Prompt:
def countCompleteDayPairs(hours: List[int]) -> int:
    """
    Given an integer array hours representing times in hours, return an integer denoting the number of pairs i, j where i < j and hours[i] + hours[j] forms a complete day.
    A complete day is defined as a time duration that is an exact multiple of 24 hours.
    For example, 1 day is 24 hours, 2 days is 48 hours, 3 days is 72 hours, and so on.

    Example 1:

    >>> countCompleteDayPairs(hours = [12,12,30,24,24])
    >>> 2
    Explanation: The pairs of indices that form a complete day are (0, 1) and (3, 4).

    Example 2:

    >>> countCompleteDayPairs(hours = [72,48,24,3])
    >>> 3
    Explanation: The pairs of indices that form a complete day are (0, 1), (0, 2), and (1, 2).
    """


Prompt:
def maximumTotalDamage(power: List[int]) -> int:
    """
    A magician has various spells.
    You are given an array power, where each element represents the damage of a spell. Multiple spells can have the same damage value.
    It is a known fact that if a magician decides to cast a spell with a damage of power[i], they cannot cast any spell with a damage of power[i] - 2, power[i] - 1, power[i] + 1, or power[i] + 2.
    Each spell can be cast only once.
    Return the maximum possible total damage that a magician can cast.

    Example 1:

    >>> maximumTotalDamage(power = [1,1,3,4])
    >>> 6
    Explanation:
    The maximum possible damage of 6 is produced by casting spells 0, 1, 3 with damage 1, 1, 4.

    Example 2:

    >>> maximumTotalDamage(power = [7,1,6,6])
    >>> 13
    Explanation:
    The maximum possible damage of 13 is produced by casting spells 1, 2, 3 with damage 1, 6, 6.
    """


Prompt:
def countOfPeaks(nums: List[int], queries: List[List[int]]) -> List[int]:
    """
    A peak in an array arr is an element that is greater than its previous and next element in arr.
    You are given an integer array nums and a 2D integer array queries.
    You have to process queries of two types:

    queries[i] = [1, li, ri], determine the count of peak elements in the subarray nums[li..ri].
    queries[i] = [2, indexi, vali], change nums[indexi] to vali.

    Return an array answer containing the results of the queries of the first type in order.
    Notes:

    The first and the last element of an array or a subarray cannot be a peak.

    Example 1:

    >>> countOfPeaks(nums = [3,1,4,2,5], queries = [[2,3,4],[1,0,4]])
    >>> [0]
    Explanation:
    First query: We change nums[3] to 4 and nums becomes [3,1,4,4,5].
    Second query: The number of peaks in the [3,1,4,4,5] is 0.

    Example 2:

    >>> countOfPeaks(nums = [4,1,4,2,1,5], queries = [[2,2,4],[1,0,2],[1,0,4]])
    >>> [0,1]
    Explanation:
    First query: nums[2] should become 4, but it is already set to 4.
    Second query: The number of peaks in the [4,1,4] is 0.
    Third query: The second 4 is a peak in the [4,1,4,2,1].
    """


Prompt:
def minMoves(rooks: List[List[int]]) -> int:
    """
    Given a 2D array rooks of length n, where rooks[i] = [xi, yi] indicates the position of a rook on an n x n chess board. Your task is to move the rooks 1 cell at a time vertically or horizontally (to an adjacent cell) such that the board becomes peaceful.
    A board is peaceful if there is exactly one rook in each row and each column.
    Return the minimum number of moves required to get a peaceful board.
    Note that at no point can there be two rooks in the same cell.

    Example 1:

    >>> minMoves(rooks = [[0,0],[1,0],[1,1]])
    >>> 3
    Explanation:

    Example 2:

    >>> minMoves(rooks = [[0,0],[0,1],[0,2],[0,3]])
    >>> 6
    Explanation:
    """


Prompt:
def minimumOperations(nums: List[int]) -> int:
    """
    You are given an integer array nums. In one operation, you can add or subtract 1 from any element of nums.
    Return the minimum number of operations to make all elements of nums divisible by 3.

    Example 1:

    >>> minimumOperations(nums = [1,2,3,4])
    >>> 3
    Explanation:
    All array elements can be made divisible by 3 using 3 operations:

    Subtract 1 from 1.
    Add 1 to 2.
    Subtract 1 from 4.

    Example 2:

    >>> minimumOperations(nums = [3,6,9])
    >>> 0
    """


Prompt:
def minOperations(nums: List[int]) -> int:
    """
    You are given a binary array nums.
    You can do the following operation on the array any number of times (possibly zero):

    Choose any 3 consecutive elements from the array and flip all of them.

    Flipping an element means changing its value from 0 to 1, and from 1 to 0.
    Return the minimum number of operations required to make all elements in nums equal to 1. If it is impossible, return -1.

    Example 1:

    >>> minOperations(nums = [0,1,1,1,0,0])
    >>> 3
    Explanation:
    We can do the following operations:

    Choose the elements at indices 0, 1 and 2. The resulting array is nums = [1,0,0,1,0,0].
    Choose the elements at indices 1, 2 and 3. The resulting array is nums = [1,1,1,0,0,0].
    Choose the elements at indices 3, 4 and 5. The resulting array is nums = [1,1,1,1,1,1].

    Example 2:

    >>> minOperations(nums = [0,1,1,1])
    >>> -1
    Explanation:
    It is impossible to make all elements equal to 1.
    """


Prompt:
def minOperations(nums: List[int]) -> int:
    """
    You are given a binary array nums.
    You can do the following operation on the array any number of times (possibly zero):

    Choose any index i from the array and flip all the elements from index i to the end of the array.

    Flipping an element means changing its value from 0 to 1, and from 1 to 0.
    Return the minimum number of operations required to make all elements in nums equal to 1.

    Example 1:

    >>> minOperations(nums = [0,1,1,0,1])
    >>> 4
    Explanation:
    We can do the following operations:

    Choose the index i = 1. The resulting array will be nums = [0,0,0,1,0].
    Choose the index i = 0. The resulting array will be nums = [1,1,1,0,1].
    Choose the index i = 4. The resulting array will be nums = [1,1,1,0,0].
    Choose the index i = 3. The resulting array will be nums = [1,1,1,1,1].

    Example 2:

    >>> minOperations(nums = [1,0,0,0])
    >>> 1
    Explanation:
    We can do the following operation:

    Choose the index i = 1. The resulting array will be nums = [1,1,1,1].
    """


Prompt:
def numberOfPermutations(n: int, requirements: List[List[int]]) -> int:
    """
    You are given an integer n and a 2D array requirements, where requirements[i] = [endi, cnti] represents the end index and the inversion count of each requirement.
    A pair of indices (i, j) from an integer array nums is called an inversion if:

    i < j and nums[i] > nums[j]

    Return the number of permutations perm of [0, 1, 2, ..., n - 1] such that for all requirements[i], perm[0..endi] has exactly cnti inversions.
    Since the answer may be very large, return it modulo 109 + 7.

    Example 1:

    >>> numberOfPermutations(n = 3, requirements = [[2,2],[0,0]])
    >>> 2
    Explanation:
    The two permutations are:

    [2, 0, 1]

    Prefix [2, 0, 1] has inversions (0, 1) and (0, 2).
    Prefix [2] has 0 inversions.

    [1, 2, 0]

    Prefix [1, 2, 0] has inversions (0, 2) and (1, 2).
    Prefix [1] has 0 inversions.

    Example 2:

    >>> numberOfPermutations(n = 3, requirements = [[2,2],[1,1],[0,0]])
    >>> 1
    Explanation:
    The only satisfying permutation is [2, 0, 1]:

    Prefix [2, 0, 1] has inversions (0, 1) and (0, 2).
    Prefix [2, 0] has an inversion (0, 1).
    Prefix [2] has 0 inversions.

    Example 3:

    >>> numberOfPermutations(n = 2, requirements = [[0,0],[1,0]])
    >>> 1
    Explanation:
    The only satisfying permutation is [0, 1]:

    Prefix [0] has 0 inversions.
    Prefix [0, 1] has an inversion (0, 1).
    """


Prompt:
def minimumAverage(nums: List[int]) -> float:
    """
    You have an array of floating point numbers averages which is initially empty. You are given an array nums of n integers where n is even.
    You repeat the following procedure n / 2 times:

    Remove the smallest element, minElement, and the largest element maxElement, from nums.
    Add (minElement + maxElement) / 2 to averages.

    Return the minimum element in averages.

    Example 1:

    >>> minimumAverage(nums = [7,8,3,4,15,13,4,1])
    >>> 5.5
    Explanation:

    step
    nums
    averages

    0
    [7,8,3,4,15,13,4,1]
    []

    1
    [7,8,3,4,13,4]
    [8]

    2
    [7,8,4,4]
    [8,8]

    3
    [7,4]
    [8,8,6]

    4
    []
    [8,8,6,5.5]

    The smallest element of averages, 5.5, is returned.
    Example 2:

    >>> minimumAverage(nums = [1,9,8,3,10,5])
    >>> 5.5
    Explanation:

    step
    nums
    averages

    0
    [1,9,8,3,10,5]
    []

    1
    [9,8,3,5]
    [5.5]

    2
    [8,5]
    [5.5,6]

    3
    []
    [5.5,6,6.5]

    Example 3:

    >>> minimumAverage(nums = [1,2,3,7,8,9])
    >>> 5.0
    Explanation:

    step
    nums
    averages

    0
    [1,2,3,7,8,9]
    []

    1
    [2,3,7,8]
    [5]

    2
    [3,7]
    [5,5]

    3
    []
    [5,5,5]
    """


Prompt:
def minimumArea(grid: List[List[int]]) -> int:
    """
    You are given a 2D binary array grid. Find a rectangle with horizontal and vertical sides with the smallest area, such that all the 1's in grid lie inside this rectangle.
    Return the minimum possible area of the rectangle.

    Example 1:

    >>> minimumArea(grid = [[0,1,0],[1,0,1]])
    >>> 6
    Explanation:

    The smallest rectangle has a height of 2 and a width of 3, so it has an area of 2 * 3 = 6.

    Example 2:

    >>> minimumArea(grid = [[1,0],[0,0]])
    >>> 1
    Explanation:

    The smallest rectangle has both height and width 1, so its area is 1 * 1 = 1.
    """


Prompt:
def maximumTotalCost(nums: List[int]) -> int:
    """
    You are given an integer array nums with length n.
    The cost of a subarray nums[l..r], where 0 <= l <= r < n, is defined as:
    cost(l, r) = nums[l] - nums[l + 1] + ... + nums[r] * (−1)r − l
    Your task is to split nums into subarrays such that the total cost of the subarrays is maximized, ensuring each element belongs to exactly one subarray.
    Formally, if nums is split into k subarrays, where k > 1, at indices i1, i2, ..., ik − 1, where 0 <= i1 < i2 < ... < ik - 1 < n - 1, then the total cost will be:
    cost(0, i1) + cost(i1 + 1, i2) + ... + cost(ik − 1 + 1, n − 1)
    Return an integer denoting the maximum total cost of the subarrays after splitting the array optimally.
    Note: If nums is not split into subarrays, i.e. k = 1, the total cost is simply cost(0, n - 1).

    Example 1:

    >>> maximumTotalCost(nums = [1,-2,3,4])
    >>> 10
    Explanation:
    One way to maximize the total cost is by splitting [1, -2, 3, 4] into subarrays [1, -2, 3] and [4]. The total cost will be (1 + 2 + 3) + 4 = 10.

    Example 2:

    >>> maximumTotalCost(nums = [1,-1,1,-1])
    >>> 4
    Explanation:
    One way to maximize the total cost is by splitting [1, -1, 1, -1] into subarrays [1, -1] and [1, -1]. The total cost will be (1 + 1) + (1 + 1) = 4.

    Example 3:

    >>> maximumTotalCost(nums = [0])
    >>> 0
    Explanation:
    We cannot split the array further, so the answer is 0.

    Example 4:

    >>> maximumTotalCost(nums = [1,-1])
    >>> 2
    Explanation:
    Selecting the whole array gives a total cost of 1 + 1 = 2, which is the maximum.
    """


Prompt:
def minimumSum(grid: List[List[int]]) -> int:
    """
    You are given a 2D binary array grid. You need to find 3 non-overlapping rectangles having non-zero areas with horizontal and vertical sides such that all the 1's in grid lie inside these rectangles.
    Return the minimum possible sum of the area of these rectangles.
    Note that the rectangles are allowed to touch.

    Example 1:

    >>> minimumSum(grid = [[1,0,1],[1,1,1]])
    >>> 5
    Explanation:

    The 1's at (0, 0) and (1, 0) are covered by a rectangle of area 2.
    The 1's at (0, 2) and (1, 2) are covered by a rectangle of area 2.
    The 1 at (1, 1) is covered by a rectangle of area 1.

    Example 2:

    >>> minimumSum(grid = [[1,0,1,0],[0,1,0,1]])
    >>> 5
    Explanation:

    The 1's at (0, 0) and (0, 2) are covered by a rectangle of area 3.
    The 1 at (1, 1) is covered by a rectangle of area 1.
    The 1 at (1, 3) is covered by a rectangle of area 1.
    """


Prompt:
def tripletCount(a: List[int], b: List[int], c: List[int]) -> int:
    """
    Given three integer arrays a, b, and c, return the number of triplets (a[i], b[j], c[k]), such that the bitwise XOR of the elements of each triplet has an even number of set bits.

    Example 1:

    >>> tripletCount(a = [1], b = [2], c = [3])
    >>> 1
    Explanation:
    The only triplet is (a[0], b[0], c[0]) and their XOR is: 1 XOR 2 XOR 3 = 002.

    Example 2:

    >>> tripletCount(a = [1,1], b = [2,3], c = [1,5])
    >>> 4
    Explanation:
    Consider these four triplets:

    (a[0], b[1], c[0]): 1 XOR 3 XOR 1 = 0112
    (a[1], b[1], c[0]): 1 XOR 3 XOR 1 = 0112
    (a[0], b[0], c[1]): 1 XOR 2 XOR 5 = 1102
    (a[1], b[0], c[1]): 1 XOR 2 XOR 5 = 1102
    """


Prompt:
def maxHeightOfTriangle(red: int, blue: int) -> int:
    """
    You are given two integers red and blue representing the count of red and blue colored balls. You have to arrange these balls to form a triangle such that the 1st row will have 1 ball, the 2nd row will have 2 balls, the 3rd row will have 3 balls, and so on.
    All the balls in a particular row should be the same color, and adjacent rows should have different colors.
    Return the maximum height of the triangle that can be achieved.

    Example 1:

    >>> maxHeightOfTriangle(red = 2, blue = 4)
    >>> 3
    Explanation:

    The only possible arrangement is shown above.

    Example 2:

    >>> maxHeightOfTriangle(red = 2, blue = 1)
    >>> 2
    Explanation:

    The only possible arrangement is shown above.

    Example 3:

    >>> maxHeightOfTriangle(red = 1, blue = 1)
    >>> 1

    Example 4:

    >>> maxHeightOfTriangle(red = 10, blue = 1)
    >>> 2
    Explanation:

    The only possible arrangement is shown above.
    """


Prompt:
def maximumLength(nums: List[int]) -> int:
    """
    You are given an integer array nums.
    A subsequence sub of nums with length x is called valid if it satisfies:

    (sub[0] + sub[1]) % 2 == (sub[1] + sub[2]) % 2 == ... == (sub[x - 2] + sub[x - 1]) % 2.

    Return the length of the longest valid subsequence of nums.
    A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

    Example 1:

    >>> maximumLength(nums = [1,2,3,4])
    >>> 4
    Explanation:
    The longest valid subsequence is [1, 2, 3, 4].

    Example 2:

    >>> maximumLength(nums = [1,2,1,1,2,1,2])
    >>> 6
    Explanation:
    The longest valid subsequence is [1, 2, 1, 2, 1, 2].

    Example 3:

    >>> maximumLength(nums = [1,3])
    >>> 2
    Explanation:
    The longest valid subsequence is [1, 3].
    """


Prompt:
def maximumLength(nums: List[int], k: int) -> int:
    """
    You are given an integer array nums and a positive integer k.
    A subsequence sub of nums with length x is called valid if it satisfies:

    (sub[0] + sub[1]) % k == (sub[1] + sub[2]) % k == ... == (sub[x - 2] + sub[x - 1]) % k.

    Return the length of the longest valid subsequence of nums.

    Example 1:

    >>> maximumLength(nums = [1,2,3,4,5], k = 2)
    >>> 5
    Explanation:
    The longest valid subsequence is [1, 2, 3, 4, 5].

    Example 2:

    >>> maximumLength(nums = [1,4,2,3,1,4], k = 3)
    >>> 4
    Explanation:
    The longest valid subsequence is [1, 4, 1, 4].
    """


Prompt:
def minimumDiameterAfterMerge(edges1: List[List[int]], edges2: List[List[int]]) -> int:
    """
    There exist two undirected trees with n and m nodes, numbered from 0 to n - 1 and from 0 to m - 1, respectively. You are given two 2D integer arrays edges1 and edges2 of lengths n - 1 and m - 1, respectively, where edges1[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the first tree and edges2[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the second tree.
    You must connect one node from the first tree with another node from the second tree with an edge.
    Return the minimum possible diameter of the resulting tree.
    The diameter of a tree is the length of the longest path between any two nodes in the tree.

    Example 1:

    >>> minimumDiameterAfterMerge(edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]])
    >>> 3
    Explanation:
    We can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.

    Example 2:

    >>> minimumDiameterAfterMerge(edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]])
    >>> 5
    Explanation:
    We can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.
    """


Prompt:
def maxScore(nums: List[int]) -> int:
    """
    Given an array nums, you have to get the maximum score starting from index 0 and hopping until you reach the last element of the array.
    In each hop, you can jump from index i to an index j > i, and you get a score of (j - i) * nums[j].
    Return the maximum score you can get.

    Example 1:

    >>> maxScore(nums = [1,5,8])
    >>> 16
    Explanation:
    There are two possible ways to reach the last element:

    0 -> 1 -> 2 with a score of (1 - 0) * 5 + (2 - 1) * 8 = 13.
    0 -> 2 with a score of (2 - 0) * 8 = 16.

    Example 2:

    >>> maxScore(nums = [4,5,2,8,9,1,3])
    >>> 42
    Explanation:
    We can do the hopping 0 -> 4 -> 6 with a score of (4 - 0) * 9 + (6 - 4) * 3 = 42.
    """


Prompt:
def numberOfAlternatingGroups(colors: List[int]) -> int:
    """
    There is a circle of red and blue tiles. You are given an array of integers colors. The color of tile i is represented by colors[i]:

    colors[i] == 0 means that tile i is red.
    colors[i] == 1 means that tile i is blue.

    Every 3 contiguous tiles in the circle with alternating colors (the middle tile has a different color from its left and right tiles) is called an alternating group.
    Return the number of alternating groups.
    Note that since colors represents a circle, the first and the last tiles are considered to be next to each other.

    Example 1:

    >>> numberOfAlternatingGroups(colors = [1,1,1])
    >>> 0
    Explanation:

    Example 2:

    >>> numberOfAlternatingGroups(colors = [0,1,0,0,1])
    >>> 3
    Explanation:

    Alternating groups:
    """


Prompt:
def maximumPoints(enemyEnergies: List[int], currentEnergy: int) -> int:
    """
    You are given an integer array enemyEnergies denoting the energy values of various enemies.
    You are also given an integer currentEnergy denoting the amount of energy you have initially.
    You start with 0 points, and all the enemies are unmarked initially.
    You can perform either of the following operations zero or multiple times to gain points:

    Choose an unmarked enemy, i, such that currentEnergy >= enemyEnergies[i]. By choosing this option:

    You gain 1 point.
    Your energy is reduced by the enemy's energy, i.e. currentEnergy = currentEnergy - enemyEnergies[i].

    If you have at least 1 point, you can choose an unmarked enemy, i. By choosing this option:

    Your energy increases by the enemy's energy, i.e. currentEnergy = currentEnergy + enemyEnergies[i].
    The enemy i is marked.

    Return an integer denoting the maximum points you can get in the end by optimally performing operations.

    Example 1:

    >>> maximumPoints(enemyEnergies = [3,2,2], currentEnergy = 2)
    >>> 3
    Explanation:
    The following operations can be performed to get 3 points, which is the maximum:

    First operation on enemy 1: points increases by 1, and currentEnergy decreases by 2. So, points = 1, and currentEnergy = 0.
    Second operation on enemy 0: currentEnergy increases by 3, and enemy 0 is marked. So, points = 1, currentEnergy = 3, and marked enemies = [0].
    First operation on enemy 2: points increases by 1, and currentEnergy decreases by 2. So, points = 2, currentEnergy = 1, and marked enemies = [0].
    Second operation on enemy 2: currentEnergy increases by 2, and enemy 2 is marked. So, points = 2, currentEnergy = 3, and marked enemies = [0, 2].
    First operation on enemy 1: points increases by 1, and currentEnergy decreases by 2. So, points = 3, currentEnergy = 1, and marked enemies = [0, 2].

    Example 2:

    >>> maximumPoints(enemyEnergies = [2], currentEnergy = 10)
    >>> 5
    Explanation:
    Performing the first operation 5 times on enemy 0 results in the maximum number of points.
    """


Prompt:
def numberOfAlternatingGroups(colors: List[int], k: int) -> int:
    """
    There is a circle of red and blue tiles. You are given an array of integers colors and an integer k. The color of tile i is represented by colors[i]:

    colors[i] == 0 means that tile i is red.
    colors[i] == 1 means that tile i is blue.

    An alternating group is every k contiguous tiles in the circle with alternating colors (each tile in the group except the first and last one has a different color from its left and right tiles).
    Return the number of alternating groups.
    Note that since colors represents a circle, the first and the last tiles are considered to be next to each other.

    Example 1:

    >>> numberOfAlternatingGroups(colors = [0,1,0,1,0], k = 3)
    >>> 3
    Explanation:

    Alternating groups:

    Example 2:

    >>> numberOfAlternatingGroups(colors = [0,1,0,0,1,0,1], k = 6)
    >>> 2
    Explanation:

    Alternating groups:

    Example 3:

    >>> numberOfAlternatingGroups(colors = [1,1,0,1], k = 4)
    >>> 0
    Explanation:
    """


Prompt:
def countSubarrays(nums: List[int], k: int) -> int:
    """
    Given an array of integers nums and an integer k, return the number of subarrays of nums where the bitwise AND of the elements of the subarray equals k.

    Example 1:

    >>> countSubarrays(nums = [1,1,1], k = 1)
    >>> 6
    Explanation:
    All subarrays contain only 1's.

    Example 2:

    >>> countSubarrays(nums = [1,1,2], k = 1)
    >>> 3
    Explanation:
    Subarrays having an AND value of 1 are: [1,1,2], [1,1,2], [1,1,2].

    Example 3:

    >>> countSubarrays(nums = [1,2,3], k = 2)
    >>> 2
    Explanation:
    Subarrays having an AND value of 2 are: [1,2,3], [1,2,3].
    """


Prompt:
def getEncryptedString(s: str, k: int) -> str:
    """
    You are given a string s and an integer k. Encrypt the string using the following algorithm:

    For each character c in s, replace c with the kth character after c in the string (in a cyclic manner).

    Return the encrypted string.

    Example 1:

    >>> getEncryptedString(s = "dart", k = 3)
    >>> "tdar"
    Explanation:

    For i = 0, the 3rd character after 'd' is 't'.
    For i = 1, the 3rd character after 'a' is 'd'.
    For i = 2, the 3rd character after 'r' is 'a'.
    For i = 3, the 3rd character after 't' is 'r'.

    Example 2:

    >>> getEncryptedString(s = "aaa", k = 1)
    >>> "aaa"
    Explanation:
    As all the characters are the same, the encrypted string will also be the same.
    """


Prompt:
def validStrings(n: int) -> List[str]:
    """
    You are given a positive integer n.
    A binary string x is valid if all substrings of x of length 2 contain at least one "1".
    Return all valid strings with length n, in any order.

    Example 1:

    >>> validStrings(n = 3)
    >>> ["010","011","101","110","111"]
    Explanation:
    The valid strings of length 3 are: "010", "011", "101", "110", and "111".

    Example 2:

    >>> validStrings(n = 1)
    >>> ["0","1"]
    Explanation:
    The valid strings of length 1 are: "0" and "1".
    """


Prompt:
def numberOfSubmatrices(grid: List[List[str]]) -> int:
    """
    Given a 2D character matrix grid, where grid[i][j] is either 'X', 'Y', or '.', return the number of submatrices that contain:

    grid[0][0]
    an equal frequency of 'X' and 'Y'.
    at least one 'X'.

    Example 1:

    >>> numberOfSubmatrices(grid = [["X","Y","."],["Y",".","."]])
    >>> 3
    Explanation:

    Example 2:

    >>> numberOfSubmatrices(grid = [["X","X"],["X","Y"]])
    >>> 0
    Explanation:
    No submatrix has an equal frequency of 'X' and 'Y'.

    Example 3:

    >>> numberOfSubmatrices(grid = [[".","."],[".","."]])
    >>> 0
    Explanation:
    No submatrix has at least one 'X'.
    """


Prompt:
def minimumCost(target: str, words: List[str], costs: List[int]) -> int:
    """
    You are given a string target, an array of strings words, and an integer array costs, both arrays of the same length.
    Imagine an empty string s.
    You can perform the following operation any number of times (including zero):

    Choose an index i in the range [0, words.length - 1].
    Append words[i] to s.
    The cost of operation is costs[i].

    Return the minimum cost to make s equal to target. If it's not possible, return -1.

    Example 1:

    >>> minimumCost(target = "abcdef", words = ["abdef","abc","d","def","ef"], costs = [100,1,1,10,5])
    >>> 7
    Explanation:
    The minimum cost can be achieved by performing the following operations:

    Select index 1 and append "abc" to s at a cost of 1, resulting in s = "abc".
    Select index 2 and append "d" to s at a cost of 1, resulting in s = "abcd".
    Select index 4 and append "ef" to s at a cost of 5, resulting in s = "abcdef".

    Example 2:

    >>> minimumCost(target = "aaaa", words = ["z","zz","zzz"], costs = [1,10,100])
    >>> -1
    Explanation:
    It is impossible to make s equal to target, so we return -1.
    """


Prompt:
def tripletCount(a: List[int], b: List[int], c: List[int]) -> int:
    """
    Given three integer arrays a, b, and c, return the number of triplets (a[i], b[j], c[k]), such that the bitwise XOR between the elements of each triplet has an even number of set bits.

    Example 1:

    >>> tripletCount(a = [1], b = [2], c = [3])
    >>> 1
    Explanation:
    The only triplet is (a[0], b[0], c[0]) and their XOR is: 1 XOR 2 XOR 3 = 002.

    Example 2:

    >>> tripletCount(a = [1,1], b = [2,3], c = [1,5])
    >>> 4
    Explanation:
    Consider these four triplets:

    (a[0], b[1], c[0]): 1 XOR 3 XOR 1 = 0112
    (a[1], b[1], c[0]): 1 XOR 3 XOR 1 = 0112
    (a[0], b[0], c[1]): 1 XOR 2 XOR 5 = 1102
    (a[1], b[0], c[1]): 1 XOR 2 XOR 5 = 1102
    """


Prompt:
def getSmallestString(s: str) -> str:
    """
    Given a string s containing only digits, return the lexicographically smallest string that can be obtained after swapping adjacent digits in s with the same parity at most once.
    Digits have the same parity if both are odd or both are even. For example, 5 and 9, as well as 2 and 4, have the same parity, while 6 and 9 do not.

    Example 1:

    >>> getSmallestString(s = "45320")
    >>> "43520"
    Explanation:
    s[1] == '5' and s[2] == '3' both have the same parity, and swapping them results in the lexicographically smallest string.

    Example 2:

    >>> getSmallestString(s = "001")
    >>> "001"
    Explanation:
    There is no need to perform a swap because s is already the lexicographically smallest.
    """


Prompt:
# class ListNode:
#     def __init__(val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
    def modifiedList(nums: List[int], head: Optional[ListNode]) -> Optional[ListNode]:
    """
    You are given an array of integers nums and the head of a linked list. Return the head of the modified linked list after removing all nodes from the linked list that have a value that exists in nums.

    Example 1:

    >>> __init__(nums = [1,2,3], head = [1,2,3,4,5])
    >>> [4,5]
    Explanation:

    Remove the nodes with values 1, 2, and 3.

    Example 2:

    >>> __init__(nums = [1], head = [1,2,1,2,1,2])
    >>> [2,2,2]
    Explanation:

    Remove the nodes with value 1.

    Example 3:

    >>> __init__(nums = [5], head = [1,2,3,4])
    >>> [1,2,3,4]
    Explanation:

    No node has value 5.
    """


Prompt:
def minimumCost(m: int, n: int, horizontalCut: List[int], verticalCut: List[int]) -> int:
    """
    There is an m x n cake that needs to be cut into 1 x 1 pieces.
    You are given integers m, n, and two arrays:

    horizontalCut of size m - 1, where horizontalCut[i] represents the cost to cut along the horizontal line i.
    verticalCut of size n - 1, where verticalCut[j] represents the cost to cut along the vertical line j.

    In one operation, you can choose any piece of cake that is not yet a 1 x 1 square and perform one of the following cuts:

    Cut along a horizontal line i at a cost of horizontalCut[i].
    Cut along a vertical line j at a cost of verticalCut[j].

    After the cut, the piece of cake is divided into two distinct pieces.
    The cost of a cut depends only on the initial cost of the line and does not change.
    Return the minimum total cost to cut the entire cake into 1 x 1 pieces.

    Example 1:

    >>> minimumCost(m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5])
    >>> 13
    Explanation:

    Perform a cut on the vertical line 0 with cost 5, current total cost is 5.
    Perform a cut on the horizontal line 0 on 3 x 1 subgrid with cost 1.
    Perform a cut on the horizontal line 0 on 3 x 1 subgrid with cost 1.
    Perform a cut on the horizontal line 1 on 2 x 1 subgrid with cost 3.
    Perform a cut on the horizontal line 1 on 2 x 1 subgrid with cost 3.

    The total cost is 5 + 1 + 1 + 3 + 3 = 13.

    Example 2:

    >>> minimumCost(m = 2, n = 2, horizontalCut = [7], verticalCut = [4])
    >>> 15
    Explanation:

    Perform a cut on the horizontal line 0 with cost 7.
    Perform a cut on the vertical line 0 on 1 x 2 subgrid with cost 4.
    Perform a cut on the vertical line 0 on 1 x 2 subgrid with cost 4.

    The total cost is 7 + 4 + 4 = 15.
    """


Prompt:
def minimumCost(m: int, n: int, horizontalCut: List[int], verticalCut: List[int]) -> int:
    """
    There is an m x n cake that needs to be cut into 1 x 1 pieces.
    You are given integers m, n, and two arrays:

    horizontalCut of size m - 1, where horizontalCut[i] represents the cost to cut along the horizontal line i.
    verticalCut of size n - 1, where verticalCut[j] represents the cost to cut along the vertical line j.

    In one operation, you can choose any piece of cake that is not yet a 1 x 1 square and perform one of the following cuts:

    Cut along a horizontal line i at a cost of horizontalCut[i].
    Cut along a vertical line j at a cost of verticalCut[j].

    After the cut, the piece of cake is divided into two distinct pieces.
    The cost of a cut depends only on the initial cost of the line and does not change.
    Return the minimum total cost to cut the entire cake into 1 x 1 pieces.

    Example 1:

    >>> minimumCost(m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5])
    >>> 13
    Explanation:

    Perform a cut on the vertical line 0 with cost 5, current total cost is 5.
    Perform a cut on the horizontal line 0 on 3 x 1 subgrid with cost 1.
    Perform a cut on the horizontal line 0 on 3 x 1 subgrid with cost 1.
    Perform a cut on the horizontal line 1 on 2 x 1 subgrid with cost 3.
    Perform a cut on the horizontal line 1 on 2 x 1 subgrid with cost 3.

    The total cost is 5 + 1 + 1 + 3 + 3 = 13.

    Example 2:

    >>> minimumCost(m = 2, n = 2, horizontalCut = [7], verticalCut = [4])
    >>> 15
    Explanation:

    Perform a cut on the horizontal line 0 with cost 7.
    Perform a cut on the vertical line 0 on 1 x 2 subgrid with cost 4.
    Perform a cut on the vertical line 0 on 1 x 2 subgrid with cost 4.

    The total cost is 7 + 4 + 4 = 15.
    """


Prompt:
def maxScore(nums: List[int]) -> int:
    """
    Given an array nums, you have to get the maximum score starting from index 0 and hopping until you reach the last element of the array.
    In each hop, you can jump from index i to an index j > i, and you get a score of (j - i) * nums[j].
    Return the maximum score you can get.

    Example 1:

    >>> maxScore(nums = [1,5,8])
    >>> 16
    Explanation:
    There are two possible ways to reach the last element:

    0 -> 1 -> 2 with a score of (1 - 0) * 5 + (2 - 1) * 8 = 13.
    0 -> 2 with a score of (2 - 0) * 8 = 16.

    Example 2:

    >>> maxScore(nums = [4,5,2,8,9,1,3])
    >>> 42
    Explanation:
    We can do the hopping 0 -> 4 -> 6 with a score of (4 - 0) * 9 + (6 - 4) * 3 = 42.
    """


Prompt:
def winningPlayer(x: int, y: int) -> str:
    """
    You are given two positive integers x and y, denoting the number of coins with values 75 and 10 respectively.
    Alice and Bob are playing a game. Each turn, starting with Alice, the player must pick up coins with a total value 115. If the player is unable to do so, they lose the game.
    Return the name of the player who wins the game if both players play optimally.

    Example 1:

    >>> winningPlayer(x = 2, y = 7)
    >>> "Alice"
    Explanation:
    The game ends in a single turn:

    Alice picks 1 coin with a value of 75 and 4 coins with a value of 10.

    Example 2:

    >>> winningPlayer(x = 4, y = 11)
    >>> "Bob"
    Explanation:
    The game ends in 2 turns:

    Alice picks 1 coin with a value of 75 and 4 coins with a value of 10.
    Bob picks 1 coin with a value of 75 and 4 coins with a value of 10.
    """


Prompt:
def minimumLength(s: str) -> int:
    """
    You are given a string s.
    You can perform the following process on s any number of times:

    Choose an index i in the string such that there is at least one character to the left of index i that is equal to s[i], and at least one character to the right that is also equal to s[i].
    Delete the closest occurrence of s[i] located to the left of i.
    Delete the closest occurrence of s[i] located to the right of i.

    Return the minimum length of the final string s that you can achieve.

    Example 1:

    >>> minimumLength(s = "abaacbcbb")
    >>> 5
    Explanation:
    We do the following operations:

    Choose index 2, then remove the characters at indices 0 and 3. The resulting string is s = "bacbcbb".
    Choose index 3, then remove the characters at indices 0 and 5. The resulting string is s = "acbcb".

    Example 2:

    >>> minimumLength(s = "aa")
    >>> 2
    Explanation:
    We cannot perform any operations, so we return the length of the original string.
    """


Prompt:
def minChanges(nums: List[int], k: int) -> int:
    """
    You are given an integer array nums of size n where n is even, and an integer k.
    You can perform some changes on the array, where in one change you can replace any element in the array with any integer in the range from 0 to k.
    You need to perform some changes (possibly none) such that the final array satisfies the following condition:

    There exists an integer X such that abs(a[i] - a[n - i - 1]) = X for all (0 <= i < n).

    Return the minimum number of changes required to satisfy the above condition.

    Example 1:

    >>> minChanges(nums = [1,0,1,2,4,3], k = 4)
    >>> 2
    Explanation:
    We can perform the following changes:

    Replace nums[1] by 2. The resulting array is nums = [1,2,1,2,4,3].
    Replace nums[3] by 3. The resulting array is nums = [1,2,1,3,4,3].

    The integer X will be 2.

    Example 2:

    >>> minChanges(nums = [0,1,2,3,3,6,5,4], k = 6)
    >>> 2
    Explanation:
    We can perform the following operations:

    Replace nums[3] by 0. The resulting array is nums = [0,1,2,0,3,6,5,4].
    Replace nums[4] by 4. The resulting array is nums = [0,1,2,0,4,6,5,4].

    The integer X will be 4.
    """


Prompt:
def maximumScore(grid: List[List[int]]) -> int:
    """
    You are given a 2D matrix grid of size n x n. Initially, all cells of the grid are colored white. In one operation, you can select any cell of indices (i, j), and color black all the cells of the jth column starting from the top row down to the ith row.
    The grid score is the sum of all grid[i][j] such that cell (i, j) is white and it has a horizontally adjacent black cell.
    Return the maximum score that can be achieved after some number of operations.

    Example 1:

    >>> maximumScore(grid = [[0,0,0,0,0],[0,0,3,0,0],[0,1,0,0,0],[5,0,0,3,0],[0,0,0,0,2]])
    >>> 11
    Explanation:

    In the first operation, we color all cells in column 1 down to row 3, and in the second operation, we color all cells in column 4 down to the last row. The score of the resulting grid is grid[3][0] + grid[1][2] + grid[3][3] which is equal to 11.

    Example 2:

    >>> maximumScore(grid = [[10,9,0,0,15],[7,1,0,8,0],[5,20,0,11,0],[0,0,0,1,2],[8,12,1,10,3]])
    >>> 94
    Explanation:

    We perform operations on 1, 2, and 3 down to rows 1, 4, and 0, respectively. The score of the resulting grid is grid[0][0] + grid[1][0] + grid[2][1] + grid[4][1] + grid[1][3] + grid[2][3] + grid[3][3] + grid[4][3] + grid[0][4] which is equal to 94.
    """


Prompt:
def minChanges(n: int, k: int) -> int:
    """
    You are given two positive integers n and k.
    You can choose any bit in the binary representation of n that is equal to 1 and change it to 0.
    Return the number of changes needed to make n equal to k. If it is impossible, return -1.

    Example 1:

    >>> minChanges(n = 13, k = 4)
    >>> 2
    Explanation:
    Initially, the binary representations of n and k are n = (1101)2 and k = (0100)2.
    We can change the first and fourth bits of n. The resulting integer is n = (0100)2 = k.

    Example 2:

    >>> minChanges(n = 21, k = 21)
    >>> 0
    Explanation:
    n and k are already equal, so no changes are needed.

    Example 3:

    >>> minChanges(n = 14, k = 13)
    >>> -1
    Explanation:
    It is not possible to make n equal to k.
    """


Prompt:
def doesAliceWin(s: str) -> bool:
    """
    Alice and Bob are playing a game on a string.
    You are given a string s, Alice and Bob will take turns playing the following game where Alice starts first:

    On Alice's turn, she has to remove any non-empty substring from s that contains an odd number of vowels.
    On Bob's turn, he has to remove any non-empty substring from s that contains an even number of vowels.

    The first player who cannot make a move on their turn loses the game. We assume that both Alice and Bob play optimally.
    Return true if Alice wins the game, and false otherwise.
    The English vowels are: a, e, i, o, and u.

    Example 1:

    >>> doesAliceWin(s = "leetcoder")
    >>> true
    Explanation:
    Alice can win the game as follows:

    Alice plays first, she can delete the underlined substring in s = "leetcoder" which contains 3 vowels. The resulting string is s = "der".
    Bob plays second, he can delete the underlined substring in s = "der" which contains 0 vowels. The resulting string is s = "er".
    Alice plays third, she can delete the whole string s = "er" which contains 1 vowel.
    Bob plays fourth, since the string is empty, there is no valid play for Bob. So Alice wins the game.

    Example 2:

    >>> doesAliceWin(s = "bbcd")
    >>> false
    Explanation:
    There is no valid play for Alice in her first turn, so Alice loses the game.
    """


Prompt:
def maxOperations(s: str) -> int:
    """
    You are given a binary string s.
    You can perform the following operation on the string any number of times:

    Choose any index i from the string where i + 1 < s.length such that s[i] == '1' and s[i + 1] == '0'.
    Move the character s[i] to the right until it reaches the end of the string or another '1'. For example, for s = "010010", if we choose i = 1, the resulting string will be s = "000110".

    Return the maximum number of operations that you can perform.

    Example 1:

    >>> maxOperations(s = "1001101")
    >>> 4
    Explanation:
    We can perform the following operations:

    Choose index i = 0. The resulting string is s = "0011101".
    Choose index i = 4. The resulting string is s = "0011011".
    Choose index i = 3. The resulting string is s = "0010111".
    Choose index i = 2. The resulting string is s = "0001111".

    Example 2:

    >>> maxOperations(s = "00111")
    >>> 0
    """


Prompt:
def minimumOperations(nums: List[int], target: List[int]) -> int:
    """
    You are given two positive integer arrays nums and target, of the same length.
    In a single operation, you can select any subarray of nums and increment each element within that subarray by 1 or decrement each element within that subarray by 1.
    Return the minimum number of operations required to make nums equal to the array target.

    Example 1:

    >>> minimumOperations(nums = [3,5,1,2], target = [4,6,2,4])
    >>> 2
    Explanation:
    We will perform the following operations to make nums equal to target:
    - Increment nums[0..3] by 1, nums = [4,6,2,3].
    - Increment nums[3..3] by 1, nums = [4,6,2,4].

    Example 2:

    >>> minimumOperations(nums = [1,3,2], target = [2,1,4])
    >>> 5
    Explanation:
    We will perform the following operations to make nums equal to target:
    - Increment nums[0..0] by 1, nums = [2,3,2].
    - Decrement nums[1..1] by 1, nums = [2,2,2].
    - Decrement nums[1..1] by 1, nums = [2,1,2].
    - Increment nums[2..2] by 1, nums = [2,1,3].
    - Increment nums[2..2] by 1, nums = [2,1,4].
    """


Prompt:
def minOperations(nums: List[int]) -> int:
    """
    Given an array of integers nums, you are allowed to perform the following operation any number of times:

    Remove a strictly increasing subsequence from the array.

    Your task is to find the minimum number of operations required to make the array empty.

    Example 1:

    >>> minOperations(nums = [5,3,1,4,2])
    >>> 3
    Explanation:
    We remove subsequences [1, 2], [3, 4], [5].

    Example 2:

    >>> minOperations(nums = [1,2,3,4,5])
    >>> 1

    Example 3:

    >>> minOperations(nums = [5,4,3,2,1])
    >>> 5
    """


Prompt:
def canAliceWin(nums: List[int]) -> bool:
    """
    You are given an array of positive integers nums.
    Alice and Bob are playing a game. In the game, Alice can choose either all single-digit numbers or all double-digit numbers from nums, and the rest of the numbers are given to Bob. Alice wins if the sum of her numbers is strictly greater than the sum of Bob's numbers.
    Return true if Alice can win this game, otherwise, return false.

    Example 1:

    >>> canAliceWin(nums = [1,2,3,4,10])
    >>> false
    Explanation:
    Alice cannot win by choosing either single-digit or double-digit numbers.

    Example 2:

    >>> canAliceWin(nums = [1,2,3,4,5,14])
    >>> true
    Explanation:
    Alice can win by choosing single-digit numbers which have a sum equal to 15.

    Example 3:

    >>> canAliceWin(nums = [5,5,5,25])
    >>> true
    Explanation:
    Alice can win by choosing double-digit numbers which have a sum equal to 25.
    """


Prompt:
def nonSpecialCount(l: int, r: int) -> int:
    """
    You are given 2 positive integers l and r. For any number x, all positive divisors of x except x are called the proper divisors of x.
    A number is called special if it has exactly 2 proper divisors. For example:

    The number 4 is special because it has proper divisors 1 and 2.
    The number 6 is not special because it has proper divisors 1, 2, and 3.

    Return the count of numbers in the range [l, r] that are not special.

    Example 1:

    >>> nonSpecialCount(l = 5, r = 7)
    >>> 3
    Explanation:
    There are no special numbers in the range [5, 7].

    Example 2:

    >>> nonSpecialCount(l = 4, r = 16)
    >>> 11
    Explanation:
    The special numbers in the range [4, 16] are 4 and 9.
    """


Prompt:
def numberOfSubstrings(s: str) -> int:
    """
    You are given a binary string s.
    Return the number of substrings with dominant ones.
    A string has dominant ones if the number of ones in the string is greater than or equal to the square of the number of zeros in the string.

    Example 1:

    >>> numberOfSubstrings(s = "00011")
    >>> 5
    Explanation:
    The substrings with dominant ones are shown in the table below.

    i
    j
    s[i..j]
    Number of Zeros
    Number of Ones

    3
    3
    1
    0
    1

    4
    4
    1
    0
    1

    2
    3
    01
    1
    1

    3
    4
    11
    0
    2

    2
    4
    011
    1
    2

    Example 2:

    >>> numberOfSubstrings(s = "101101")
    >>> 16
    Explanation:
    The substrings with non-dominant ones are shown in the table below.
    Since there are 21 substrings total and 5 of them have non-dominant ones, it follows that there are 16 substrings with dominant ones.

    i
    j
    s[i..j]
    Number of Zeros
    Number of Ones

    1
    1
    0
    1
    0

    4
    4
    0
    1
    0

    1
    4
    0110
    2
    2

    0
    4
    10110
    2
    3

    1
    5
    01101
    2
    3
    """


Prompt:
def canReachCorner(xCorner: int, yCorner: int, circles: List[List[int]]) -> bool:
    """
    You are given two positive integers xCorner and yCorner, and a 2D array circles, where circles[i] = [xi, yi, ri] denotes a circle with center at (xi, yi) and radius ri.
    There is a rectangle in the coordinate plane with its bottom left corner at the origin and top right corner at the coordinate (xCorner, yCorner). You need to check whether there is a path from the bottom left corner to the top right corner such that the entire path lies inside the rectangle, does not touch or lie inside any circle, and touches the rectangle only at the two corners.
    Return true if such a path exists, and false otherwise.

    Example 1:

    >>> canReachCorner(xCorner = 3, yCorner = 4, circles = [[2,1,1]])
    >>> true
    Explanation:

    The black curve shows a possible path between (0, 0) and (3, 4).

    Example 2:

    >>> canReachCorner(xCorner = 3, yCorner = 3, circles = [[1,1,2]])
    >>> false
    Explanation:

    No path exists from (0, 0) to (3, 3).

    Example 3:

    >>> canReachCorner(xCorner = 3, yCorner = 3, circles = [[2,1,1],[1,2,1]])
    >>> false
    Explanation:

    No path exists from (0, 0) to (3, 3).

    Example 4:

    >>> canReachCorner(xCorner = 4, yCorner = 4, circles = [[5,5,1]])
    >>> true
    Explanation:
    """


Prompt:
def simulationResult(windows: List[int], queries: List[int]) -> List[int]:
    """
    There are n windows open numbered from 1 to n, we want to simulate using alt + tab to navigate between the windows.
    You are given an array windows which contains the initial order of the windows (the first element is at the top and the last one is at the bottom).
    You are also given an array queries where for each query, the window queries[i] is brought to the top.
    Return the final state of the array windows.

    Example 1:

    >>> simulationResult(windows = [1,2,3], queries = [3,3,2])
    >>> [2,3,1]
    Explanation:
    Here is the window array after each query:

    Initial order: [1,2,3]
    After the first query: [3,1,2]
    After the second query: [3,1,2]
    After the last query: [2,3,1]

    Example 2:

    >>> simulationResult(windows = [1,4,2,3], queries = [4,1,3])
    >>> [3,1,4,2]
    Explanation:
    Here is the window array after each query:

    Initial order: [1,4,2,3]
    After the first query: [4,1,2,3]
    After the second query: [1,4,2,3]
    After the last query: [3,1,4,2]
    """


Prompt:
def winningPlayerCount(n: int, pick: List[List[int]]) -> int:
    """
    You are given an integer n representing the number of players in a game and a 2D array pick where pick[i] = [xi, yi] represents that the player xi picked a ball of color yi.
    Player i wins the game if they pick strictly more than i balls of the same color. In other words,

    Player 0 wins if they pick any ball.
    Player 1 wins if they pick at least two balls of the same color.
    ...
    Player i wins if they pick at leasti + 1 balls of the same color.

    Return the number of players who win the game.
    Note that multiple players can win the game.

    Example 1:

    >>> winningPlayerCount(n = 4, pick = [[0,0],[1,0],[1,0],[2,1],[2,1],[2,0]])
    >>> 2
    Explanation:
    Player 0 and player 1 win the game, while players 2 and 3 do not win.

    Example 2:

    >>> winningPlayerCount(n = 5, pick = [[1,1],[1,2],[1,3],[1,4]])
    >>> 0
    Explanation:
    No player wins the game.

    Example 3:

    >>> winningPlayerCount(n = 5, pick = [[1,1],[2,4],[2,4],[2,4]])
    >>> 1
    Explanation:
    Player 2 wins the game by picking 3 balls with color 4.
    """


Prompt:
def minFlips(grid: List[List[int]]) -> int:
    """
    You are given an m x n binary matrix grid.
    A row or column is considered palindromic if its values read the same forward and backward.
    You can flip any number of cells in grid from 0 to 1, or from 1 to 0.
    Return the minimum number of cells that need to be flipped to make either all rows palindromic or all columns palindromic.

    Example 1:

    >>> minFlips(grid = [[1,0,0],[0,0,0],[0,0,1]])
    >>> 2
    Explanation:

    Flipping the highlighted cells makes all the rows palindromic.

    Example 2:

    >>> minFlips(grid = [[0,1],[0,1],[0,0]])
    >>> 1
    Explanation:

    Flipping the highlighted cell makes all the columns palindromic.

    Example 3:

    >>> minFlips(grid = [[1],[0]])
    >>> 0
    Explanation:
    All rows are already palindromic.
    """


Prompt:
def minFlips(grid: List[List[int]]) -> int:
    """
    You are given an m x n binary matrix grid.
    A row or column is considered palindromic if its values read the same forward and backward.
    You can flip any number of cells in grid from 0 to 1, or from 1 to 0.
    Return the minimum number of cells that need to be flipped to make all rows and columns palindromic, and the total number of 1's in grid divisible by 4.

    Example 1:

    >>> minFlips(grid = [[1,0,0],[0,1,0],[0,0,1]])
    >>> 3
    Explanation:

    Example 2:

    >>> minFlips(grid = [[0,1],[0,1],[0,0]])
    >>> 2
    Explanation:

    Example 3:

    >>> minFlips(grid = [[1],[1]])
    >>> 2
    Explanation:
    """


Prompt:
def timeTaken(edges: List[List[int]]) -> List[int]:
    """
    There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree.
    Initially, all nodes are unmarked. For each node i:

    If i is odd, the node will get marked at time x if there is at least one node adjacent to it which was marked at time x - 1.
    If i is even, the node will get marked at time x if there is at least one node adjacent to it which was marked at time x - 2.

    Return an array times where times[i] is the time when all nodes get marked in the tree, if you mark node i at time t = 0.
    Note that the answer for each times[i] is independent, i.e. when you mark node i all other nodes are unmarked.

    Example 1:

    >>> timeTaken(edges = [[0,1],[0,2]])
    >>> [2,4,3]
    Explanation:

    For i = 0:

    Node 1 is marked at t = 1, and Node 2 at t = 2.

    For i = 1:

    Node 0 is marked at t = 2, and Node 2 at t = 4.

    For i = 2:

    Node 0 is marked at t = 2, and Node 1 at t = 3.

    Example 2:

    >>> timeTaken(edges = [[0,1]])
    >>> [1,2]
    Explanation:

    For i = 0:

    Node 1 is marked at t = 1.

    For i = 1:

    Node 0 is marked at t = 2.

    Example 3:

    >>> timeTaken(edges = [[2,4],[0,1],[2,3],[0,2]])
    >>> [4,6,3,5,5]
    Explanation:
    """