Prompt:
from typing import List
def matrixSumQueries(n: int, queries: List[List[int]]) -> int:
    """
    You are given an integer n and a 0-indexed 2D array queries where queries[i] = [typei, indexi, vali].
    Initially, there is a 0-indexed n x n matrix filled with 0's. For each query, you must apply one of the following changes:

    if typei == 0, set the values in the row with indexi to vali, overwriting any previous values.
    if typei == 1, set the values in the column with indexi to vali, overwriting any previous values.

    Return the sum of integers in the matrix after all queries are applied.

    Example 1:

    >>> matrixSumQueries(n = 3, queries = [[0,0,1],[1,2,2],[0,2,3],[1,0,4]])
    >>> 23
    Explanation: The image above describes the matrix after each query. The sum of the matrix after all queries are applied is 23.

    Example 2:

    >>> matrixSumQueries(n = 3, queries = [[0,0,4],[0,1,2],[1,0,1],[0,2,3],[1,2,1]])
    >>> 17
    Explanation: The image above describes the matrix after each query. The sum of the matrix after all queries are applied is 17.
    """


Prompt:
def count(num1: str, num2: str, min_sum: int, max_sum: int) -> int:
    """
    You are given two numeric strings num1 and num2 and two integers max_sum and min_sum. We denote an integer x to be good if:

    num1 <= x <= num2
    min_sum <= digit_sum(x) <= max_sum.

    Return the number of good integers. Since the answer may be large, return it modulo 109 + 7.
    Note that digit_sum(x) denotes the sum of the digits of x.

    Example 1:

    >>> count(num1 = "1", num2 = "12", min_sum = 1, max_sum = 8)
    >>> 11
    Explanation: There are 11 integers whose sum of digits lies between 1 and 8 are 1,2,3,4,5,6,7,8,10,11, and 12. Thus, we return 11.

    Example 2:

    >>> count(num1 = "1", num2 = "5", min_sum = 1, max_sum = 5)
    >>> 5
    Explanation: The 5 integers whose sum of digits lies between 1 and 5 are 1,2,3,4, and 5. Thus, we return 5.
    """


Prompt:
def isFascinating(n: int) -> bool:
    """
    You are given an integer n that consists of exactly 3 digits.
    We call the number n fascinating if, after the following modification, the resulting number contains all the digits from 1 to 9 exactly once and does not contain any 0's:

    Concatenate n with the numbers 2 * n and 3 * n.

    Return true if n is fascinating, or false otherwise.
    Concatenating two numbers means joining them together. For example, the concatenation of 121 and 371 is 121371.

    Example 1:

    >>> isFascinating(n = 192)
    >>> true
    Explanation: We concatenate the numbers n = 192 and 2 * n = 384 and 3 * n = 576. The resulting number is 192384576. This number contains all the digits from 1 to 9 exactly once.

    Example 2:

    >>> isFascinating(n = 100)
    >>> false
    Explanation: We concatenate the numbers n = 100 and 2 * n = 200 and 3 * n = 300. The resulting number is 100200300. This number does not satisfy any of the conditions.
    """


Prompt:
def longestSemiRepetitiveSubstring(s: str) -> int:
    """
    You are given a digit string s that consists of digits from 0 to 9.
    A string is called semi-repetitive if there is at most one adjacent pair of the same digit. For example, "0010", "002020", "0123", "2002", and "54944" are semi-repetitive while the following are not: "00101022" (adjacent same digit pairs are 00 and 22), and "1101234883" (adjacent same digit pairs are 11 and 88).
    Return the length of the longest semi-repetitive substring of s.

    Example 1:

    >>> longestSemiRepetitiveSubstring(s = "52233")
    >>> 4
    Explanation:
    The longest semi-repetitive substring is "5223". Picking the whole string "52233" has two adjacent same digit pairs 22 and 33, but at most one is allowed.

    Example 2:

    >>> longestSemiRepetitiveSubstring(s = "5494")
    >>> 4
    Explanation:
    s is a semi-repetitive string.

    Example 3:

    >>> longestSemiRepetitiveSubstring(s = "1111111")
    >>> 2
    Explanation:
    The longest semi-repetitive substring is "11". Picking the substring "111" has two adjacent same digit pairs, but at most one is allowed.
    """


Prompt:
from typing import List
def sumDistance(nums: List[int], s: str, d: int) -> int:
    """
    Some robots are standing on an infinite number line with their initial coordinates given by a 0-indexed integer array nums and will start moving once given the command to move. The robots will move a unit distance each second.
    You are given a string s denoting the direction in which robots will move on command. 'L' means the robot will move towards the left side or negative side of the number line, whereas 'R' means the robot will move towards the right side or positive side of the number line.
    If two robots collide, they will start moving in opposite directions.
    Return the sum of distances between all the pairs of robots d seconds after the command. Since the sum can be very large, return it modulo 109 + 7.
    Note:

    For two robots at the index i and j, pair (i,j) and pair (j,i) are considered the same pair.
    When robots collide, they instantly change their directions without wasting any time.
    Collision happens when two robots share the same place in a moment.

    For example, if a robot is positioned in 0 going to the right and another is positioned in 2 going to the left, the next second they'll be both in 1 and they will change direction and the next second the first one will be in 0, heading left, and another will be in 2, heading right.
    For example, if a robot is positioned in 0 going to the right and another is positioned in 1 going to the left, the next second the first one will be in 0, heading left, and another will be in 1, heading right.

    Example 1:

    >>> sumDistance(nums = [-2,0,2], s = "RLL", d = 3)
    >>> 8
    Explanation:
    After 1 second, the positions are [-1,-1,1]. Now, the robot at index 0 will move left, and the robot at index 1 will move right.
    After 2 seconds, the positions are [-2,0,0]. Now, the robot at index 1 will move left, and the robot at index 2 will move right.
    After 3 seconds, the positions are [-3,-1,1].
    The distance between the robot at index 0 and 1 is abs(-3 - (-1)) = 2.
    The distance between the robot at index 0 and 2 is abs(-3 - 1) = 4.
    The distance between the robot at index 1 and 2 is abs(-1 - 1) = 2.
    The sum of the pairs of all distances = 2 + 4 + 2 = 8.

    Example 2:

    >>> sumDistance(nums = [1,0], s = "RL", d = 2)
    >>> 5
    Explanation:
    After 1 second, the positions are [2,-1].
    After 2 seconds, the positions are [3,-2].
    The distance between the two robots is abs(-2 - 3) = 5.
    """


Prompt:
from typing import List
def goodSubsetofBinaryMatrix(grid: List[List[int]]) -> List[int]:
    """
    You are given a 0-indexed m x n binary matrix grid.
    Let us call a non-empty subset of rows good if the sum of each column of the subset is at most half of the length of the subset.
    More formally, if the length of the chosen subset of rows is k, then the sum of each column should be at most floor(k / 2).
    Return an integer array that contains row indices of a good subset sorted in ascending order.
    If there are multiple good subsets, you can return any of them. If there are no good subsets, return an empty array.
    A subset of rows of the matrix grid is any matrix that can be obtained by deleting some (possibly none or all) rows from grid.

    Example 1:

    >>> goodSubsetofBinaryMatrix(grid = [[0,1,1,0],[0,0,0,1],[1,1,1,1]])
    >>> [0,1]
    Explanation: We can choose the 0th and 1st rows to create a good subset of rows.
    The length of the chosen subset is 2.
    - The sum of the 0th column is 0 + 0 = 0, which is at most half of the length of the subset.
    - The sum of the 1st column is 1 + 0 = 1, which is at most half of the length of the subset.
    - The sum of the 2nd column is 1 + 0 = 1, which is at most half of the length of the subset.
    - The sum of the 3rd column is 0 + 1 = 1, which is at most half of the length of the subset.

    Example 2:

    >>> goodSubsetofBinaryMatrix(grid = [[0]])
    >>> [0]
    Explanation: We can choose the 0th row to create a good subset of rows.
    The length of the chosen subset is 1.
    - The sum of the 0th column is 0, which is at most half of the length of the subset.

    Example 3:

    >>> goodSubsetofBinaryMatrix(grid = [[1,1,1],[1,1,1]])
    >>> []
    Explanation: It is impossible to choose any subset of rows to create a good subset.
    """


Prompt:
from typing import List
def findNonMinOrMax(nums: List[int]) -> int:
    """
    Given an integer array nums containing distinct positive integers, find and return any number from the array that is neither the minimum nor the maximum value in the array, or -1 if there is no such number.
    Return the selected integer.

    Example 1:

    >>> findNonMinOrMax(nums = [3,2,1,4])
    >>> 2
    Explanation: In this example, the minimum value is 1 and the maximum value is 4. Therefore, either 2 or 3 can be valid answers.

    Example 2:

    >>> findNonMinOrMax(nums = [1,2])
    >>> -1
    Explanation: Since there is no number in nums that is neither the maximum nor the minimum, we cannot select a number that satisfies the given condition. Therefore, there is no answer.

    Example 3:

    >>> findNonMinOrMax(nums = [2,1,3])
    >>> 2
    Explanation: Since 2 is neither the maximum nor the minimum value in nums, it is the only valid answer.
    """


Prompt:
def smallestString(s: str) -> str:
    """
    Given a string s consisting of lowercase English letters. Perform the following operation:

    Select any non-empty substring then replace every letter of the substring with the preceding letter of the English alphabet. For example, 'b' is converted to 'a', and 'a' is converted to 'z'.

    Return the lexicographically smallest string after performing the operation.

    Example 1:

    >>> smallestString(s = "cbabc")
    >>> "baabc"
    Explanation:
    Perform the operation on the substring starting at index 0, and ending at index 1 inclusive.

    Example 2:

    >>> smallestString(s = "aa")
    >>> "az"
    Explanation:
    Perform the operation on the last letter.

    Example 3:

    >>> smallestString(s = "acbbc")
    >>> "abaab"
    Explanation:
    Perform the operation on the substring starting at index 1, and ending at index 4 inclusive.

    Example 4:

    >>> smallestString(s = "leetcode")
    >>> "kddsbncd"
    Explanation:
    Perform the operation on the entire string.
    """


Prompt:
from typing import List
def minCost(nums: List[int], x: int) -> int:
    """
    You are given a 0-indexed integer array nums of size n representing the cost of collecting different chocolates. The cost of collecting the chocolate at the index i is nums[i]. Each chocolate is of a different type, and initially, the chocolate at the index i is of ith type.
    In one operation, you can do the following with an incurred cost of x:

    Simultaneously change the chocolate of ith type to ((i + 1) mod n)th type for all chocolates.

    Return the minimum cost to collect chocolates of all types, given that you can perform as many operations as you would like.

    Example 1:

    >>> minCost(nums = [20,1,15], x = 5)
    >>> 13
    Explanation: Initially, the chocolate types are [0,1,2]. We will buy the 1st type of chocolate at a cost of 1.
    Now, we will perform the operation at a cost of 5, and the types of chocolates will become [1,2,0]. We will buy the 2nd type of chocolate at a cost of 1.
    Now, we will again perform the operation at a cost of 5, and the chocolate types will become [2,0,1]. We will buy the 0th type of chocolate at a cost of 1.
    Thus, the total cost will become (1 + 5 + 1 + 5 + 1) = 13. We can prove that this is optimal.

    Example 2:

    >>> minCost(nums = [1,2,3], x = 4)
    >>> 6
    Explanation: We will collect all three types of chocolates at their own price without performing any operations. Therefore, the total cost is 1 + 2 + 3 = 6.
    """


Prompt:
from typing import List
def maximumSumQueries(nums1: List[int], nums2: List[int], queries: List[List[int]]) -> List[int]:
    """
    You are given two 0-indexed integer arrays nums1 and nums2, each of length n, and a 1-indexed 2D array queries where queries[i] = [xi, yi].
    For the ith query, find the maximum value of nums1[j] + nums2[j] among all indices j (0 <= j < n), where nums1[j] >= xi and nums2[j] >= yi, or -1 if there is no j satisfying the constraints.
    Return an array answer where answer[i] is the answer to the ith query.

    Example 1:

    >>> maximumSumQueries(nums1 = [4,3,1,2], nums2 = [2,4,9,5], queries = [[4,1],[1,3],[2,5]])
    >>> [6,10,7]
    Explanation:
    For the 1st query xi = 4 and yi = 1, we can select index j = 0 since nums1[j] >= 4 and nums2[j] >= 1. The sum nums1[j] + nums2[j] is 6, and we can show that 6 is the maximum we can obtain.

    For the 2nd query xi = 1 and yi = 3, we can select index j = 2 since nums1[j] >= 1 and nums2[j] >= 3. The sum nums1[j] + nums2[j] is 10, and we can show that 10 is the maximum we can obtain.

    For the 3rd query xi = 2 and yi = 5, we can select index j = 3 since nums1[j] >= 2 and nums2[j] >= 5. The sum nums1[j] + nums2[j] is 7, and we can show that 7 is the maximum we can obtain.

    Therefore, we return [6,10,7].

    Example 2:

    >>> maximumSumQueries(nums1 = [3,2,5], nums2 = [2,3,4], queries = [[4,4],[3,2],[1,1]])
    >>> [9,9,9]
    Explanation: For this example, we can use index j = 2 for all the queries since it satisfies the constraints for each query.

    Example 3:

    >>> maximumSumQueries(nums1 = [2,1], nums2 = [2,3], queries = [[3,3]])
    >>> [-1]
    Explanation: There is one query in this example with xi = 3 and yi = 3. For every index, j, either nums1[j] < xi or nums2[j] < yi. Hence, there is no solution.
    """


Prompt:
from typing import List
def minimumDistance(n: int, edges: List[List[int]], s: int, marked: List[int]) -> int:
    """
    You are given a positive integer n which is the number of nodes of a 0-indexed directed weighted graph and a 0-indexed 2D array edges where edges[i] = [ui, vi, wi] indicates that there is an edge from node ui to node vi with weight wi.
    You are also given a node s and a node array marked; your task is to find the minimum distance from s to any of the nodes in marked.
    Return an integer denoting the minimum distance from s to any node in marked or -1 if there are no paths from s to any of the marked nodes.

    Example 1:

    >>> minimumDistance(n = 4, edges = [[0,1,1],[1,2,3],[2,3,2],[0,3,4]], s = 0, marked = [2,3])
    >>> 4
    Explanation: There is one path from node 0 (the green node) to node 2 (a red node), which is 0->1->2, and has a distance of 1 + 3 = 4.
    There are two paths from node 0 to node 3 (a red node), which are 0->1->2->3 and 0->3, the first one has a distance of 1 + 3 + 2 = 6 and the second one has a distance of 4.
    The minimum of them is 4.

    Example 2:

    >>> minimumDistance(n = 5, edges = [[0,1,2],[0,2,4],[1,3,1],[2,3,3],[3,4,2]], s = 1, marked = [0,4])
    >>> 3
    Explanation: There are no paths from node 1 (the green node) to node 0 (a red node).
    There is one path from node 1 to node 4 (a red node), which is 1->3->4, and has a distance of 1 + 2 = 3.
    So the answer is 3.

    Example 3:

    >>> minimumDistance(n = 4, edges = [[0,1,1],[1,2,3],[2,3,2]], s = 3, marked = [0,1])
    >>> -1
    Explanation: There are no paths from node 3 (the green node) to any of the marked nodes (the red nodes), so the answer is -1.
    """


Prompt:
def distanceTraveled(mainTank: int, additionalTank: int) -> int:
    """
    A truck has two fuel tanks. You are given two integers, mainTank representing the fuel present in the main tank in liters and additionalTank representing the fuel present in the additional tank in liters.
    The truck has a mileage of 10 km per liter. Whenever 5 liters of fuel get used up in the main tank, if the additional tank has at least 1 liters of fuel, 1 liters of fuel will be transferred from the additional tank to the main tank.
    Return the maximum distance which can be traveled.
    Note: Injection from the additional tank is not continuous. It happens suddenly and immediately for every 5 liters consumed.

    Example 1:

    >>> distanceTraveled(mainTank = 5, additionalTank = 10)
    >>> 60
    Explanation:
    After spending 5 litre of fuel, fuel remaining is (5 - 5 + 1) = 1 litre and distance traveled is 50km.
    After spending another 1 litre of fuel, no fuel gets injected in the main tank and the main tank becomes empty.
    Total distance traveled is 60km.

    Example 2:

    >>> distanceTraveled(mainTank = 1, additionalTank = 2)
    >>> 10
    Explanation:
    After spending 1 litre of fuel, the main tank becomes empty.
    Total distance traveled is 10km.
    """


Prompt:
from typing import List
def findValueOfPartition(nums: List[int]) -> int:
    """
    You are given a positive integer array nums.
    Partition nums into two arrays, nums1 and nums2, such that:

    Each element of the array nums belongs to either the array nums1 or the array nums2.
    Both arrays are non-empty.
    The value of the partition is minimized.

    The value of the partition is |max(nums1) - min(nums2)|.
    Here, max(nums1) denotes the maximum element of the array nums1, and min(nums2) denotes the minimum element of the array nums2.
    Return the integer denoting the value of such partition.

    Example 1:

    >>> findValueOfPartition(nums = [1,3,2,4])
    >>> 1
    Explanation: We can partition the array nums into nums1 = [1,2] and nums2 = [3,4].
    - The maximum element of the array nums1 is equal to 2.
    - The minimum element of the array nums2 is equal to 3.
    The value of the partition is |2 - 3| = 1.
    It can be proven that 1 is the minimum value out of all partitions.

    Example 2:

    >>> findValueOfPartition(nums = [100,1,10])
    >>> 9
    Explanation: We can partition the array nums into nums1 = [10] and nums2 = [100,1].
    - The maximum element of the array nums1 is equal to 10.
    - The minimum element of the array nums2 is equal to 1.
    The value of the partition is |10 - 1| = 9.
    It can be proven that 9 is the minimum value out of all partitions.
    """


Prompt:
from typing import List
def specialPerm(nums: List[int]) -> int:
    """
    You are given a 0-indexed integer array nums containing n distinct positive integers. A permutation of nums is called special if:

    For all indexes 0 <= i < n - 1, either nums[i] % nums[i+1] == 0 or nums[i+1] % nums[i] == 0.

    Return the total number of special permutations. As the answer could be large, return it modulo 109 + 7.

    Example 1:

    >>> specialPerm(nums = [2,3,6])
    >>> 2
    Explanation: [3,6,2] and [2,6,3] are the two special permutations of nums.

    Example 2:

    >>> specialPerm(nums = [1,4,3])
    >>> 2
    Explanation: [3,1,4] and [4,1,3] are the two special permutations of nums.
    """


Prompt:
from typing import List
def paintWalls(cost: List[int], time: List[int]) -> int:
    """
    You are given two 0-indexed integer arrays, cost and time, of size n representing the costs and the time taken to paint n different walls respectively. There are two painters available:

    A paid painter that paints the ith wall in time[i] units of time and takes cost[i] units of money.
    A free painter that paints any wall in 1 unit of time at a cost of 0. But the free painter can only be used if the paid painter is already occupied.

    Return the minimum amount of money required to paint the n walls.

    Example 1:

    >>> paintWalls(cost = [1,2,3,2], time = [1,2,3,2])
    >>> 3
    Explanation: The walls at index 0 and 1 will be painted by the paid painter, and it will take 3 units of time; meanwhile, the free painter will paint the walls at index 2 and 3, free of cost in 2 units of time. Thus, the total cost is 1 + 2 = 3.

    Example 2:

    >>> paintWalls(cost = [2,3,4,2], time = [1,1,1,1])
    >>> 4
    Explanation: The walls at index 0 and 3 will be painted by the paid painter, and it will take 2 units of time; meanwhile, the free painter will paint the walls at index 1 and 2, free of cost in 2 units of time. Thus, the total cost is 2 + 2 = 4.
    """


Prompt:
from typing import Any
def numberOfSpecialSubstrings(s: str) -> int:
    """
    You are given a string s consisting only of lowercase English letters. We call a substring special if it contains no character which has occurred at least twice (in other words, it does not contain a repeating character). Your task is to count the number of special substrings. For example, in the string "pop", the substring "po" is a special substring, however, "pop" is not special (since 'p' has occurred twice).
    Return the number of special substrings.
    A substring is a contiguous sequence of characters within a string. For example, "abc" is a substring of "abcd", but "acd" is not.

    Example 1:

    >>> numberOfSpecialSubstrings(s = "abcd")
    >>> 10
    Explanation: Since each character occurs once, every substring is a special substring. We have 4 substrings of length one, 3 of length two, 2 of length three, and 1 substring of length four. So overall there are 4 + 3 + 2 + 1 = 10 special substrings.

    Example 2:

    >>> numberOfSpecialSubstrings(s = "ooo")
    >>> 3
    Explanation: Any substring with a length of at least two contains a repeating character. So we have to count the number of substrings of length one, which is 3.

    Example 3:

    >>> numberOfSpecialSubstrings(s = "abab")
    >>> 7
    Explanation: Special substrings are as follows (sorted by their start positions):
    Special substrings of length 1: "a", "b", "a", "b"
    Special substrings of length 2: "ab", "ba", "ab"
    And it can be shown that there are no special substrings with a length of at least three. So the answer would be 4 + 3 = 7.
    """


Prompt:
from typing import List
def maximumNumberOfStringPairs(words: List[str]) -> int:
    """
    You are given a 0-indexed array words consisting of distinct strings.
    The string words[i] can be paired with the string words[j] if:

    The string words[i] is equal to the reversed string of words[j].
    0 <= i < j < words.length.

    Return the maximum number of pairs that can be formed from the array words.
    Note that each string can belong in at most one pair.

    Example 1:

    >>> maximumNumberOfStringPairs(words = ["cd","ac","dc","ca","zz"])
    >>> 2
    Explanation: In this example, we can form 2 pair of strings in the following way:
    - We pair the 0th string with the 2nd string, as the reversed string of word[0] is "dc" and is equal to words[2].
    - We pair the 1st string with the 3rd string, as the reversed string of word[1] is "ca" and is equal to words[3].
    It can be proven that 2 is the maximum number of pairs that can be formed.
    Example 2:

    >>> maximumNumberOfStringPairs(words = ["ab","ba","cc"])
    >>> 1
    Explanation: In this example, we can form 1 pair of strings in the following way:
    - We pair the 0th string with the 1st string, as the reversed string of words[1] is "ab" and is equal to words[0].
    It can be proven that 1 is the maximum number of pairs that can be formed.

    Example 3:

    >>> maximumNumberOfStringPairs(words = ["aa","ab"])
    >>> 0
    Explanation: In this example, we are unable to form any pair of strings.
    """


Prompt:
def longestString(x: int, y: int, z: int) -> int:
    """
    You are given three integers x, y, and z.
    You have x strings equal to "AA", y strings equal to "BB", and z strings equal to "AB". You want to choose some (possibly all or none) of these strings and concatenate them in some order to form a new string. This new string must not contain "AAA" or "BBB" as a substring.
    Return the maximum possible length of the new string.
    A substring is a contiguous non-empty sequence of characters within a string.

    Example 1:

    >>> longestString(x = 2, y = 5, z = 1)
    >>> 12
    Explanation: We can concatenate the strings "BB", "AA", "BB", "AA", "BB", and "AB" in that order. Then, our new string is "BBAABBAABBAB".
    That string has length 12, and we can show that it is impossible to construct a string of longer length.

    Example 2:

    >>> longestString(x = 3, y = 2, z = 2)
    >>> 14
    Explanation: We can concatenate the strings "AB", "AB", "AA", "BB", "AA", "BB", and "AA" in that order. Then, our new string is "ABABAABBAABBAA".
    That string has length 14, and we can show that it is impossible to construct a string of longer length.
    """


Prompt:
from typing import List
def minimizeConcatenatedLength(words: List[str]) -> int:
    """
    You are given a 0-indexed array words containing n strings.
    Let's define a join operation join(x, y) between two strings x and y as concatenating them into xy. However, if the last character of x is equal to the first character of y, one of them is deleted.
    For example join("ab", "ba") = "aba" and join("ab", "cde") = "abcde".
    You are to perform n - 1 join operations. Let str0 = words[0]. Starting from i = 1 up to i = n - 1, for the ith operation, you can do one of the following:

    Make stri = join(stri - 1, words[i])
    Make stri = join(words[i], stri - 1)

    Your task is to minimize the length of strn - 1.
    Return an integer denoting the minimum possible length of strn - 1.

    Example 1:

    >>> minimizeConcatenatedLength(words = ["aa","ab","bc"])
    >>> 4
    Explanation: In this example, we can perform join operations in the following order to minimize the length of str2:
    str0 = "aa"
    str1 = join(str0, "ab") = "aab"
    str2 = join(str1, "bc") = "aabc"
    It can be shown that the minimum possible length of str2 is 4.
    Example 2:

    >>> minimizeConcatenatedLength(words = ["ab","b"])
    >>> 2
    Explanation: In this example, str0 = "ab", there are two ways to get str1:
    join(str0, "b") = "ab" or join("b", str0) = "bab".
    The first string, "ab", has the minimum length. Hence, the answer is 2.

    Example 3:

    >>> minimizeConcatenatedLength(words = ["aaa","c","aba"])
    >>> 6
    Explanation: In this example, we can perform join operations in the following order to minimize the length of str2:
    str0 = "aaa"
    str1 = join(str0, "c") = "aaac"
    str2 = join("aba", str1) = "abaaac"
    It can be shown that the minimum possible length of str2 is 6.
    """


Prompt:
from typing import List
def countServers(n: int, logs: List[List[int]], x: int, queries: List[int]) -> List[int]:
    """
    You are given an integer n denoting the total number of servers and a 2D 0-indexed integer array logs, where logs[i] = [server_id, time] denotes that the server with id server_id received a request at time time.
    You are also given an integer x and a 0-indexed integer array queries.
    Return a 0-indexed integer array arr of length queries.length where arr[i] represents the number of servers that did not receive any requests during the time interval [queries[i] - x, queries[i]].
    Note that the time intervals are inclusive.

    Example 1:

    >>> countServers(n = 3, logs = [[1,3],[2,6],[1,5]], x = 5, queries = [10,11])
    >>> [1,2]
    Explanation:
    For queries[0]: The servers with ids 1 and 2 get requests in the duration of [5, 10]. Hence, only server 3 gets zero requests.
    For queries[1]: Only the server with id 2 gets a request in duration of [6,11]. Hence, the servers with ids 1 and 3 are the only servers that do not receive any requests during that time period.

    Example 2:

    >>> countServers(n = 3, logs = [[2,4],[2,1],[1,2],[3,1]], x = 2, queries = [3,4])
    >>> [0,1]
    Explanation:
    For queries[0]: All servers get at least one request in the duration of [1, 3].
    For queries[1]: Only server with id 3 gets no request in the duration [2,4].
    """


Prompt:
from typing import List
def countBeautifulPairs(nums: List[int]) -> int:
    """
    You are given a 0-indexed integer array nums. A pair of indices i, j where 0 <= i < j < nums.length is called beautiful if the first digit of nums[i] and the last digit of nums[j] are coprime.
    Return the total number of beautiful pairs in nums.
    Two integers x and y are coprime if there is no integer greater than 1 that divides both of them. In other words, x and y are coprime if gcd(x, y) == 1, where gcd(x, y) is the greatest common divisor of x and y.

    Example 1:

    >>> countBeautifulPairs(nums = [2,5,1,4])
    >>> 5
    Explanation: There are 5 beautiful pairs in nums:
    When i = 0 and j = 1: the first digit of nums[0] is 2, and the last digit of nums[1] is 5. We can confirm that 2 and 5 are coprime, since gcd(2,5) == 1.
    When i = 0 and j = 2: the first digit of nums[0] is 2, and the last digit of nums[2] is 1. Indeed, gcd(2,1) == 1.
    When i = 1 and j = 2: the first digit of nums[1] is 5, and the last digit of nums[2] is 1. Indeed, gcd(5,1) == 1.
    When i = 1 and j = 3: the first digit of nums[1] is 5, and the last digit of nums[3] is 4. Indeed, gcd(5,4) == 1.
    When i = 2 and j = 3: the first digit of nums[2] is 1, and the last digit of nums[3] is 4. Indeed, gcd(1,4) == 1.
    Thus, we return 5.

    Example 2:

    >>> countBeautifulPairs(nums = [11,21,12])
    >>> 2
    Explanation: There are 2 beautiful pairs:
    When i = 0 and j = 1: the first digit of nums[0] is 1, and the last digit of nums[1] is 1. Indeed, gcd(1,1) == 1.
    When i = 0 and j = 2: the first digit of nums[0] is 1, and the last digit of nums[2] is 2. Indeed, gcd(1,2) == 1.
    Thus, we return 2.
    """


Prompt:
def makeTheIntegerZero(num1: int, num2: int) -> int:
    """
    You are given two integers num1 and num2.
    In one operation, you can choose integer i in the range [0, 60] and subtract 2i + num2 from num1.
    Return the integer denoting the minimum number of operations needed to make num1 equal to 0.
    If it is impossible to make num1 equal to 0, return -1.

    Example 1:

    >>> makeTheIntegerZero(num1 = 3, num2 = -2)
    >>> 3
    Explanation: We can make 3 equal to 0 with the following operations:
    - We choose i = 2 and subtract 22 + (-2) from 3, 3 - (4 + (-2)) = 1.
    - We choose i = 2 and subtract 22 + (-2) from 1, 1 - (4 + (-2)) = -1.
    - We choose i = 0 and subtract 20 + (-2) from -1, (-1) - (1 + (-2)) = 0.
    It can be proven, that 3 is the minimum number of operations that we need to perform.

    Example 2:

    >>> makeTheIntegerZero(num1 = 5, num2 = 7)
    >>> -1
    Explanation: It can be proven, that it is impossible to make 5 equal to 0 with the given operation.
    """


Prompt:
from typing import List
def numberOfGoodSubarraySplits(nums: List[int]) -> int:
    """
    You are given a binary array nums.
    A subarray of an array is good if it contains exactly one element with the value 1.
    Return an integer denoting the number of ways to split the array nums into good subarrays. As the number may be too large, return it modulo 109 + 7.
    A subarray is a contiguous non-empty sequence of elements within an array.

    Example 1:

    >>> numberOfGoodSubarraySplits(nums = [0,1,0,0,1])
    >>> 3
    Explanation: There are 3 ways to split nums into good subarrays:
    - [0,1] [0,0,1]
    - [0,1,0] [0,1]
    - [0,1,0,0] [1]

    Example 2:

    >>> numberOfGoodSubarraySplits(nums = [0,1,0])
    >>> 1
    Explanation: There is 1 way to split nums into good subarrays:
    - [0,1,0]
    """


Prompt:
from typing import List
def survivedRobotsHealths(positions: List[int], healths: List[int], directions: str) -> List[int]:
    """
    There are n 1-indexed robots, each having a position on a line, health, and movement direction.
    You are given 0-indexed integer arrays positions, healths, and a string directions (directions[i] is either 'L' for left or 'R' for right). All integers in positions are unique.
    All robots start moving on the line simultaneously at the same speed in their given directions. If two robots ever share the same position while moving, they will collide.
    If two robots collide, the robot with lower health is removed from the line, and the health of the other robot decreases by one. The surviving robot continues in the same direction it was going. If both robots have the same health, they are both removed from the line.
    Your task is to determine the health of the robots that survive the collisions, in the same order that the robots were given, i.e. final health of robot 1 (if survived), final health of robot 2 (if survived), and so on. If there are no survivors, return an empty array.
    Return an array containing the health of the remaining robots (in the order they were given in the input), after no further collisions can occur.
    Note: The positions may be unsorted.

    Example 1:

    >>> survivedRobotsHealths(positions = [5,4,3,2,1], healths = [2,17,9,15,10], directions = "RRRRR")
    >>> [2,17,9,15,10]
    Explanation: No collision occurs in this example, since all robots are moving in the same direction. So, the health of the robots in order from the first robot is returned, [2, 17, 9, 15, 10].

    Example 2:

    >>> survivedRobotsHealths(positions = [3,5,2,6], healths = [10,10,15,12], directions = "RLRL")
    >>> [14]
    Explanation: There are 2 collisions in this example. Firstly, robot 1 and robot 2 will collide, and since both have the same health, they will be removed from the line. Next, robot 3 and robot 4 will collide and since robot 4's health is smaller, it gets removed, and robot 3's health becomes 15 - 1 = 14. Only robot 3 remains, so we return [14].

    Example 3:

    >>> survivedRobotsHealths(positions = [1,2,5,6], healths = [10,10,11,11], directions = "RLRL")
    >>> []
    Explanation: Robot 1 and robot 2 will collide and since both have the same health, they are both removed. Robot 3 and 4 will collide and since both have the same health, they are both removed. So, we return an empty array, [].
    """


Prompt:
from typing import List
def longestAlternatingSubarray(nums: List[int], threshold: int) -> int:
    """
    You are given a 0-indexed integer array nums and an integer threshold.
    Find the length of the longest subarray of nums starting at index l and ending at index r (0 <= l <= r < nums.length) that satisfies the following conditions:

    nums[l] % 2 == 0
    For all indices i in the range [l, r - 1], nums[i] % 2 != nums[i + 1] % 2
    For all indices i in the range [l, r], nums[i] <= threshold

    Return an integer denoting the length of the longest such subarray.
    Note: A subarray is a contiguous non-empty sequence of elements within an array.

    Example 1:

    >>> longestAlternatingSubarray(nums = [3,2,5,4], threshold = 5)
    >>> 3
    Explanation: In this example, we can select the subarray that starts at l = 1 and ends at r = 3 => [2,5,4]. This subarray satisfies the conditions.
    Hence, the answer is the length of the subarray, 3. We can show that 3 is the maximum possible achievable length.
    Example 2:

    >>> longestAlternatingSubarray(nums = [1,2], threshold = 2)
    >>> 1
    Explanation: In this example, we can select the subarray that starts at l = 1 and ends at r = 1 => [2].
    It satisfies all the conditions and we can show that 1 is the maximum possible achievable length.

    Example 3:

    >>> longestAlternatingSubarray(nums = [2,3,4,5], threshold = 4)
    >>> 3
    Explanation: In this example, we can select the subarray that starts at l = 0 and ends at r = 2 => [2,3,4].
    It satisfies all the conditions.
    Hence, the answer is the length of the subarray, 3. We can show that 3 is the maximum possible achievable length.
    """


Prompt:
from typing import List
def findPrimePairs(n: int) -> List[List[int]]:
    """
    You are given an integer n. We say that two integers x and y form a prime number pair if:

    1 <= x <= y <= n
    x + y == n
    x and y are prime numbers

    Return the 2D sorted list of prime number pairs [xi, yi]. The list should be sorted in increasing order of xi. If there are no prime number pairs at all, return an empty array.
    Note: A prime number is a natural number greater than 1 with only two factors, itself and 1.

    Example 1:

    >>> findPrimePairs(n = 10)
    >>> [[3,7],[5,5]]
    Explanation: In this example, there are two prime pairs that satisfy the criteria.
    These pairs are [3,7] and [5,5], and we return them in the sorted order as described in the problem statement.

    Example 2:

    >>> findPrimePairs(n = 2)
    >>> []
    Explanation: We can show that there is no prime number pair that gives a sum of 2, so we return an empty array.
    """


Prompt:
from typing import List
def continuousSubarrays(nums: List[int]) -> int:
    """
    You are given a 0-indexed integer array nums. A subarray of nums is called continuous if:

    Let i, i + 1, ..., j be the indices in the subarray. Then, for each pair of indices i <= i1, i2 <= j, 0 <= |nums[i1] - nums[i2]| <= 2.

    Return the total number of continuous subarrays.
    A subarray is a contiguous non-empty sequence of elements within an array.

    Example 1:

    >>> continuousSubarrays(nums = [5,4,2,4])
    >>> 8
    Explanation:
    Continuous subarray of size 1: [5], [4], [2], [4].
    Continuous subarray of size 2: [5,4], [4,2], [2,4].
    Continuous subarray of size 3: [4,2,4].
    There are no subarrys of size 4.
    Total continuous subarrays = 4 + 3 + 1 = 8.
    It can be shown that there are no more continuous subarrays.

    Example 2:

    >>> continuousSubarrays(nums = [1,2,3])
    >>> 6
    Explanation:
    Continuous subarray of size 1: [1], [2], [3].
    Continuous subarray of size 2: [1,2], [2,3].
    Continuous subarray of size 3: [1,2,3].
    Total continuous subarrays = 3 + 2 + 1 = 6.
    """


Prompt:
from typing import List
def sumImbalanceNumbers(nums: List[int]) -> int:
    """
    The imbalance number of a 0-indexed integer array arr of length n is defined as the number of indices in sarr = sorted(arr) such that:

    0 <= i < n - 1, and
    sarr[i+1] - sarr[i] > 1

    Here, sorted(arr) is the function that returns the sorted version of arr.
    Given a 0-indexed integer array nums, return the sum of imbalance numbers of all its subarrays.
    A subarray is a contiguous non-empty sequence of elements within an array.

    Example 1:

    >>> sumImbalanceNumbers(nums = [2,3,1,4])
    >>> 3
    Explanation: There are 3 subarrays with non-zero imbalance numbers:
    - Subarray [3, 1] with an imbalance number of 1.
    - Subarray [3, 1, 4] with an imbalance number of 1.
    - Subarray [1, 4] with an imbalance number of 1.
    The imbalance number of all other subarrays is 0. Hence, the sum of imbalance numbers of all the subarrays of nums is 3.

    Example 2:

    >>> sumImbalanceNumbers(nums = [1,3,3,3,5])
    >>> 8
    Explanation: There are 7 subarrays with non-zero imbalance numbers:
    - Subarray [1, 3] with an imbalance number of 1.
    - Subarray [1, 3, 3] with an imbalance number of 1.
    - Subarray [1, 3, 3, 3] with an imbalance number of 1.
    - Subarray [1, 3, 3, 3, 5] with an imbalance number of 2.
    - Subarray [3, 3, 3, 5] with an imbalance number of 1.
    - Subarray [3, 3, 5] with an imbalance number of 1.
    - Subarray [3, 5] with an imbalance number of 1.
    The imbalance number of all other subarrays is 0. Hence, the sum of imbalance numbers of all the subarrays of nums is 8.
    """


Prompt:
from typing import List
def isPreorder(nodes: List[List[int]]) -> bool:
    """
    Given a 0-indexed integer 2D array nodes, your task is to determine if the given array represents the preorder traversal of some binary tree.
    For each index i, nodes[i] = [id, parentId], where id is the id of the node at the index i and parentId is the id of its parent in the tree (if the node has no parent, then parentId == -1).
    Return true if the given array represents the preorder traversal of some tree, and false otherwise.
    Note: the preorder traversal of a tree is a recursive way to traverse a tree in which we first visit the current node, then we do the preorder traversal for the left child, and finally, we do it for the right child.

    Example 1:

    >>> isPreorder(nodes = [[0,-1],[1,0],[2,0],[3,2],[4,2]])
    >>> true
    Explanation: The given nodes make the tree in the picture below.
    We can show that this is the preorder traversal of the tree, first we visit node 0, then we do the preorder traversal of the right child which is [1], then we do the preorder traversal of the left child which is [2,3,4].

    Example 2:

    >>> isPreorder(nodes = [[0,-1],[1,0],[2,0],[3,1],[4,1]])
    >>> false
    Explanation: The given nodes make the tree in the picture below.
    For the preorder traversal, first we visit node 0, then we do the preorder traversal of the right child which is [1,3,4], but we can see that in the given order, 2 comes between 1 and 3, so, it's not the preorder traversal of the tree.
    """


Prompt:
from typing import List
def alternatingSubarray(nums: List[int]) -> int:
    """
    You are given a 0-indexed integer array nums. A subarray s of length m is called alternating if:

    m is greater than 1.
    s1 = s0 + 1.
    The 0-indexed subarray s looks like [s0, s1, s0, s1,...,s(m-1) % 2]. In other words, s1 - s0 = 1, s2 - s1 = -1, s3 - s2 = 1, s4 - s3 = -1, and so on up to s[m - 1] - s[m - 2] = (-1)m.

    Return the maximum length of all alternating subarrays present in nums or -1 if no such subarray exists.
    A subarray is a contiguous non-empty sequence of elements within an array.

    Example 1:

    >>> alternatingSubarray(nums = [2,3,4,3,4])
    >>> 4
    Explanation:
    The alternating subarrays are [2, 3], [3,4], [3,4,3], and [3,4,3,4]. The longest of these is [3,4,3,4], which is of length 4.

    Example 2:

    >>> alternatingSubarray(nums = [4,5,6])
    >>> 2
    Explanation:
    [4,5] and [5,6] are the only two alternating subarrays. They are both of length 2.
    """


Prompt:
from typing import List
def relocateMarbles(nums: List[int], moveFrom: List[int], moveTo: List[int]) -> List[int]:
    """
    You are given a 0-indexed integer array nums representing the initial positions of some marbles. You are also given two 0-indexed integer arrays moveFrom and moveTo of equal length.
    Throughout moveFrom.length steps, you will change the positions of the marbles. On the ith step, you will move all marbles at position moveFrom[i] to position moveTo[i].
    After completing all the steps, return the sorted list of occupied positions.
    Notes:

    We call a position occupied if there is at least one marble in that position.
    There may be multiple marbles in a single position.

    Example 1:

    >>> relocateMarbles(nums = [1,6,7,8], moveFrom = [1,7,2], moveTo = [2,9,5])
    >>> [5,6,8,9]
    Explanation: Initially, the marbles are at positions 1,6,7,8.
    At the i = 0th step, we move the marbles at position 1 to position 2. Then, positions 2,6,7,8 are occupied.
    At the i = 1st step, we move the marbles at position 7 to position 9. Then, positions 2,6,8,9 are occupied.
    At the i = 2nd step, we move the marbles at position 2 to position 5. Then, positions 5,6,8,9 are occupied.
    At the end, the final positions containing at least one marbles are [5,6,8,9].
    Example 2:

    >>> relocateMarbles(nums = [1,1,3,3], moveFrom = [1,3], moveTo = [2,2])
    >>> [2]
    Explanation: Initially, the marbles are at positions [1,1,3,3].
    At the i = 0th step, we move all the marbles at position 1 to position 2. Then, the marbles are at positions [2,2,3,3].
    At the i = 1st step, we move all the marbles at position 3 to position 2. Then, the marbles are at positions [2,2,2,2].
    Since 2 is the only occupied position, we return [2].
    """


Prompt:
def minimumBeautifulSubstrings(s: str) -> int:
    """
    Given a binary string s, partition the string into one or more substrings such that each substring is beautiful.
    A string is beautiful if:

    It doesn't contain leading zeros.
    It's the binary representation of a number that is a power of 5.

    Return the minimum number of substrings in such partition. If it is impossible to partition the string s into beautiful substrings, return -1.
    A substring is a contiguous sequence of characters in a string.

    Example 1:

    >>> minimumBeautifulSubstrings(s = "1011")
    >>> 2
    Explanation: We can paritition the given string into ["101", "1"].
    - The string "101" does not contain leading zeros and is the binary representation of integer 51 = 5.
    - The string "1" does not contain leading zeros and is the binary representation of integer 50 = 1.
    It can be shown that 2 is the minimum number of beautiful substrings that s can be partitioned into.

    Example 2:

    >>> minimumBeautifulSubstrings(s = "111")
    >>> 3
    Explanation: We can paritition the given string into ["1", "1", "1"].
    - The string "1" does not contain leading zeros and is the binary representation of integer 50 = 1.
    It can be shown that 3 is the minimum number of beautiful substrings that s can be partitioned into.

    Example 3:

    >>> minimumBeautifulSubstrings(s = "0")
    >>> -1
    Explanation: We can not partition the given string into beautiful substrings.
    """


Prompt:
from typing import List
def countBlackBlocks(m: int, n: int, coordinates: List[List[int]]) -> List[int]:
    """
    You are given two integers m and n representing the dimensions of a 0-indexed m x n grid.
    You are also given a 0-indexed 2D integer matrix coordinates, where coordinates[i] = [x, y] indicates that the cell with coordinates [x, y] is colored black. All cells in the grid that do not appear in coordinates are white.
    A block is defined as a 2 x 2 submatrix of the grid. More formally, a block with cell [x, y] as its top-left corner where 0 <= x < m - 1 and 0 <= y < n - 1 contains the coordinates [x, y], [x + 1, y], [x, y + 1], and [x + 1, y + 1].
    Return a 0-indexed integer array arr of size 5 such that arr[i] is the number of blocks that contains exactly i black cells.

    Example 1:

    >>> countBlackBlocks(m = 3, n = 3, coordinates = [[0,0]])
    >>> [3,1,0,0,0]
    Explanation: The grid looks like this:

    There is only 1 block with one black cell, and it is the block starting with cell [0,0].
    The other 3 blocks start with cells [0,1], [1,0] and [1,1]. They all have zero black cells.
    Thus, we return [3,1,0,0,0].

    Example 2:

    >>> countBlackBlocks(m = 3, n = 3, coordinates = [[0,0],[1,1],[0,2]])
    >>> [0,2,2,0,0]
    Explanation: The grid looks like this:

    There are 2 blocks with two black cells (the ones starting with cell coordinates [0,0] and [0,1]).
    The other 2 blocks have starting cell coordinates of [1,0] and [1,1]. They both have 1 black cell.
    Therefore, we return [0,2,2,0,0].
    """


Prompt:
def theMaximumAchievableX(num: int, t: int) -> int:
    """
    Given two integers, num and t. A number x is achievable if it can become equal to num after applying the following operation at most t times:

    Increase or decrease x by 1, and simultaneously increase or decrease num by 1.

    Return the maximum possible value of x.

    Example 1:

    >>> theMaximumAchievableX(num = 4, t = 1)
    >>> 6
    Explanation:
    Apply the following operation once to make the maximum achievable number equal to num:

    Decrease the maximum achievable number by 1, and increase num by 1.

    Example 2:

    >>> theMaximumAchievableX(num = 3, t = 2)
    >>> 7
    Explanation:
    Apply the following operation twice to make the maximum achievable number equal to num:

    Decrease the maximum achievable number by 1, and increase num by 1.
    """


Prompt:
from typing import List
def maximumJumps(nums: List[int], target: int) -> int:
    """
    You are given a 0-indexed array nums of n integers and an integer target.
    You are initially positioned at index 0. In one step, you can jump from index i to any index j such that:

    0 <= i < j < n
    -target <= nums[j] - nums[i] <= target

    Return the maximum number of jumps you can make to reach index n - 1.
    If there is no way to reach index n - 1, return -1.

    Example 1:

    >>> maximumJumps(nums = [1,3,6,4,1,2], target = 2)
    >>> 3
    Explanation: To go from index 0 to index n - 1 with the maximum number of jumps, you can perform the following jumping sequence:
    - Jump from index 0 to index 1.
    - Jump from index 1 to index 3.
    - Jump from index 3 to index 5.
    It can be proven that there is no other jumping sequence that goes from 0 to n - 1 with more than 3 jumps. Hence, the answer is 3.
    Example 2:

    >>> maximumJumps(nums = [1,3,6,4,1,2], target = 3)
    >>> 5
    Explanation: To go from index 0 to index n - 1 with the maximum number of jumps, you can perform the following jumping sequence:
    - Jump from index 0 to index 1.
    - Jump from index 1 to index 2.
    - Jump from index 2 to index 3.
    - Jump from index 3 to index 4.
    - Jump from index 4 to index 5.
    It can be proven that there is no other jumping sequence that goes from 0 to n - 1 with more than 5 jumps. Hence, the answer is 5.
    Example 3:

    >>> maximumJumps(nums = [1,3,6,4,1,2], target = 0)
    >>> -1
    Explanation: It can be proven that there is no jumping sequence that goes from 0 to n - 1. Hence, the answer is -1.
    """


Prompt:
from typing import List
def maxNonDecreasingLength(nums1: List[int], nums2: List[int]) -> int:
    """
    You are given two 0-indexed integer arrays nums1 and nums2 of length n.
    Let's define another 0-indexed integer array, nums3, of length n. For each index i in the range [0, n - 1], you can assign either nums1[i] or nums2[i] to nums3[i].
    Your task is to maximize the length of the longest non-decreasing subarray in nums3 by choosing its values optimally.
    Return an integer representing the length of the longest non-decreasing subarray in nums3.
    Note: A subarray is a contiguous non-empty sequence of elements within an array.

    Example 1:

    >>> maxNonDecreasingLength(nums1 = [2,3,1], nums2 = [1,2,1])
    >>> 2
    Explanation: One way to construct nums3 is:
    nums3 = [nums1[0], nums2[1], nums2[2]] => [2,2,1].
    The subarray starting from index 0 and ending at index 1, [2,2], forms a non-decreasing subarray of length 2.
    We can show that 2 is the maximum achievable length.
    Example 2:

    >>> maxNonDecreasingLength(nums1 = [1,3,2,1], nums2 = [2,2,3,4])
    >>> 4
    Explanation: One way to construct nums3 is:
    nums3 = [nums1[0], nums2[1], nums2[2], nums2[3]] => [1,2,3,4].
    The entire array forms a non-decreasing subarray of length 4, making it the maximum achievable length.

    Example 3:

    >>> maxNonDecreasingLength(nums1 = [1,1], nums2 = [2,2])
    >>> 2
    Explanation: One way to construct nums3 is:
    nums3 = [nums1[0], nums1[1]] => [1,1].
    The entire array forms a non-decreasing subarray of length 2, making it the maximum achievable length.
    """


Prompt:
from typing import List
def checkArray(nums: List[int], k: int) -> bool:
    """
    You are given a 0-indexed integer array nums and a positive integer k.
    You can apply the following operation on the array any number of times:

    Choose any subarray of size k from the array and decrease all its elements by 1.

    Return true if you can make all the array elements equal to 0, or false otherwise.
    A subarray is a contiguous non-empty part of an array.

    Example 1:

    >>> checkArray(nums = [2,2,3,1,1,0], k = 3)
    >>> true
    Explanation: We can do the following operations:
    - Choose the subarray [2,2,3]. The resulting array will be nums = [1,1,2,1,1,0].
    - Choose the subarray [2,1,1]. The resulting array will be nums = [1,1,1,0,0,0].
    - Choose the subarray [1,1,1]. The resulting array will be nums = [0,0,0,0,0,0].

    Example 2:

    >>> checkArray(nums = [1,3,1,1], k = 2)
    >>> false
    Explanation: It is not possible to make all the array elements equal to 0.
    """


Prompt:
from typing import Optional
class TreeNode:
    def __init__(val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
def heightOfTree(root: Optional[TreeNode]) -> int:
"""
You are given a root, which is the root of a special binary tree with n nodes. The nodes of the special binary tree are numbered from 1 to n. Suppose the tree has k leaves in the following order: b1 < b2 < ... < bk.
The leaves of this tree have a special property! That is, for every leaf bi, the following conditions hold:

The right child of bi is bi + 1 if i < k, and b1 otherwise.
The left child of bi is bi - 1 if i > 1, and bk otherwise.

Return the height of the given tree.
Note: The height of a binary tree is the length of the longest path from the root to any other node.

Example 1:

>>> heightOfTree(root = [1,2,3,null,null,4,5])
>>> 2
Explanation: The given tree is shown in the following picture. Each leaf's left child is the leaf to its left (shown with the blue edges). Each leaf's right child is the leaf to its right (shown with the red edges). We can see that the graph has a height of 2.

Example 2:

>>> heightOfTree(root = [1,2])
>>> 1
Explanation: The given tree is shown in the following picture. There is only one leaf, so it doesn't have any left or right child. We can see that the graph has a height of 1.

Example 3:

>>> heightOfTree(root = [1,2,3,null,null,4,null,5,6])
>>> 3
Explanation: The given tree is shown in the following picture. Each leaf's left child is the leaf to its left (shown with the blue edges). Each leaf's right child is the leaf to its right (shown with the red edges). We can see that the graph has a height of 3.
"""


Prompt:
from typing import List
def sumOfSquares(nums: List[int]) -> int:
    """
    You are given a 1-indexed integer array nums of length n.
    An element nums[i] of nums is called special if i divides n, i.e. n % i == 0.
    Return the sum of the squares of all special elements of nums.

    Example 1:

    >>> sumOfSquares(nums = [1,2,3,4])
    >>> 21
    Explanation: There are exactly 3 special elements in nums: nums[1] since 1 divides 4, nums[2] since 2 divides 4, and nums[4] since 4 divides 4.
    Hence, the sum of the squares of all special elements of nums is nums[1] * nums[1] + nums[2] * nums[2] + nums[4] * nums[4] = 1 * 1 + 2 * 2 + 4 * 4 = 21.

    Example 2:

    >>> sumOfSquares(nums = [2,7,1,19,18,3])
    >>> 63
    Explanation: There are exactly 4 special elements in nums: nums[1] since 1 divides 6, nums[2] since 2 divides 6, nums[3] since 3 divides 6, and nums[6] since 6 divides 6.
    Hence, the sum of the squares of all special elements of nums is nums[1] * nums[1] + nums[2] * nums[2] + nums[3] * nums[3] + nums[6] * nums[6] = 2 * 2 + 7 * 7 + 1 * 1 + 3 * 3 = 63.
    """


Prompt:
from typing import List
def maximumBeauty(nums: List[int], k: int) -> int:
    """
    You are given a 0-indexed array nums and a non-negative integer k.
    In one operation, you can do the following:

    Choose an index i that hasn't been chosen before from the range [0, nums.length - 1].
    Replace nums[i] with any integer from the range [nums[i] - k, nums[i] + k].

    The beauty of the array is the length of the longest subsequence consisting of equal elements.
    Return the maximum possible beauty of the array nums after applying the operation any number of times.
    Note that you can apply the operation to each index only once.
    A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the order of the remaining elements.

    Example 1:

    >>> maximumBeauty(nums = [4,6,1,2], k = 2)
    >>> 3
    Explanation: In this example, we apply the following operations:
    - Choose index 1, replace it with 4 (from range [4,8]), nums = [4,4,1,2].
    - Choose index 3, replace it with 4 (from range [0,4]), nums = [4,4,1,4].
    After the applied operations, the beauty of the array nums is 3 (subsequence consisting of indices 0, 1, and 3).
    It can be proven that 3 is the maximum possible length we can achieve.

    Example 2:

    >>> maximumBeauty(nums = [1,1,1,1], k = 10)
    >>> 4
    Explanation: In this example we don't have to apply any operations.
    The beauty of the array nums is 4 (whole array).
    """


Prompt:
from typing import List
def minimumIndex(nums: List[int]) -> int:
    """
    An element x of an integer array arr of length m is dominant if more than half the elements of arr have a value of x.
    You are given a 0-indexed integer array nums of length n with one dominant element.
    You can split nums at an index i into two arrays nums[0, ..., i] and nums[i + 1, ..., n - 1], but the split is only valid if:

    0 <= i < n - 1
    nums[0, ..., i], and nums[i + 1, ..., n - 1] have the same dominant element.

    Here, nums[i, ..., j] denotes the subarray of nums starting at index i and ending at index j, both ends being inclusive. Particularly, if j < i then nums[i, ..., j] denotes an empty subarray.
    Return the minimum index of a valid split. If no valid split exists, return -1.

    Example 1:

    >>> minimumIndex(nums = [1,2,2,2])
    >>> 2
    Explanation: We can split the array at index 2 to obtain arrays [1,2,2] and [2].
    In array [1,2,2], element 2 is dominant since it occurs twice in the array and 2 * 2 > 3.
    In array [2], element 2 is dominant since it occurs once in the array and 1 * 2 > 1.
    Both [1,2,2] and [2] have the same dominant element as nums, so this is a valid split.
    It can be shown that index 2 is the minimum index of a valid split.
    Example 2:

    >>> minimumIndex(nums = [2,1,3,1,1,1,7,1,2,1])
    >>> 4
    Explanation: We can split the array at index 4 to obtain arrays [2,1,3,1,1] and [1,7,1,2,1].
    In array [2,1,3,1,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.
    In array [1,7,1,2,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.
    Both [2,1,3,1,1] and [1,7,1,2,1] have the same dominant element as nums, so this is a valid split.
    It can be shown that index 4 is the minimum index of a valid split.
    Example 3:

    >>> minimumIndex(nums = [3,3,3,3,7,2,2])
    >>> -1
    Explanation: It can be shown that there is no valid split.
    """


Prompt:
from typing import List
def longestValidSubstring(word: str, forbidden: List[str]) -> int:
    """
    You are given a string word and an array of strings forbidden.
    A string is called valid if none of its substrings are present in forbidden.
    Return the length of the longest valid substring of the string word.
    A substring is a contiguous sequence of characters in a string, possibly empty.

    Example 1:

    >>> longestValidSubstring(word = "cbaaaabc", forbidden = ["aaa","cb"])
    >>> 4
    Explanation: There are 11 valid substrings in word: "c", "b", "a", "ba", "aa", "bc", "baa", "aab", "ab", "abc" and "aabc". The length of the longest valid substring is 4.
    It can be shown that all other substrings contain either "aaa" or "cb" as a substring.
    Example 2:

    >>> longestValidSubstring(word = "leetcode", forbidden = ["de","le","e"])
    >>> 4
    Explanation: There are 11 valid substrings in word: "l", "t", "c", "o", "d", "tc", "co", "od", "tco", "cod", and "tcod". The length of the longest valid substring is 4.
    It can be shown that all other substrings contain either "de", "le", or "e" as a substring.
    """


Prompt:
from typing import Optional
# class CategoryHandler:
#     def haveSameCategory(a: int, b: int) -> bool:
#         pass
def numberOfCategories(n: int, categoryHandler: Optional['CategoryHandler']) -> int:
"""
You are given an integer n and an object categoryHandler of class CategoryHandler.
There are n elements, numbered from 0 to n - 1. Each element has a category, and your task is to find the number of unique categories.
The class CategoryHandler contains the following function, which may help you:

boolean haveSameCategory(integer a, integer b): Returns true if a and b are in the same category and false otherwise. Also, if either a or b is not a valid number (i.e. it's greater than or equal to nor less than 0), it returns false.

Return the number of unique categories.

Example 1:

>>> haveSameCategory(n = 6, categoryHandler = [1,1,2,2,3,3])
>>> 3
Explanation: There are 6 elements in this example. The first two elements belong to category 1, the second two belong to category 2, and the last two elements belong to category 3. So there are 3 unique categories.

Example 2:

>>> haveSameCategory(n = 5, categoryHandler = [1,2,3,4,5])
>>> 5
Explanation: There are 5 elements in this example. Each element belongs to a unique category. So there are 5 unique categories.

Example 3:

>>> haveSameCategory(n = 3, categoryHandler = [1,1,1])
>>> 1
Explanation: There are 3 elements in this example. All of them belong to one category. So there is only 1 unique category.
"""


Prompt:
from typing import List
def isGood(nums: List[int]) -> bool:
    """
    You are given an integer array nums. We consider an array good if it is a permutation of an array base[n].
    base[n] = [1, 2, ..., n - 1, n, n] (in other words, it is an array of length n + 1 which contains 1 to n - 1 exactly once, plus two occurrences of n). For example, base[1] = [1, 1] and base[3] = [1, 2, 3, 3].
    Return true if the given array is good, otherwise return false.
    Note: A permutation of integers represents an arrangement of these numbers.

    Example 1:

    >>> isGood(nums = [2, 1, 3])
    >>> false
    Explanation: Since the maximum element of the array is 3, the only candidate n for which this array could be a permutation of base[n], is n = 3. However, base[3] has four elements but array nums has three. Therefore, it can not be a permutation of base[3] = [1, 2, 3, 3]. So the answer is false.

    Example 2:

    >>> isGood(nums = [1, 3, 3, 2])
    >>> true
    Explanation: Since the maximum element of the array is 3, the only candidate n for which this array could be a permutation of base[n], is n = 3. It can be seen that nums is a permutation of base[3] = [1, 2, 3, 3] (by swapping the second and fourth elements in nums, we reach base[3]). Therefore, the answer is true.
    Example 3:

    >>> isGood(nums = [1, 1])
    >>> true
    Explanation: Since the maximum element of the array is 1, the only candidate n for which this array could be a permutation of base[n], is n = 1. It can be seen that nums is a permutation of base[1] = [1, 1]. Therefore, the answer is true.
    Example 4:

    >>> isGood(nums = [3, 4, 4, 1, 2, 1])
    >>> false
    Explanation: Since the maximum element of the array is 4, the only candidate n for which this array could be a permutation of base[n], is n = 4. However, base[4] has five elements but array nums has six. Therefore, it can not be a permutation of base[4] = [1, 2, 3, 4, 4]. So the answer is false.
    """


Prompt:
def sortVowels(s: str) -> str:
    """
    Given a 0-indexed string s, permute s to get a new string t such that:

    All consonants remain in their original places. More formally, if there is an index i with 0 <= i < s.length such that s[i] is a consonant, then t[i] = s[i].
    The vowels must be sorted in the nondecreasing order of their ASCII values. More formally, for pairs of indices i, j with 0 <= i < j < s.length such that s[i] and s[j] are vowels, then t[i] must not have a higher ASCII value than t[j].

    Return the resulting string.
    The vowels are 'a', 'e', 'i', 'o', and 'u', and they can appear in lowercase or uppercase. Consonants comprise all letters that are not vowels.

    Example 1:

    >>> sortVowels(s = "lEetcOde")
    >>> "lEOtcede"
    Explanation: 'E', 'O', and 'e' are the vowels in s; 'l', 't', 'c', and 'd' are all consonants. The vowels are sorted according to their ASCII values, and the consonants remain in the same places.

    Example 2:

    >>> sortVowels(s = "lYmpH")
    >>> "lYmpH"
    Explanation: There are no vowels in s (all characters in s are consonants), so we return "lYmpH".
    """


Prompt:
from typing import List
def maxScore(nums: List[int], x: int) -> int:
    """
    You are given a 0-indexed integer array nums and a positive integer x.
    You are initially at position 0 in the array and you can visit other positions according to the following rules:

    If you are currently in position i, then you can move to any position j such that i < j.
    For each position i that you visit, you get a score of nums[i].
    If you move from a position i to a position j and the parities of nums[i] and nums[j] differ, then you lose a score of x.

    Return the maximum total score you can get.
    Note that initially you have nums[0] points.

    Example 1:

    >>> maxScore(nums = [2,3,6,1,9,2], x = 5)
    >>> 13
    Explanation: We can visit the following positions in the array: 0 -> 2 -> 3 -> 4.
    The corresponding values are 2, 6, 1 and 9. Since the integers 6 and 1 have different parities, the move 2 -> 3 will make you lose a score of x = 5.
    The total score will be: 2 + 6 + 1 + 9 - 5 = 13.

    Example 2:

    >>> maxScore(nums = [2,4,6,8], x = 3)
    >>> 20
    Explanation: All the integers in the array have the same parities, so we can visit all of them without losing any score.
    The total score is: 2 + 4 + 6 + 8 = 20.
    """


Prompt:
def numberOfWays(n: int, x: int) -> int:
    """
    Given two positive integers n and x.
    Return the number of ways n can be expressed as the sum of the xth power of unique positive integers, in other words, the number of sets of unique integers [n1, n2, ..., nk] where n = n1x + n2x + ... + nkx.
    Since the result can be very large, return it modulo 109 + 7.
    For example, if n = 160 and x = 3, one way to express n is n = 23 + 33 + 53.

    Example 1:

    >>> numberOfWays(n = 10, x = 2)
    >>> 1
    Explanation: We can express n as the following: n = 32 + 12 = 10.
    It can be shown that it is the only way to express 10 as the sum of the 2nd power of unique integers.

    Example 2:

    >>> numberOfWays(n = 4, x = 1)
    >>> 2
    Explanation: We can express n in the following ways:
    - n = 41 = 4.
    - n = 31 + 11 = 4.
    """


Prompt:
from typing import List
def splitWordsBySeparator(words: List[str], separator: str) -> List[str]:
    """
    Given an array of strings words and a character separator, split each string in words by separator.
    Return an array of strings containing the new strings formed after the splits, excluding empty strings.
    Notes

    separator is used to determine where the split should occur, but it is not included as part of the resulting strings.
    A split may result in more than two strings.
    The resulting strings must maintain the same order as they were initially given.

    Example 1:

    >>> splitWordsBySeparator(words = ["one.two.three","four.five","six"], separator = ".")
    >>> ["one","two","three","four","five","six"]
    Explanation: In this example we split as follows:

    "one.two.three" splits into "one", "two", "three"
    "four.five" splits into "four", "five"
    "six" splits into "six"

    Hence, the resulting array is ["one","two","three","four","five","six"].
    Example 2:

    >>> splitWordsBySeparator(words = ["$easy$","$problem$"], separator = "$")
    >>> ["easy","problem"]
    Explanation: In this example we split as follows:

    "$easy$" splits into "easy" (excluding empty strings)
    "$problem$" splits into "problem" (excluding empty strings)

    Hence, the resulting array is ["easy","problem"].

    Example 3:

    >>> splitWordsBySeparator(words = ["|||"], separator = "|")
    >>> []
    Explanation: In this example the resulting split of "|||" will contain only empty strings, so we return an empty array [].
    """


Prompt:
from typing import List
def maxArrayValue(nums: List[int]) -> int:
    """
    You are given a 0-indexed array nums consisting of positive integers.
    You can do the following operation on the array any number of times:

    Choose an integer i such that 0 <= i < nums.length - 1 and nums[i] <= nums[i + 1]. Replace the element nums[i + 1] with nums[i] + nums[i + 1] and delete the element nums[i] from the array.

    Return the value of the largest element that you can possibly obtain in the final array.

    Example 1:

    >>> maxArrayValue(nums = [2,3,7,9,3])
    >>> 21
    Explanation: We can apply the following operations on the array:
    - Choose i = 0. The resulting array will be nums = [5,7,9,3].
    - Choose i = 1. The resulting array will be nums = [5,16,3].
    - Choose i = 0. The resulting array will be nums = [21,3].
    The largest element in the final array is 21. It can be shown that we cannot obtain a larger element.

    Example 2:

    >>> maxArrayValue(nums = [5,3,3])
    >>> 11
    Explanation: We can do the following operations on the array:
    - Choose i = 1. The resulting array will be nums = [5,6].
    - Choose i = 0. The resulting array will be nums = [11].
    There is only one element in the final array, which is 11.
    """


Prompt:
from typing import List
def maxIncreasingGroups(usageLimits: List[int]) -> int:
    """
    You are given a 0-indexed array usageLimits of length n.
    Your task is to create groups using numbers from 0 to n - 1, ensuring that each number, i, is used no more than usageLimits[i] times in total across all groups. You must also satisfy the following conditions:

    Each group must consist of distinct numbers, meaning that no duplicate numbers are allowed within a single group.
    Each group (except the first one) must have a length strictly greater than the previous group.

    Return an integer denoting the maximum number of groups you can create while satisfying these conditions.

    Example 1:

    >>> maxIncreasingGroups(usageLimits = [1,2,5])
    >>> 3
    Explanation: In this example, we can use 0 at most once, 1 at most twice, and 2 at most five times.
    One way of creating the maximum number of groups while satisfying the conditions is:
    Group 1 contains the number [2].
    Group 2 contains the numbers [1,2].
    Group 3 contains the numbers [0,1,2].
    It can be shown that the maximum number of groups is 3.
    So, the output is 3.
    Example 2:

    >>> maxIncreasingGroups(usageLimits = [2,1,2])
    >>> 2
    Explanation: In this example, we can use 0 at most twice, 1 at most once, and 2 at most twice.
    One way of creating the maximum number of groups while satisfying the conditions is:
    Group 1 contains the number [0].
    Group 2 contains the numbers [1,2].
    It can be shown that the maximum number of groups is 2.
    So, the output is 2.

    Example 3:

    >>> maxIncreasingGroups(usageLimits = [1,1])
    >>> 1
    Explanation: In this example, we can use both 0 and 1 at most once.
    One way of creating the maximum number of groups while satisfying the conditions is:
    Group 1 contains the number [0].
    It can be shown that the maximum number of groups is 1.
    So, the output is 1.
    """


Prompt:
from typing import Any, List
def countPalindromePaths(parent: List[int], s: str) -> int:
    """
    You are given a tree (i.e. a connected, undirected graph that has no cycles) rooted at node 0 consisting of n nodes numbered from 0 to n - 1. The tree is represented by a 0-indexed array parent of size n, where parent[i] is the parent of node i. Since node 0 is the root, parent[0] == -1.
    You are also given a string s of length n, where s[i] is the character assigned to the edge between i and parent[i]. s[0] can be ignored.
    Return the number of pairs of nodes (u, v) such that u < v and the characters assigned to edges on the path from u to v can be rearranged to form a palindrome.
    A string is a palindrome when it reads the same backwards as forwards.

    Example 1:

    >>> countPalindromePaths(parent = [-1,0,0,1,1,2], s = "acaabc")
    >>> 8
    Explanation: The valid pairs are:
    - All the pairs (0,1), (0,2), (1,3), (1,4) and (2,5) result in one character which is always a palindrome.
    - The pair (2,3) result in the string "aca" which is a palindrome.
    - The pair (1,5) result in the string "cac" which is a palindrome.
    - The pair (3,5) result in the string "acac" which can be rearranged into the palindrome "acca".

    Example 2:

    >>> countPalindromePaths(parent = [-1,0,0,0,0], s = "aaaaa")
    >>> 10
    Explanation: Any pair of nodes (u,v) where u < v is valid.
    """


Prompt:
from typing import Optional
class TreeNode:
    def __init__(val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
def countGreatEnoughNodes(root: Optional[TreeNode], k: int) -> int:
"""
You are given a root to a binary tree and an integer k. A node of this tree is called great enough if the followings hold:

Its subtree has at least k nodes.
Its value is greater than the value of at least k nodes in its subtree.

Return the number of nodes in this tree that are great enough.
The node u is in the subtree of the node v, if u == v or v is an ancestor of u.

Example 1:

>>> countGreatEnoughNodes(root = [7,6,5,4,3,2,1], k = 2)
>>> 3
Explanation: Number the nodes from 1 to 7.
The values in the subtree of node 1: {1,2,3,4,5,6,7}. Since node.val == 7, there are 6 nodes having a smaller value than its value. So it's great enough.
The values in the subtree of node 2: {3,4,6}. Since node.val == 6, there are 2 nodes having a smaller value than its value. So it's great enough.
The values in the subtree of node 3: {1,2,5}. Since node.val == 5, there are 2 nodes having a smaller value than its value. So it's great enough.
It can be shown that other nodes are not great enough.
See the picture below for a better understanding.

Example 2:

>>> countGreatEnoughNodes(root = [1,2,3], k = 1)
>>> 0
Explanation: Number the nodes from 1 to 3.
The values in the subtree of node 1: {1,2,3}. Since node.val == 1, there are no nodes having a smaller value than its value. So it's not great enough.
The values in the subtree of node 2: {2}. Since node.val == 2, there are no nodes having a smaller value than its value. So it's not great enough.
The values in the subtree of node 3: {3}. Since node.val == 3, there are no nodes having a smaller value than its value. So it's not great enough.
See the picture below for a better understanding.

Example 3:

>>> countGreatEnoughNodes(root = [3,2,2], k = 2)
>>> 1
Explanation: Number the nodes from 1 to 3.
The values in the subtree of node 1: {2,2,3}. Since node.val == 3, there are 2 nodes having a smaller value than its value. So it's great enough.
The values in the subtree of node 2: {2}. Since node.val == 2, there are no nodes having a smaller value than its value. So it's not great enough.
The values in the subtree of node 3: {2}. Since node.val == 2, there are no nodes having a smaller value than its value. So it's not great enough.
See the picture below for a better understanding.
"""


Prompt:
from typing import List
def numberOfEmployeesWhoMetTarget(hours: List[int], target: int) -> int:
    """
    There are n employees in a company, numbered from 0 to n - 1. Each employee i has worked for hours[i] hours in the company.
    The company requires each employee to work for at least target hours.
    You are given a 0-indexed array of non-negative integers hours of length n and a non-negative integer target.
    Return the integer denoting the number of employees who worked at least target hours.

    Example 1:

    >>> numberOfEmployeesWhoMetTarget(hours = [0,1,2,3,4], target = 2)
    >>> 3
    Explanation: The company wants each employee to work for at least 2 hours.
    - Employee 0 worked for 0 hours and didn't meet the target.
    - Employee 1 worked for 1 hours and didn't meet the target.
    - Employee 2 worked for 2 hours and met the target.
    - Employee 3 worked for 3 hours and met the target.
    - Employee 4 worked for 4 hours and met the target.
    There are 3 employees who met the target.

    Example 2:

    >>> numberOfEmployeesWhoMetTarget(hours = [5,1,4,2,2], target = 6)
    >>> 0
    Explanation: The company wants each employee to work for at least 6 hours.
    There are 0 employees who met the target.
    """


Prompt:
from typing import List
def countCompleteSubarrays(nums: List[int]) -> int:
    """
    You are given an array nums consisting of positive integers.
    We call a subarray of an array complete if the following condition is satisfied:

    The number of distinct elements in the subarray is equal to the number of distinct elements in the whole array.

    Return the number of complete subarrays.
    A subarray is a contiguous non-empty part of an array.

    Example 1:

    >>> countCompleteSubarrays(nums = [1,3,1,2,2])
    >>> 4
    Explanation: The complete subarrays are the following: [1,3,1,2], [1,3,1,2,2], [3,1,2] and [3,1,2,2].

    Example 2:

    >>> countCompleteSubarrays(nums = [5,5,5,5])
    >>> 10
    Explanation: The array consists only of the integer 5, so any subarray is complete. The number of subarrays that we can choose is 10.
    """


Prompt:
def minimumString(a: str, b: str, c: str) -> str:
    """
    Given three strings a, b, and c, your task is to find a string that has the minimum length and contains all three strings as substrings.
    If there are multiple such strings, return the lexicographically smallest one.
    Return a string denoting the answer to the problem.
    Notes

    A string a is lexicographically smaller than a string b (of the same length) 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.
    A substring is a contiguous sequence of characters within a string.

    Example 1:

    >>> minimumString(a = "abc", b = "bca", c = "aaa")
    >>> "aaabca"
    Explanation:  We show that "aaabca" contains all the given strings: a = ans[2...4], b = ans[3..5], c = ans[0..2]. It can be shown that the length of the resulting string would be at least 6 and "aaabca" is the lexicographically smallest one.
    Example 2:

    >>> minimumString(a = "ab", b = "ba", c = "aba")
    >>> "aba"
    Explanation: We show that the string "aba" contains all the given strings: a = ans[0..1], b = ans[1..2], c = ans[0..2]. Since the length of c is 3, the length of the resulting string would be at least 3. It can be shown that "aba" is the lexicographically smallest one.
    """


Prompt:
def countSteppingNumbers(low: str, high: str) -> int:
    """
    Given two positive integers low and high represented as strings, find the count of stepping numbers in the inclusive range [low, high].
    A stepping number is an integer such that all of its adjacent digits have an absolute difference of exactly 1.
    Return an integer denoting the count of stepping numbers in the inclusive range [low, high].
    Since the answer may be very large, return it modulo 109 + 7.
    Note: A stepping number should not have a leading zero.

    Example 1:

    >>> countSteppingNumbers(low = "1", high = "11")
    >>> 10
    Explanation: The stepping numbers in the range [1,11] are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. There are a total of 10 stepping numbers in the range. Hence, the output is 10.
    Example 2:

    >>> countSteppingNumbers(low = "90", high = "101")
    >>> 2
    Explanation: The stepping numbers in the range [90,101] are 98 and 101. There are a total of 2 stepping numbers in the range. Hence, the output is 2.
    """


Prompt:
def kthLuckyNumber(k: int) -> str:
    """
    We know that 4 and 7 are lucky digits. Also, a number is called lucky if it contains only lucky digits.
    You are given an integer k, return the kth lucky number represented as a string.

    Example 1:

    >>> kthLuckyNumber(k = 4)
    >>> "47"
    Explanation: The first lucky number is 4, the second one is 7, the third one is 44 and the fourth one is 47.

    Example 2:

    >>> kthLuckyNumber(k = 10)
    >>> "477"
    Explanation: Here are lucky numbers sorted in increasing order:
    4, 7, 44, 47, 74, 77, 444, 447, 474, 477. So the 10th lucky number is 477.
    Example 3:

    >>> kthLuckyNumber(k = 1000)
    >>> "777747447"
    Explanation: It can be shown that the 1000th lucky number is 777747447.
    """


Prompt:
def accountBalanceAfterPurchase(purchaseAmount: int) -> int:
    """
    Initially, you have a bank account balance of 100 dollars.
    You are given an integer purchaseAmount representing the amount you will spend on a purchase in dollars, in other words, its price.
    When making the purchase, first the purchaseAmount is rounded to the nearest multiple of 10. Let us call this value roundedAmount. Then, roundedAmount dollars are removed from your bank account.
    Return an integer denoting your final bank account balance after this purchase.
    Notes:

    0 is considered to be a multiple of 10 in this problem.
    When rounding, 5 is rounded upward (5 is rounded to 10, 15 is rounded to 20, 25 to 30, and so on).

    Example 1:

    >>> accountBalanceAfterPurchase(purchaseAmount = 9)
    >>> 90
    Explanation:
    The nearest multiple of 10 to 9 is 10. So your account balance becomes 100 - 10 = 90.

    Example 2:

    >>> accountBalanceAfterPurchase(purchaseAmount = 15)
    >>> 80
    Explanation:
    The nearest multiple of 10 to 15 is 20. So your account balance becomes 100 - 20 = 80.

    Example 3:

    >>> accountBalanceAfterPurchase(purchaseAmount = 10)
    >>> 90
    Explanation:
    10 is a multiple of 10 itself. So your account balance becomes 100 - 10 = 90.
    """


Prompt:
from typing import Optional
class ListNode:
    def __init__(val=0, next=None):
        self.val = val
        self.next = next
def insertGreatestCommonDivisors(head: Optional[ListNode]) -> Optional[ListNode]:
"""
Given the head of a linked list head, in which each node contains an integer value.
Between every pair of adjacent nodes, insert a new node with a value equal to the greatest common divisor of them.
Return the linked list after insertion.
The greatest common divisor of two numbers is the largest positive integer that evenly divides both numbers.

Example 1:

>>> insertGreatestCommonDivisors(head = [18,6,10,3])
>>> [18,6,6,2,10,1,3]
Explanation: The 1st diagram denotes the initial linked list and the 2nd diagram denotes the linked list after inserting the new nodes (nodes in blue are the inserted nodes).
- We insert the greatest common divisor of 18 and 6 = 6 between the 1st and the 2nd nodes.
- We insert the greatest common divisor of 6 and 10 = 2 between the 2nd and the 3rd nodes.
- We insert the greatest common divisor of 10 and 3 = 1 between the 3rd and the 4th nodes.
There are no more adjacent nodes, so we return the linked list.

Example 2:

>>> insertGreatestCommonDivisors(head = [7])
>>> [7]
Explanation: The 1st diagram denotes the initial linked list and the 2nd diagram denotes the linked list after inserting the new nodes.
There are no pairs of adjacent nodes, so we return the initial linked list.
"""


Prompt:
from typing import List
def minimumSeconds(nums: List[int]) -> int:
    """
    You are given a 0-indexed array nums containing n integers.
    At each second, you perform the following operation on the array:

    For every index i in the range [0, n - 1], replace nums[i] with either nums[i], nums[(i - 1 + n) % n], or nums[(i + 1) % n].

    Note that all the elements get replaced simultaneously.
    Return the minimum number of seconds needed to make all elements in the array nums equal.

    Example 1:

    >>> minimumSeconds(nums = [1,2,1,2])
    >>> 1
    Explanation: We can equalize the array in 1 second in the following way:
    - At 1st second, replace values at each index with [nums[3],nums[1],nums[3],nums[3]]. After replacement, nums = [2,2,2,2].
    It can be proven that 1 second is the minimum amount of seconds needed for equalizing the array.

    Example 2:

    >>> minimumSeconds(nums = [2,1,3,3,2])
    >>> 2
    Explanation: We can equalize the array in 2 seconds in the following way:
    - At 1st second, replace values at each index with [nums[0],nums[2],nums[2],nums[2],nums[3]]. After replacement, nums = [2,3,3,3,3].
    - At 2nd second, replace values at each index with [nums[1],nums[1],nums[2],nums[3],nums[4]]. After replacement, nums = [3,3,3,3,3].
    It can be proven that 2 seconds is the minimum amount of seconds needed for equalizing the array.

    Example 3:

    >>> minimumSeconds(nums = [5,5,5,5])
    >>> 0
    Explanation: We don't need to perform any operations as all elements in the initial array are the same.
    """


Prompt:
from typing import List
def minimumTime(nums1: List[int], nums2: List[int], x: int) -> int:
    """
    You are given two 0-indexed integer arrays nums1 and nums2 of equal length. Every second, for all indices 0 <= i < nums1.length, value of nums1[i] is incremented by nums2[i]. After this is done, you can do the following operation:

    Choose an index 0 <= i < nums1.length and make nums1[i] = 0.

    You are also given an integer x.
    Return the minimum time in which you can make the sum of all elements of nums1 to be less than or equal to x, or -1 if this is not possible.

    Example 1:

    >>> minimumTime(nums1 = [1,2,3], nums2 = [1,2,3], x = 4)
    >>> 3
    Explanation:
    For the 1st second, we apply the operation on i = 0. Therefore nums1 = [0,2+2,3+3] = [0,4,6].
    For the 2nd second, we apply the operation on i = 1. Therefore nums1 = [0+1,0,6+3] = [1,0,9].
    For the 3rd second, we apply the operation on i = 2. Therefore nums1 = [1+1,0+2,0] = [2,2,0].
    Now sum of nums1 = 4. It can be shown that these operations are optimal, so we return 3.

    Example 2:

    >>> minimumTime(nums1 = [1,2,3], nums2 = [3,3,3], x = 4)
    >>> -1
    Explanation: It can be shown that the sum of nums1 will always be greater than x, no matter which operations are performed.
    """


Prompt:
def finalString(s: str) -> str:
    """
    Your laptop keyboard is faulty, and whenever you type a character 'i' on it, it reverses the string that you have written. Typing other characters works as expected.
    You are given a 0-indexed string s, and you type each character of s using your faulty keyboard.
    Return the final string that will be present on your laptop screen.

    Example 1:

    >>> finalString(s = "string")
    >>> "rtsng"
    Explanation:
    After typing first character, the text on the screen is "s".
    After the second character, the text is "st".
    After the third character, the text is "str".
    Since the fourth character is an 'i', the text gets reversed and becomes "rts".
    After the fifth character, the text is "rtsn".
    After the sixth character, the text is "rtsng".
    Therefore, we return "rtsng".

    Example 2:

    >>> finalString(s = "poiinter")
    >>> "ponter"
    Explanation:
    After the first character, the text on the screen is "p".
    After the second character, the text is "po".
    Since the third character you type is an 'i', the text gets reversed and becomes "op".
    Since the fourth character you type is an 'i', the text gets reversed and becomes "po".
    After the fifth character, the text is "pon".
    After the sixth character, the text is "pont".
    After the seventh character, the text is "ponte".
    After the eighth character, the text is "ponter".
    Therefore, we return "ponter".
    """


Prompt:
from typing import List
def canSplitArray(nums: List[int], m: int) -> bool:
    """
    You are given an array nums of length n and an integer m. You need to determine if it is possible to split the array into n arrays of size 1 by performing a series of steps.
    An array is called good if:

    The length of the array is one, or
    The sum of the elements of the array is greater than or equal to m.

    In each step, you can select an existing array (which may be the result of previous steps) with a length of at least two and split it into two arrays, if both resulting arrays are good.
    Return true if you can split the given array into n arrays, otherwise return false.

    Example 1:

    >>> canSplitArray(nums = [2, 2, 1], m = 4)
    >>> true
    Explanation:

    Split [2, 2, 1] to [2, 2] and [1]. The array [1] has a length of one, and the array [2, 2] has the sum of its elements equal to 4 >= m, so both are good arrays.
    Split [2, 2] to [2] and [2]. both arrays have the length of one, so both are good arrays.

    Example 2:

    >>> canSplitArray(nums = [2, 1, 3], m = 5)
    >>> false
    Explanation:
    The first move has to be either of the following:

    Split [2, 1, 3] to [2, 1] and [3]. The array [2, 1] has neither length of one nor sum of elements greater than or equal to m.
    Split [2, 1, 3] to [2] and [1, 3]. The array [1, 3] has neither length of one nor sum of elements greater than or equal to m.

    So as both moves are invalid (they do not divide the array into two good arrays), we are unable to split nums into n arrays of size 1.

    Example 3:

    >>> canSplitArray(nums = [2, 3, 3, 2, 3], m = 6)
    >>> true
    Explanation:

    Split [2, 3, 3, 2, 3] to [2] and [3, 3, 2, 3].
    Split [3, 3, 2, 3] to [3, 3, 2] and [3].
    Split [3, 3, 2] to [3, 3] and [2].
    Split [3, 3] to [3] and [3].
    """


Prompt:
from typing import List
def maximumSafenessFactor(grid: List[List[int]]) -> int:
    """
    You are given a 0-indexed 2D matrix grid of size n x n, where (r, c) represents:

    A cell containing a thief if grid[r][c] = 1
    An empty cell if grid[r][c] = 0

    You are initially positioned at cell (0, 0). In one move, you can move to any adjacent cell in the grid, including cells containing thieves.
    The safeness factor of a path on the grid is defined as the minimum manhattan distance from any cell in the path to any thief in the grid.
    Return the maximum safeness factor of all paths leading to cell (n - 1, n - 1).
    An adjacent cell of cell (r, c), is one of the cells (r, c + 1), (r, c - 1), (r + 1, c) and (r - 1, c) if it exists.
    The Manhattan distance between two cells (a, b) and (x, y) is equal to |a - x| + |b - y|, where |val| denotes the absolute value of val.

    Example 1:

    >>> maximumSafenessFactor(grid = [[1,0,0],[0,0,0],[0,0,1]])
    >>> 0
    Explanation: All paths from (0, 0) to (n - 1, n - 1) go through the thieves in cells (0, 0) and (n - 1, n - 1).

    Example 2:

    >>> maximumSafenessFactor(grid = [[0,0,1],[0,0,0],[0,0,0]])
    >>> 2
    Explanation: The path depicted in the picture above has a safeness factor of 2 since:
    - The closest cell of the path to the thief at cell (0, 2) is cell (0, 0). The distance between them is | 0 - 0 | + | 0 - 2 | = 2.
    It can be shown that there are no other paths with a higher safeness factor.

    Example 3:

    >>> maximumSafenessFactor(grid = [[0,0,0,1],[0,0,0,0],[0,0,0,0],[1,0,0,0]])
    >>> 2
    Explanation: The path depicted in the picture above has a safeness factor of 2 since:
    - The closest cell of the path to the thief at cell (0, 3) is cell (1, 2). The distance between them is | 0 - 1 | + | 3 - 2 | = 2.
    - The closest cell of the path to the thief at cell (3, 0) is cell (3, 2). The distance between them is | 3 - 3 | + | 0 - 2 | = 2.
    It can be shown that there are no other paths with a higher safeness factor.
    """


Prompt:
from typing import List
def findMaximumElegance(items: List[List[int]], k: int) -> int:
    """
    You are given a 0-indexed 2D integer array items of length n and an integer k.
    items[i] = [profiti, categoryi], where profiti and categoryi denote the profit and category of the ith item respectively.
    Let's define the elegance of a subsequence of items as total_profit + distinct_categories2, where total_profit is the sum of all profits in the subsequence, and distinct_categories is the number of distinct categories from all the categories in the selected subsequence.
    Your task is to find the maximum elegance from all subsequences of size k in items.
    Return an integer denoting the maximum elegance of a subsequence of items with size exactly k.
    Note: A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements' relative order.

    Example 1:

    >>> findMaximumElegance(items = [[3,2],[5,1],[10,1]], k = 2)
    >>> 17
    Explanation: In this example, we have to select a subsequence of size 2.
    We can select items[0] = [3,2] and items[2] = [10,1].
    The total profit in this subsequence is 3 + 10 = 13, and the subsequence contains 2 distinct categories [2,1].
    Hence, the elegance is 13 + 22 = 17, and we can show that it is the maximum achievable elegance.

    Example 2:

    >>> findMaximumElegance(items = [[3,1],[3,1],[2,2],[5,3]], k = 3)
    >>> 19
    Explanation: In this example, we have to select a subsequence of size 3.
    We can select items[0] = [3,1], items[2] = [2,2], and items[3] = [5,3].
    The total profit in this subsequence is 3 + 2 + 5 = 10, and the subsequence contains 3 distinct categories [1,2,3].
    Hence, the elegance is 10 + 32 = 19, and we can show that it is the maximum achievable elegance.
    Example 3:

    >>> findMaximumElegance(items = [[1,1],[2,1],[3,1]], k = 3)
    >>> 7
    Explanation: In this example, we have to select a subsequence of size 3.
    We should select all the items.
    The total profit will be 1 + 2 + 3 = 6, and the subsequence contains 1 distinct category [1].
    Hence, the maximum elegance is 6 + 12 = 7.
    """


Prompt:
from typing import List
def minimumSeconds(land: List[List[str]]) -> int:
    """
    You are given an n * m 0-indexed grid of string land. Right now, you are standing at the cell that contains "S", and you want to get to the cell containing "D". There are three other types of cells in this land:

    ".": These cells are empty.
    "X": These cells are stone.
    "*": These cells are flooded.

    At each second, you can move to a cell that shares a side with your current cell (if it exists). Also, at each second, every empty cell that shares a side with a flooded cell becomes flooded as well.
    There are two problems ahead of your journey:

    You can't step on stone cells.
    You can't step on flooded cells since you will drown (also, you can't step on a cell that will be flooded at the same time as you step on it).

    Return the minimum time it takes you to reach the destination in seconds, or -1 if it is impossible.
    Note that the destination will never be flooded.

    Example 1:

    >>> minimumSeconds(land = [["D",".","*"],[".",".","."],[".","S","."]])
    >>> 3
    Explanation: The picture below shows the simulation of the land second by second. The blue cells are flooded, and the gray cells are stone.
    Picture (0) shows the initial state and picture (3) shows the final state when we reach destination. As you see, it takes us 3 second to reach destination and the answer would be 3.
    It can be shown that 3 is the minimum time needed to reach from S to D.

    Example 2:

    >>> minimumSeconds(land = [["D","X","*"],[".",".","."],[".",".","S"]])
    >>> -1
    Explanation: The picture below shows the simulation of the land second by second. The blue cells are flooded, and the gray cells are stone.
    Picture (0) shows the initial state. As you see, no matter which paths we choose, we will drown at the 3rd second. Also the minimum path takes us 4 seconds to reach from S to D.
    So the answer would be -1.

    Example 3:

    >>> minimumSeconds(land = [["D",".",".",".","*","."],[".","X",".","X",".","."],[".",".",".",".","S","."]])
    >>> 6
    Explanation: It can be shown that we can reach destination in 6 seconds. Also it can be shown that 6 is the minimum seconds one need to reach from S to D.
    """


Prompt:
from typing import List
def maxSum(nums: List[int]) -> int:
    """
    You are given an integer array nums. You have to find the maximum sum of a pair of numbers from nums such that the largest digit in both numbers is equal.
    For example, 2373 is made up of three distinct digits: 2, 3, and 7, where 7 is the largest among them.
    Return the maximum sum or -1 if no such pair exists.

    Example 1:

    >>> maxSum(nums = [112,131,411])
    >>> -1
    Explanation:
    Each numbers largest digit in order is [2,3,4].

    Example 2:

    >>> maxSum(nums = [2536,1613,3366,162])
    >>> 5902
    Explanation:
    All the numbers have 6 as their largest digit, so the answer is 2536 + 3366 = 5902.

    Example 3:

    >>> maxSum(nums = [51,71,17,24,42])
    >>> 88
    Explanation:
    Each number's largest digit in order is [5,7,7,4,4].
    So we have only two possible pairs, 71 + 17 = 88 and 24 + 42 = 66.
    """


Prompt:
from typing import Optional
class ListNode:
    def __init__(val=0, next=None):
        self.val = val
        self.next = next
def doubleIt(head: Optional[ListNode]) -> Optional[ListNode]:
"""
You are given the head of a non-empty linked list representing a non-negative integer without leading zeroes.
Return the head of the linked list after doubling it.

Example 1:

>>> doubleIt(head = [1,8,9])
>>> [3,7,8]
Explanation: The figure above corresponds to the given linked list which represents the number 189. Hence, the returned linked list represents the number 189 * 2 = 378.

Example 2:

>>> doubleIt(head = [9,9,9])
>>> [1,9,9,8]
Explanation: The figure above corresponds to the given linked list which represents the number 999. Hence, the returned linked list reprersents the number 999 * 2 = 1998.
"""


Prompt:
from typing import List
def minAbsoluteDifference(nums: List[int], x: int) -> int:
    """
    You are given a 0-indexed integer array nums and an integer x.
    Find the minimum absolute difference between two elements in the array that are at least x indices apart.
    In other words, find two indices i and j such that abs(i - j) >= x and abs(nums[i] - nums[j]) is minimized.
    Return an integer denoting the minimum absolute difference between two elements that are at least x indices apart.

    Example 1:

    >>> minAbsoluteDifference(nums = [4,3,2,4], x = 2)
    >>> 0
    Explanation: We can select nums[0] = 4 and nums[3] = 4.
    They are at least 2 indices apart, and their absolute difference is the minimum, 0.
    It can be shown that 0 is the optimal answer.

    Example 2:

    >>> minAbsoluteDifference(nums = [5,3,2,10,15], x = 1)
    >>> 1
    Explanation: We can select nums[1] = 3 and nums[2] = 2.
    They are at least 1 index apart, and their absolute difference is the minimum, 1.
    It can be shown that 1 is the optimal answer.

    Example 3:

    >>> minAbsoluteDifference(nums = [1,2,3,4], x = 3)
    >>> 3
    Explanation: We can select nums[0] = 1 and nums[3] = 4.
    They are at least 3 indices apart, and their absolute difference is the minimum, 3.
    It can be shown that 3 is the optimal answer.
    """