19

Answer: assert Solution().longestSubsequence(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 15

Answer: assert Solution().longestSubsequence(nums = [250, 200, 225, 150, 175, 100, 125, 50, 75, 0, 25, 100, 50, 75, 25]) == 8

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

Answer: assert Solution().longestSubsequence(nums = [100, 200, 300, 200, 100, 200, 300, 200, 100, 200, 300, 200, 100]) == 13

Answer: assert Solution().longestSubsequence(nums = [150, 200, 100, 150, 250, 200, 150, 100, 50, 100, 150, 200, 250, 300, 250, 200, 150, 100, 50, 100, 150, 200, 250]) == 21

Answer: assert Solution().longestSubsequence(nums = [50, 60, 70, 80, 90, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 15

Answer: assert Solution().longestSubsequence(nums = [10, 20, 30, 25, 15, 10, 5, 15, 25, 35, 45]) == 8

Answer: assert Solution().longestSubsequence(nums = [120, 140, 130, 150, 160, 170, 180, 190, 200, 190, 180, 170, 160, 150, 140]) == 14

Answer: assert Solution().longestSubsequence(nums = [20, 40, 30, 50, 40, 60, 50, 70, 60, 80, 70, 90, 80, 100, 90, 110, 100]) == 10

Answer: assert Solution().longestSubsequence(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 14

Answer: assert Solution().longestSubsequence(nums = [300, 250, 200, 150, 100, 50, 0]) == 7

Answer: assert Solution().longestSubsequence(nums = [300, 299, 298, 297, 296, 295, 294, 293, 292, 291]) == 10

Answer: assert Solution().longestSubsequence(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10]) == 11

Answer: assert Solution().longestSubsequence(nums = [50, 100, 150, 200, 250, 300, 250, 200, 150, 100, 50, 100, 150, 200, 250, 300, 250, 200, 150, 100, 50]) == 21

Answer: assert Solution().longestSubsequence(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]) == 16

Answer: assert Solution().longestSubsequence(nums = [300, 200, 100, 50, 25, 10, 5, 2, 1]) == 9

Answer: assert Solution().longestSubsequence(nums = [20, 10, 30, 25, 40, 15, 50, 35, 10, 5, 60]) == 5

Answer: assert Solution().longestSubsequence(nums = [5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5]) == 11

Answer: assert Solution().longestSubsequence(nums = [10, 30, 20, 40, 30, 50, 40, 60, 50, 70, 60, 80, 70, 90, 80]) == 9

Answer: assert Solution().longestSubsequence(nums = [1, 5, 3, 9, 7, 13, 11, 17, 15, 21, 19, 25, 23, 29, 27, 33, 31, 37, 35, 41, 39, 45, 43, 49, 47, 53, 51, 57, 55, 61, 59, 65]) == 17

Answer: assert Solution().longestSubsequence(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 18

Answer: assert Solution().longestSubsequence(nums = [150, 200, 250, 300, 250, 200, 150, 100, 50, 0]) == 10

Answer: assert Solution().longestSubsequence(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 19

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

Answer: assert Solution().longestSubsequence(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, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]) == 50

Answer: assert Solution().longestSubsequence(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 28

Answer: assert Solution().longestSubsequence(nums = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 21

Answer: assert Solution().longestSubsequence(nums = [300, 1, 300, 2, 300, 3, 300, 4, 300, 5]) == 10

Answer: assert Solution().longestSubsequence(nums = [299, 200, 199, 150, 250, 100, 50, 200, 100]) == 6

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

Answer: assert Solution().longestSubsequence(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7]) == 6

Answer: assert Solution().longestSubsequence(nums = [10, 20, 30, 25, 40, 35, 50, 45, 60, 55, 70, 65, 80, 75]) == 9

Answer: assert Solution().longestSubsequence(nums = [300, 200, 100, 200, 300, 200, 100, 200, 300, 200, 100]) == 11

Answer: assert Solution().longestSubsequence(nums = [1, 10, 1, 20, 1, 30, 1, 40, 1, 50, 1, 60, 1, 70, 1, 80, 1, 90, 1, 100]) == 11

Answer: assert Solution().longestSubsequence(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 37

Answer: assert Solution().longestSubsequence(nums = [10, 20, 15, 25, 30, 20, 10, 30, 20, 10, 40, 30, 20, 10, 50, 40, 30, 20, 10]) == 11

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

Answer: assert Solution().longestSubsequence(nums = [10, 20, 15, 30, 25, 40, 35, 50, 45, 60]) == 6

Answer: assert Solution().longestSubsequence(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 25

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

Answer: assert Solution().longestSubsequence(nums = [300, 1, 300, 2, 300, 3, 300, 4, 300]) == 9

Answer: assert Solution().longestSubsequence(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 20

Answer: assert Solution().longestSubsequence(nums = [15, 30, 15, 45, 30, 60, 45, 75, 60, 90, 75, 105, 90, 120, 105]) == 9

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

Answer: assert Solution().longestSubsequence(nums = [150, 100, 50, 100, 150, 200, 250, 300, 250, 200, 150, 100, 50]) == 13

Answer: assert Solution().longestSubsequence(nums = [300, 100, 200, 300, 100, 200, 300, 100, 200, 300, 100, 200, 300, 100, 200]) == 11

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

Answer: assert Solution().longestSubsequence(nums = [100, 100, 200, 200, 100, 100, 200, 200, 100, 100]) == 6

Answer: assert Solution().longestSubsequence(nums = [150, 200, 150, 100, 150, 200, 150, 100, 150]) == 9

Answer: assert Solution().longestSubsequence(nums = [100, 150, 100, 200, 100, 150, 100, 200, 100, 150, 100, 200, 100, 150]) == 8

Answer: assert Solution().longestSubsequence(nums = [10, 20, 10, 30, 20, 40, 30, 50, 40, 60, 50, 70, 60, 80, 70]) == 9

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

Answer: assert Solution().longestSubsequence(nums = [150, 100, 200, 150, 100, 250, 150, 100, 300, 200]) == 6

Answer: assert Solution().longestSubsequence(nums = [250, 100, 150, 200, 100, 150, 200, 100, 150, 200]) == 8

Answer: assert Solution().longestSubsequence(nums = [300, 299, 298, 297, 296, 295, 294, 293, 292, 291, 290, 289, 288, 287, 286, 285, 284, 283, 282, 281, 280]) == 21

Answer: assert Solution().longestSubsequence(nums = [50, 100, 50, 150, 100, 200, 150, 250, 200, 300]) == 6

Answer: assert Solution().longestSubsequence(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 17

Answer: assert Solution().longestSubsequence(nums = [300, 299, 298, 297, 296, 295, 294, 293, 292, 291, 290]) == 11

Answer: assert Solution().longestSubsequence(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11]) == 10

Answer: assert Solution().longestSubsequence(nums = [200, 150, 250, 100, 300, 50, 150, 250, 200, 100, 300, 50]) == 6

Answer: assert Solution().longestSubsequence(nums = [1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1]) == 25

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

Answer: assert Solution().longestSubsequence(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5]) == 19

Answer: assert Solution().longestSubsequence(nums = [100, 150, 100, 150, 100, 150, 100, 150, 100, 150]) == 10

Answer: assert Solution().longestSubsequence(nums = [1, 300, 2, 299, 3, 298, 4, 297, 5, 296, 6, 295, 7, 294, 8, 293]) == 16

Answer: assert Solution().longestSubsequence(nums = [200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100]) == 14

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

Answer: assert Solution().longestSubsequence(nums = [1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2]) == 13

Answer: assert Solution().longestSubsequence(nums = [300, 250, 200, 150, 100, 50, 100, 150, 200, 250, 300, 250, 200, 150, 100, 50]) == 16

Answer: assert Solution().longestSubsequence(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == 20

Answer: assert Solution().longestSubsequence(nums = [300, 250, 200, 150, 100, 50, 100, 150, 200, 250, 300]) == 11

Answer: assert Solution().longestSubsequence(nums = [300, 299, 298, 297, 296, 295, 294, 293, 292, 291, 290, 289, 288, 287, 286, 285]) == 16

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

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

Answer: assert Solution().longestSubsequence(nums = [100, 150, 200, 250, 300, 250, 200, 150, 100, 50, 0, 50, 100, 150, 200]) == 13

Answer: assert Solution().longestSubsequence(nums = [50, 100, 75, 125, 100, 150, 125, 175, 150, 200, 175, 225, 200]) == 8

Answer: assert Solution().longestSubsequence(nums = [300, 290, 280, 270, 260, 250, 240, 230, 220, 210, 200, 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 1]) == 31

Answer: assert Solution().longestSubsequence(nums = [300, 250, 200, 150, 100, 50, 100, 150, 200, 250, 300, 250, 200, 150, 100, 50, 100, 150, 200, 250, 300, 250, 200]) == 23

Answer: assert Solution().longestSubsequence(nums = [50, 100, 150, 100, 50, 100, 150, 100, 50, 100, 150, 100, 50]) == 13

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 longestSubsequence(self, nums: list[int]) -> int:
    mx = max(nums)
    # dp[num][diff] := the length of the longest subsequence ending in `num`
    # s.t. the last absolute difference between consecutive elements is `diff`
    dp = [[0] * (mx + 1) for _ in range(mx + 1)]

    for num in nums:
      for prev in range(1, mx + 1):
        diff = abs(num - prev)
        dp[num][diff] = max(dp[num][diff], dp[prev][diff] + 1)
      # dp[num][diff] := max(dp[num][j]) for j >= diff
      for j in range(mx - 1, -1, -1):
        dp[num][j] = max(dp[num][j], dp[num][j + 1])

    return max(map(max, dp))


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 array nums.
You can do the following operation on the array at most once:

Choose any integer x such that nums remains non-empty on removing all occurrences of x.
Remove all occurrences of x from the array.

Return the maximum subarray sum across all possible resulting arrays.

Example 1:

Input: nums = [-3,2,-2,-1,3,-2,3]
Output: 7
Explanation:
We can have the following arrays after at most one operation:

The original array is nums = [-3, 2, -2, -1, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = -3 results in nums = [2, -2, -1, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = -2 results in nums = [-3, 2, -1, 3, 3]. The maximum subarray sum is 2 + (-1) + 3 + 3 = 7.
Deleting all occurences of x = -1 results in nums = [-3, 2, -2, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = 3 results in nums = [-3, 2, -2, -1, -2]. The maximum subarray sum is 2.

The output is max(4, 4, 7, 4, 2) = 7.

Example 2:

Input: nums = [1,2,3,4]
Output: 10
Explanation:
It is optimal to not perform any operations.

Constraints:

1 <= nums.length <= 105
-106 <= nums[i] <= 106

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

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums.
You can do the following operation on the array at most once:

Choose any integer x such that nums remains non-empty on removing all occurrences of x.
Remove all occurrences of x from the array.

Return the maximum subarray sum across all possible resulting arrays.

Example 1:

Input: nums = [-3,2,-2,-1,3,-2,3]
Output: 7
Explanation:
We can have the following arrays after at most one operation:

The original array is nums = [-3, 2, -2, -1, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = -3 results in nums = [2, -2, -1, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = -2 results in nums = [-3, 2, -1, 3, 3]. The maximum subarray sum is 2 + (-1) + 3 + 3 = 7.
Deleting all occurences of x = -1 results in nums = [-3, 2, -2, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = 3 results in nums = [-3, 2, -2, -1, -2]. The maximum subarray sum is 2.

The output is max(4, 4, 7, 4, 2) = 7.

Example 2:

Input: nums = [1,2,3,4]
Output: 10
Explanation:
It is optimal to not perform any operations.

Constraints:

1 <= nums.length <= 105
-106 <= nums[i] <= 106

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

SOLUTION:

assert Solution().maxSubarraySum(nums = [1,2,-1,3,-2,4,-3,5]) == 12

assert Solution().maxSubarraySum(nums = [1,-1,1,-1,1]) == 3

assert Solution().maxSubarraySum(nums = [1,2,2,1]) == 6

assert Solution().maxSubarraySum(nums = [5,-3,5,-2,5,-1,5]) == 17

assert Solution().maxSubarraySum(nums = [-3,2,-2,-1,3,-2,3]) == 7

assert Solution().maxSubarraySum(nums = [1,-1,1,-1,1,-1]) == 3

assert Solution().maxSubarraySum(nums = [1]) == 1

assert Solution().maxSubarraySum(nums = [-1,1,-1,1,-1,1]) == 3

assert Solution().maxSubarraySum(nums = [1,2,3,4]) == 10

assert Solution().maxSubarraySum(nums = [10,20,30,40,50]) == 150

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

assert Solution().maxSubarraySum(nums = [-5,-4,-3,-2,-1]) == -1

assert Solution().maxSubarraySum(nums = [0,0,0,0,0]) == 0

assert Solution().maxSubarraySum(nums = [5,5,5,5]) == 20

assert Solution().maxSubarraySum(nums = [1,2,-1,2,-1,1,-1]) == 6

assert Solution().maxSubarraySum(nums = [1,2,2,2,3,4,2,5]) == 21

assert Solution().maxSubarraySum(nums = [0,0,0,0]) == 0

assert Solution().maxSubarraySum(nums = [-1,-2,-3,-4]) == -1

assert Solution().maxSubarraySum(nums = [5,-1,5,-1,5]) == 15

assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 0, 0, 0, 0, 0]) == 15

assert Solution().maxSubarraySum(nums = [1,2,3,4,5,6,7,8,9,10]) == 55

assert Solution().maxSubarraySum(nums = [0, -1, -2, -3, -4, -5, 0]) == 0

assert Solution().maxSubarraySum(nums = [1, -2, 3, 4, -1, 2, 1, -5, 4]) == 13

assert Solution().maxSubarraySum(nums = [0,0,0,0,0,0,0,0,0,0]) == 0

assert Solution().maxSubarraySum(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 55

assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55

assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0

assert Solution().maxSubarraySum(nums = [5,-1,3,-2,5,6,-1,5]) == 22

assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10

Answer: assert Solution().maxSubarraySum(nums = [1,2,-1,3,-2,4,-3,5]) == 12

Answer: assert Solution().maxSubarraySum(nums = [1,-1,1,-1,1]) == 3

Answer: assert Solution().maxSubarraySum(nums = [1,2,2,1]) == 6

Answer: assert Solution().maxSubarraySum(nums = [5,-3,5,-2,5,-1,5]) == 17

Answer: assert Solution().maxSubarraySum(nums = [-3,2,-2,-1,3,-2,3]) == 7

Answer: assert Solution().maxSubarraySum(nums = [1,-1,1,-1,1,-1]) == 3

Answer: assert Solution().maxSubarraySum(nums = [1]) == 1

Answer: assert Solution().maxSubarraySum(nums = [-1,1,-1,1,-1,1]) == 3

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4]) == 10

Answer: assert Solution().maxSubarraySum(nums = [-1000000,-1000000,-1000000,-1000000]) == -1000000

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,-6,4,5,6,-7,8,9,10,-11]) == 42

Answer: assert Solution().maxSubarraySum(nums = [10,20,30,40,50]) == 150

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

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

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0,0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [5,5,5,5]) == 20

Answer: assert Solution().maxSubarraySum(nums = [1,-1000000,1000000,-1,1]) == 1000001

Answer: assert Solution().maxSubarraySum(nums = [1,2,-1,2,-1,1,-1]) == 6

Answer: assert Solution().maxSubarraySum(nums = [1,2,2,2,3,4,2,5]) == 21

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [-1,-2,-3,-4]) == -1

Answer: assert Solution().maxSubarraySum(nums = [5,-1,5,-1,5]) == 15

Answer: assert Solution().maxSubarraySum(nums = [1000000,-1000000,1000000,-1000000,1000000]) == 3000000

Answer: assert Solution().maxSubarraySum(nums = [1000000,1000000,1000000,1000000]) == 4000000

Answer: assert Solution().maxSubarraySum(nums = [1000000,-1000000,1000000]) == 2000000

Answer: assert Solution().maxSubarraySum(nums = [-1000000,1000000,-1000000,1000000]) == 2000000

Answer: assert Solution().maxSubarraySum(nums = [-1000000,1000000,-1000000,1000000,-1000000]) == 2000000

Answer: assert Solution().maxSubarraySum(nums = [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10]) == 19

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 0, 0, 0, 0, 0]) == 15

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, -10, -20, -30, 10, 20, 30, -40]) == 90

Answer: assert Solution().maxSubarraySum(nums = [-1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3]) == -1

Answer: assert Solution().maxSubarraySum(nums = [-1, -2, -3, -4, -5, 6, -7, -8, 6, -9, 6]) == 12

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 165

Answer: assert Solution().maxSubarraySum(nums = [5, 4, 3, 2, 1, -1, -2, -3, -4, -5, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5]) == 20

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4,5,6,7,8,9,10]) == 55

Answer: assert Solution().maxSubarraySum(nums = [3, -2, -3, 4, -1, -2, 1, 5, -3]) == 9

Answer: assert Solution().maxSubarraySum(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]) == 27

Answer: assert Solution().maxSubarraySum(nums = [5, -3, 5, -2, 5, -1, 5, -4, 5]) == 19

Answer: assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, -5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 14

Answer: assert Solution().maxSubarraySum(nums = [0, -1, -2, -3, -4, -5, 0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 210

Answer: assert Solution().maxSubarraySum(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55

Answer: assert Solution().maxSubarraySum(nums = [1, -2, 3, 4, -1, 2, 1, -5, 4]) == 13

Answer: assert Solution().maxSubarraySum(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]) == 29

Answer: assert Solution().maxSubarraySum(nums = [10,-5,10,-5,10,-5,10,-5,10,-5]) == 50

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, -6, 3, 2, 1, -6, 1, 2, 3]) == 18

Answer: assert Solution().maxSubarraySum(nums = [-1, -2, -3, 4, 5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20]) == 41

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 55

Answer: assert Solution().maxSubarraySum(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]) == 20

Answer: assert Solution().maxSubarraySum(nums = [5, -3, 5, -3, 5, -3, 5, -3, 5, -3]) == 25

Answer: assert Solution().maxSubarraySum(nums = [0, 1, -1, 2, -2, 3, -3, 4, -4, 5]) == 9

Answer: assert Solution().maxSubarraySum(nums = [10, -20, 10, -20, 10, -20, 10]) == 40

Answer: assert Solution().maxSubarraySum(nums = [10,-10,20,-20,30,-30,40,-40,50,-50,60,-60]) == 110

Answer: assert Solution().maxSubarraySum(nums = [1000000, -1000000, 1000000, -1000000, 1000000, -1000000, 1000000, -1000000, 1000000, -1000000, 1000000, -1000000]) == 6000000

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0,0,0,0,0,0,0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [10, 20, -30, 40, -50, 60, -70, 80, -90]) == 140

Answer: assert Solution().maxSubarraySum(nums = [1000000,-1000000,1000000,-1000000,1000000,-1000000,1000000,-1000000]) == 4000000

Answer: assert Solution().maxSubarraySum(nums = [5,4,-1,7,8,-2,4,-5,4,5,6,-7,8,9]) == 52

Answer: assert Solution().maxSubarraySum(nums = [1000000, -500000, 2000000, -1000000, 500000, -1500000, 2500000, -3000000]) == 4500000

Answer: assert Solution().maxSubarraySum(nums = [-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4,-5,4]) == 92

Answer: assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2]) == 15

Answer: assert Solution().maxSubarraySum(nums = [-10, 20, -30, 40, -50, 60, -70, 80, -90, 100, -110, 120, -130, 140, -150, 160, -170, 180, -190, 200]) == 380

Answer: assert Solution().maxSubarraySum(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]) == 29

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, -50, -100, -150, -200, -250, -300, -350, -400, -450, -500]) == 550

Answer: assert Solution().maxSubarraySum(nums = [100, 200, 300, 400, 500, -100, -200, -300, -400, -500, 100, 200, 300, 400, 500, -100, -200, -300, -400, -500]) == 2000

Answer: assert Solution().maxSubarraySum(nums = [-5, 5, -10, 10, -15, 15, -20, 20, -25, 25, -30, 30, -35, 35, -40, 40]) == 75

Answer: assert Solution().maxSubarraySum(nums = [5, 4, -1, 7, 8, -5, 4, -3, 2, 1, -4, 6, -7, 8, -9, 10, -11, 12]) == 38

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7]) == 13

Answer: assert Solution().maxSubarraySum(nums = [-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,16,-17,18,-19,20]) == 38

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6]) == 91

Answer: assert Solution().maxSubarraySum(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -50, -50, -50, -50, -50]) == 50

Answer: assert Solution().maxSubarraySum(nums = [-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]) == 210

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

Answer: assert Solution().maxSubarraySum(nums = [10, 20, -30, 40, -50, 60, -70, 80, -90, 100, -110, 120, -130, 140, -150, 160, -170, 180, -190, 200]) == 380

Answer: assert Solution().maxSubarraySum(nums = [-2, -3, -4, -5, 6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16]) == 31

Answer: assert Solution().maxSubarraySum(nums = [5, -3, 20, -7, 15, -10, 10, -5, 8]) == 43

Answer: assert Solution().maxSubarraySum(nums = [100, -50, 100, -50, 100, -50, 100, -50, 100, -50, 100, -50, 100]) == 700

Answer: assert Solution().maxSubarraySum(nums = [1000000, -1000000, 1000000, -1000000, 1000000, -1000000, 1000000, -1000000, 1000000, -1000000]) == 5000000

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4,5,4,3,2,1,1,2,3,4,5,5,4,3,2,1]) == 55

Answer: assert Solution().maxSubarraySum(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 55

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10]) == 19

Answer: assert Solution().maxSubarraySum(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 100, 200, 300, 400, 500]) == 1500

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, 40, 50, -5, -5, -5, -5, -5, 10, 20, 30, 40, 50, -5, -5, -5, -5, -5]) == 300

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 55

Answer: assert Solution().maxSubarraySum(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == -1

Answer: assert Solution().maxSubarraySum(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10]) == 16

Answer: assert Solution().maxSubarraySum(nums = [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12]) == 22

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10]) == 19

Answer: assert Solution().maxSubarraySum(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, -1000, -900, -800, -700, -600, -500, -400, -300, -200, -100]) == 5500

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 15

Answer: assert Solution().maxSubarraySum(nums = [10, -1, 10, -1, 10, -1, 10, -1, 10, -1, 10, -1, 10, -1, 10, -1, 10, -1, 10, -1]) == 100

Answer: assert Solution().maxSubarraySum(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 9

Answer: assert Solution().maxSubarraySum(nums = [5,-1,3,-2,5,6,-1,5]) == 22

Answer: assert Solution().maxSubarraySum(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 210

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 210

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -55, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 210

Answer: assert Solution().maxSubarraySum(nums = [1000000, 1000000, -1000000, -1000000, 1000000, 1000000, -1000000, -1000000, 1000000, 1000000, -1000000, -1000000]) == 6000000

Answer: assert Solution().maxSubarraySum(nums = [100, -100, 200, -200, 300, -300, 400, -400, 500, -500, 600, -600, 700, -700, 800, -800, 900, -900, 1000, -1000]) == 1900

Answer: assert Solution().maxSubarraySum(nums = [10,10,10,10,10,-10,-10,-10,-10,-10,20,20,20,20,20,-20,-20,-20,-20,-20]) == 150

Answer: assert Solution().maxSubarraySum(nums = [-2,1,-3,4,-1,2,1,-5,4,3,2,1]) == 16

Answer: assert Solution().maxSubarraySum(nums = [3, -1, -2, 4, 3, 2, 3, -5, 3, 1, -1, 3]) == 18

Answer: assert Solution().maxSubarraySum(nums = [100, -50, 200, -150, 300, -200, 400]) == 800

Answer: assert Solution().maxSubarraySum(nums = [1000000, -1, 2000000, -2, 3000000, -3, 4000000, -4, 5000000, -5]) == 14999994

Answer: assert Solution().maxSubarraySum(nums = [0, -1, 0, -1, 0, -1, 0, -1, 0, -1]) == 0

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

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10]) == 110

Answer: assert Solution().maxSubarraySum(nums = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]) == 0

Answer: assert Solution().maxSubarraySum(nums = [5, -1, 3, -2, 5, -4, 5, -6, 5]) == 16

Answer: assert Solution().maxSubarraySum(nums = [-1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10]) == 19

Answer: assert Solution().maxSubarraySum(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]) == 100

Answer: assert Solution().maxSubarraySum(nums = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == 53

Answer: assert Solution().maxSubarraySum(nums = [1,2,3,4,5,6,7,8,9,10,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10]) == 55

Answer: assert Solution().maxSubarraySum(nums = [3, -2, 5, -1, 4, 3, -2, 1, 5, -6]) == 20

Answer: assert Solution().maxSubarraySum(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]) == 160

Answer: assert Solution().maxSubarraySum(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 0, -5, -4, -3, -2, -1, 0, 1, 2]) == 15

Answer: assert Solution().maxSubarraySum(nums = [-1,2,3,-4,5,-6,7,-8,9,-10,11,-12,13,-14,15,-16,17,-18,19,-20]) == 36

Answer: assert Solution().maxSubarraySum(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]) == 56

Answer: assert Solution().maxSubarraySum(nums = [1,-1,1,-1,1,-1,1,-1,1,-1]) == 5

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

Answer: assert Solution().maxSubarraySum(nums = [1, 2, 3, 4, 5, -15, 6, 7, 8, 9, 10]) == 55

Answer: assert Solution().maxSubarraySum(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55

Answer: assert Solution().maxSubarraySum(nums = [-5,1,-4,2,3,-5,3,-5,2]) == 10

Answer: assert Solution().maxSubarraySum(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == 9

Answer: assert Solution().maxSubarraySum(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80, -80]) == 150

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

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

Answer: assert Solution().maxSubarraySum(nums = [1, 1, 1, 1, 1, -5, 1, 1, 1, 1, 1]) == 10

Answer: assert Solution().maxSubarraySum(nums = [-1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1]) == 6

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

Answer: assert Solution().maxSubarraySum(nums = [10, 20, 30, -10, -20, -30, 40, 50, -50, 60]) == 150

Answer: assert Solution().maxSubarraySum(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15]) == 28

Answer: assert Solution().maxSubarraySum(nums = [5, -1, 4, -2, 3, -3, 2, -2, 1, -1]) == 11

Answer: assert Solution().maxSubarraySum(nums = [1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,8,-8,9,-9]) == 17

Answer: assert Solution().maxSubarraySum(nums = [-1000, 1000, -1000, 1000, -1000, 1000, -1000, 1000, -1000, 1000]) == 5000

Answer: assert Solution().maxSubarraySum(nums = [1, -2, 3, 4, -5, 6, -7, 8, -9, 10]) == 19

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 maxSubarraySum(self, nums: list[int]) -> int:
    ans = max(nums)
    prefix = 0
    minPrefix = 0
    # the minimum prefix sum that can have a negative number removed
    modifiedMinPrefix = 0
    count = collections.Counter()
    # minPrefixPlusRemoval[num] := the minimum prefix sum plus removed `num`
    minPrefixPlusRemoval = {}

    for num in nums:
      prefix += num
      ans = max(ans, prefix - modifiedMinPrefix)
      if num < 0:
        count[num] += 1
        minPrefixPlusRemoval[num] = (
            min(minPrefixPlusRemoval.get(num, 0), minPrefix) + num)
        modifiedMinPrefix = min(modifiedMinPrefix,
                                count[num] * num,
                                minPrefixPlusRemoval[num])
      minPrefix = min(minPrefix, prefix)
      modifiedMinPrefix = min(modifiedMinPrefix, minPrefix)

    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 a string s.
We define the mirror of a letter in the English alphabet as its corresponding letter when the alphabet is reversed. For example, the mirror of 'a' is 'z', and the mirror of 'y' is 'b'.
Initially, all characters in the string s are unmarked.
You start with a score of 0, and you perform the following process on the string s:

Iterate through the string from left to right.
At each index i, find the closest unmarked index j such that j < i and s[j] is the mirror of s[i]. Then, mark both indices i and j, and add the value i - j to the total score.
If no such index j exists for the index i, move on to the next index without making any changes.

Return the total score at the end of the process.

Example 1:

Input: s = "aczzx"
Output: 5
Explanation:

i = 0. There is no index j that satisfies the conditions, so we skip.
i = 1. There is no index j that satisfies the conditions, so we skip.
i = 2. The closest index j that satisfies the conditions is j = 0, so we mark both indices 0 and 2, and then add 2 - 0 = 2 to the score.
i = 3. There is no index j that satisfies the conditions, so we skip.
i = 4. The closest index j that satisfies the conditions is j = 1, so we mark both indices 1 and 4, and then add 4 - 1 = 3 to the score.

Example 2:

Input: s = "abcdef"
Output: 0
Explanation:
For each index i, there is no index j that satisfies the conditions.

Constraints:

1 <= s.length <= 105
s consists only of lowercase English letters.

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

SOLUTION:

Question:
PROBLEM:
You are given a string s.
We define the mirror of a letter in the English alphabet as its corresponding letter when the alphabet is reversed. For example, the mirror of 'a' is 'z', and the mirror of 'y' is 'b'.
Initially, all characters in the string s are unmarked.
You start with a score of 0, and you perform the following process on the string s:

Iterate through the string from left to right.
At each index i, find the closest unmarked index j such that j < i and s[j] is the mirror of s[i]. Then, mark both indices i and j, and add the value i - j to the total score.
If no such index j exists for the index i, move on to the next index without making any changes.

Return the total score at the end of the process.

Example 1:

Input: s = "aczzx"
Output: 5
Explanation:

i = 0. There is no index j that satisfies the conditions, so we skip.
i = 1. There is no index j that satisfies the conditions, so we skip.
i = 2. The closest index j that satisfies the conditions is j = 0, so we mark both indices 0 and 2, and then add 2 - 0 = 2 to the score.
i = 3. There is no index j that satisfies the conditions, so we skip.
i = 4. The closest index j that satisfies the conditions is j = 1, so we mark both indices 1 and 4, and then add 4 - 1 = 3 to the score.

Example 2:

Input: s = "abcdef"
Output: 0
Explanation:
For each index i, there is no index j that satisfies the conditions.

Constraints:

1 <= s.length <= 105
s consists only of lowercase English letters.

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

SOLUTION:

assert Solution().calculateScore(s = "b") == 0

assert Solution().calculateScore(s = "mirror") == 1

assert Solution().calculateScore(s = "az") == 1

assert Solution().calculateScore(s = "abbabba") == 0

assert Solution().calculateScore(s = "abcba") == 0

assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyz") == 169

assert Solution().calculateScore(s = "qpwoeirutyplkjhgfdsazxcvbnm") == 96

assert Solution().calculateScore(s = "abzabzabz") == 6

assert Solution().calculateScore(s = "abcdef") == 0

assert Solution().calculateScore(s = "zazbzczdz") == 1

assert Solution().calculateScore(s = "a") == 0

assert Solution().calculateScore(s = "azbzczdzezfz") == 1

assert Solution().calculateScore(s = "ab") == 0

assert Solution().calculateScore(s = "aa") == 0

assert Solution().calculateScore(s = "abcddcba") == 0

assert Solution().calculateScore(s = "zxyyxz") == 0

assert Solution().calculateScore(s = "racecar") == 0

assert Solution().calculateScore(s = "abba") == 0

assert Solution().calculateScore(s = "aczzx") == 5

assert Solution().calculateScore(s = "azbzczdzez") == 1

assert Solution().calculateScore(s = "aabbccddeeffgg") == 0

assert Solution().calculateScore(s = "abccba") == 0

assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz") == 676

assert Solution().calculateScore(s = "aaabbbccczzzyyyxxxwwwvvvuutttrrrqqqpppoonnmmlkkjjiihhggffeeddccbbaa") == 438

assert Solution().calculateScore(s = "zazbzazbza") == 3

assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcba") == 169

assert Solution().calculateScore(s = "qzqyqxpqowqovqouqovqowqoxpqyqz") == 0

assert Solution().calculateScore(s = "azbzczdzdzcybxaybxaybxay") == 68

assert Solution().calculateScore(s = "mnopqrqpomnopqrqpomn") == 3

assert Solution().calculateScore(s = "racecarracecar") == 0

assert Solution().calculateScore(s = "abxyzaacxyxzbcdwvutbcddwvut") == 36

assert Solution().calculateScore(s = "qpwoeirutyplkjhgfdsazxcvbnmaabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz") == 807

assert Solution().calculateScore(s = "mnopqrstuvwxyzabcdefghijkl") == 145

assert Solution().calculateScore(s = "abcdwxyzzyxwvutslkjihgfeponmabcdwxyzzyxwvutslkjihgfeponm") == 194

assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

assert Solution().calculateScore(s = "azbzczdzdzcybxczbxazcyaxbycxaybzcz") == 68

assert Solution().calculateScore(s = "mnmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba") == 170

assert Solution().calculateScore(s = "abacabadabacaba") == 0

assert Solution().calculateScore(s = "abcdefgihgfedcba") == 0

assert Solution().calculateScore(s = "xyzzyxwvutuvwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba") == 356

assert Solution().calculateScore(s = "abcabcabcabcabcabcabcabcabcabc") == 0

assert Solution().calculateScore(s = "mnbvcxzlkjhgfdsapoiuytrewqzxcvbnmlkjhgfdsapoiuytrewqmnbvcxzlkjhgfdsapoiuytrewq") == 361

assert Solution().calculateScore(s = "thisisazerozeroscenario") == 28

assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzyxwvutsrqponmlkjihgfedcba") == 845

assert Solution().calculateScore(s = "qwertypoiuzxcvbnmkjhgfdaslkjhgfdaslkjhgfdas") == 151

assert Solution().calculateScore(s = "abcdefgihgfedcbazyxz") == 28

assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

assert Solution().calculateScore(s = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa") == 0

assert Solution().calculateScore(s = "mnopqrstuvwxyzzzzzxyvwutsrqpomn") == 2

assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba") == 338

assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz") == 338

assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzz") == 676

assert Solution().calculateScore(s = "zzzzzzzzzz") == 0

assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcbaedcba") == 169

assert Solution().calculateScore(s = "qzjihgfedcbazyxwvutsrqponmlk") == 101

assert Solution().calculateScore(s = "mnopqrstuvwxyzzxyvwutsrqpomn") == 2

assert Solution().calculateScore(s = "abcdefghijkjihgfedcbaabcdefghijkjihgfedcbaabcdefghijkjihgfedcba") == 0

assert Solution().calculateScore(s = "aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmnnnooopppqqqrrrssstttuuuuvvvvwwwwxxxxyyyyzzzz") == 2214

assert Solution().calculateScore(s = "abacabadabacabad") == 0

assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

assert Solution().calculateScore(s = "ababababababababababababab") == 0

assert Solution().calculateScore(s = "zzzzyyyyxxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeedcbaa") == 545

assert Solution().calculateScore(s = "mnbvcxzlkjhgfdsapoiuytrewqamnbvcxzlkjhgfdsapoiuytrewq") == 236

assert Solution().calculateScore(s = "amazingracecar") == 8

assert Solution().calculateScore(s = "mnopqrstuvzxywvutsrqponmlkjihgfedcba") == 170

assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

assert Solution().calculateScore(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc") == 0

assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba") == 338

assert Solution().calculateScore(s = "abzyba") == 4

assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzz") == 676

assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyzyxwvutsrqponmlkjihgfedcba") == 313

assert Solution().calculateScore(s = "zazazazazazazazazazazazazazazazazazazazazazazazazazazazaza") == 29

assert Solution().calculateScore(s = "aaaazzzz") == 16

assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcbaaabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz") == 845

Answer: assert Solution().calculateScore(s = "b") == 0

Answer: assert Solution().calculateScore(s = "mirror") == 1

Answer: assert Solution().calculateScore(s = "az") == 1

Answer: assert Solution().calculateScore(s = "abbabba") == 0

Answer: assert Solution().calculateScore(s = "abcba") == 0

Answer: assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyz") == 169

Answer: assert Solution().calculateScore(s = "qpwoeirutyplkjhgfdsazxcvbnm") == 96

Answer: assert Solution().calculateScore(s = "abzabzabz") == 6

Answer: assert Solution().calculateScore(s = "abcdef") == 0

Answer: assert Solution().calculateScore(s = "zazbzczdz") == 1

Answer: assert Solution().calculateScore(s = "a") == 0

Answer: assert Solution().calculateScore(s = "azbzczdzezfz") == 1

Answer: assert Solution().calculateScore(s = "ab") == 0

Answer: assert Solution().calculateScore(s = "aa") == 0

Answer: assert Solution().calculateScore(s = "abcddcba") == 0

Answer: assert Solution().calculateScore(s = "zxyyxz") == 0

Answer: assert Solution().calculateScore(s = "racecar") == 0

Answer: assert Solution().calculateScore(s = "abba") == 0

Answer: assert Solution().calculateScore(s = "aczzx") == 5

Answer: assert Solution().calculateScore(s = "azbzczdzez") == 1

Answer: assert Solution().calculateScore(s = "aabbccddeeffgg") == 0

Answer: assert Solution().calculateScore(s = "abccba") == 0

Answer: assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz") == 676

Answer: assert Solution().calculateScore(s = "aaabbbccczzzyyyxxxwwwvvvuutttrrrqqqpppoonnmmlkkjjiihhggffeeddccbbaa") == 438

Answer: assert Solution().calculateScore(s = "zazbzazbza") == 3

Answer: assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcba") == 169

Answer: assert Solution().calculateScore(s = "qzqyqxpqowqovqouqovqowqoxpqyqz") == 0

Answer: assert Solution().calculateScore(s = "azbzczdzdzcybxaybxaybxay") == 68

Answer: assert Solution().calculateScore(s = "mnopqrqpomnopqrqpomn") == 3

Answer: assert Solution().calculateScore(s = "racecarracecar") == 0

Answer: assert Solution().calculateScore(s = "abxyzaacxyxzbcdwvutbcddwvut") == 36

Answer: assert Solution().calculateScore(s = "qpwoeirutyplkjhgfdsazxcvbnmaabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz") == 807

Answer: assert Solution().calculateScore(s = "mnopqrstuvwxyzabcdefghijkl") == 145

Answer: assert Solution().calculateScore(s = "abcdwxyzzyxwvutslkjihgfeponmabcdwxyzzyxwvutslkjihgfeponm") == 194

Answer: assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

Answer: assert Solution().calculateScore(s = "azbzczdzdzcybxczbxazcyaxbycxaybzcz") == 68

Answer: assert Solution().calculateScore(s = "mnmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba") == 170

Answer: assert Solution().calculateScore(s = "abacabadabacaba") == 0

Answer: assert Solution().calculateScore(s = "abcdefgihgfedcba") == 0

Answer: assert Solution().calculateScore(s = "xyzzyxwvutuvwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba") == 356

Answer: assert Solution().calculateScore(s = "abcabcabcabcabcabcabcabcabcabc") == 0

Answer: assert Solution().calculateScore(s = "mnbvcxzlkjhgfdsapoiuytrewqzxcvbnmlkjhgfdsapoiuytrewqmnbvcxzlkjhgfdsapoiuytrewq") == 361

Answer: assert Solution().calculateScore(s = "thisisazerozeroscenario") == 28

Answer: assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzyxwvutsrqponmlkjihgfedcba") == 845

Answer: assert Solution().calculateScore(s = "qwertypoiuzxcvbnmkjhgfdaslkjhgfdaslkjhgfdas") == 151

Answer: assert Solution().calculateScore(s = "abcdefgihgfedcbazyxz") == 28

Answer: assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

Answer: assert Solution().calculateScore(s = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa") == 0

Answer: assert Solution().calculateScore(s = "mnopqrstuvwxyzzzzzxyvwutsrqpomn") == 2

Answer: assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba") == 338

Answer: assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz") == 338

Answer: assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzz") == 676

Answer: assert Solution().calculateScore(s = "zzzzzzzzzz") == 0

Answer: assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcbaedcba") == 169

Answer: assert Solution().calculateScore(s = "qzjihgfedcbazyxwvutsrqponmlk") == 101

Answer: assert Solution().calculateScore(s = "mnopqrstuvwxyzzxyvwutsrqpomn") == 2

Answer: assert Solution().calculateScore(s = "abcdefghijkjihgfedcbaabcdefghijkjihgfedcbaabcdefghijkjihgfedcba") == 0

Answer: assert Solution().calculateScore(s = "aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmnnnooopppqqqrrrssstttuuuuvvvvwwwwxxxxyyyyzzzz") == 2214

Answer: assert Solution().calculateScore(s = "abacabadabacabad") == 0

Answer: assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

Answer: assert Solution().calculateScore(s = "ababababababababababababab") == 0

Answer: assert Solution().calculateScore(s = "zzzzyyyyxxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeedcbaa") == 545

Answer: assert Solution().calculateScore(s = "mnbvcxzlkjhgfdsapoiuytrewqamnbvcxzlkjhgfdsapoiuytrewq") == 236

Answer: assert Solution().calculateScore(s = "amazingracecar") == 8

Answer: assert Solution().calculateScore(s = "mnopqrstuvzxywvutsrqponmlkjihgfedcba") == 170

Answer: assert Solution().calculateScore(s = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz") == 0

Answer: assert Solution().calculateScore(s = "abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc") == 0

Answer: assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba") == 338

Answer: assert Solution().calculateScore(s = "abzyba") == 4

Answer: assert Solution().calculateScore(s = "aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzz") == 676

Answer: assert Solution().calculateScore(s = "abcdefghijklmnopqrstuvwxyzyxwvutsrqponmlkjihgfedcba") == 313

Answer: assert Solution().calculateScore(s = "zazazazazazazazazazazazazazazazazazazazazazazazazazazazaza") == 29

Answer: assert Solution().calculateScore(s = "aaaazzzz") == 16

Answer: assert Solution().calculateScore(s = "zyxwvutsrqponmlkjihgfedcbaaabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz") == 845

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 calculateScore(self, s: str) -> int:
        d = defaultdict(list)
        ans = 0
        for i, x in enumerate(s):
            y = chr(ord("a") + ord("z") - ord(x))
            if d[y]:
                j = d[y].pop()
                ans += i - j
            else:
                d[x].append(i)
        return ans