![](\"https://assets.leetcode.com/uploads/2024/08/01/chess_knight.jpg\")
There is a 50 x 50 chessboard with one knight and some pawns on it. You are given two integers kx and ky where (kx, ky) denotes the position of the knight, and a 2D array positions where positions[i] = [xi, yi] denotes the position of the pawns on the chessboard.
Alice and Bob play a turn-based game, where Alice goes first. In each player's turn:
\n\nAlice is trying to maximize the sum of the number of moves made by both players until there are no more pawns on the board, whereas Bob tries to minimize them.
\n\nReturn the maximum total number of moves made during the game that Alice can achieve, assuming both players play optimally.
\n\nNote that in one move, a chess knight has eight possible positions it can move to, as illustrated below. Each move is two cells in a cardinal direction, then one cell in an orthogonal direction.
\n\n
\n
Example 1:
\n\nInput: kx = 1, ky = 1, positions = [[0,0]]
\n\nOutput: 4
\n\nExplanation:
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2024/08/16/gif3.gif\")
The knight takes 4 moves to reach the pawn at (0, 0).
Example 2:
\n\nInput: kx = 0, ky = 2, positions = [[1,1],[2,2],[3,3]]
\n\nOutput: 8
\n\nExplanation:
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2024/08/16/gif4.gif\")
(2, 2) and captures it in two moves: (0, 2) -> (1, 4) -> (2, 2).(3, 3) and captures it in two moves: (2, 2) -> (4, 1) -> (3, 3).(1, 1) and captures it in four moves: (3, 3) -> (4, 1) -> (2, 2) -> (0, 3) -> (1, 1).Example 3:
\n\nInput: kx = 0, ky = 0, positions = [[1,2],[2,4]]
\n\nOutput: 3
\n\nExplanation:
\n\n(2, 4) and captures it in two moves: (0, 0) -> (1, 2) -> (2, 4). Note that the pawn at (1, 2) is not captured.(1, 2) and captures it in one move: (2, 4) -> (1, 2).\n
Constraints:
\n\n0 <= kx, ky <= 491 <= positions.length <= 15positions[i].length == 20 <= positions[i][0], positions[i][1] <= 49positions[i] are unique.positions[i] != [kx, ky] for all 0 <= i < positions.length.给你一个 50 x 50 的国际象棋棋盘，棋盘上有 一个 马和一些兵。给你两个整数 kx 和 ky ，其中 (kx, ky) 表示马所在的位置，同时还有一个二维数组 positions ，其中 positions[i] = [xi, yi] 表示第 i 个兵在棋盘上的位置。
Alice 和 Bob 玩一个回合制游戏，Alice 先手。玩家的一次操作中，可以执行以下操作：
\n\nAlice 的目标是 最大化 两名玩家的 总 移动次数，直到棋盘上不再存在兵，而 Bob 的目标是 最小化 总移动次数。
\n\n假设两名玩家都采用 最优 策略，请你返回可以达到的 最大 总移动次数。
\n\n在一次 移动 中，如下图所示，马有 8 个可以移动到的位置，每个移动位置都是沿着坐标轴的一个方向前进 2 格，然后沿着垂直的方向前进 1 格。
\n\n
\n\n
示例 1：
\n\n输入：kx = 1, ky = 1, positions = [[0,0]]
\n\n输出：4
\n\n解释：
\n\n
马需要移动 4 步吃掉 (0, 0) 处的兵。
示例 2：
\n\n输入：kx = 0, ky = 2, positions = [[1,1],[2,2],[3,3]]
\n\n输出：8
\n\n解释：
\n\n
(2, 2) 处的兵，移动马吃掉它需要 2 步：(0, 2) -> (1, 4) -> (2, 2) 。(3, 3) 处的兵，移动马吃掉它需要 2 步：(2, 2) -> (4, 1) -> (3, 3) 。(1, 1) 处的兵，移动马吃掉它需要 4 步：(3, 3) -> (4, 1) -> (2, 2) -> (0, 3) -> (1, 1) 。示例 3：
\n\n输入：kx = 0, ky = 0, positions = [[1,2],[2,4]]
\n\n输出：3
\n\n解释：
\n\n(2, 4) 处的兵，移动马吃掉它需要 2 步：(0, 0) -> (1, 2) -> (2, 4) 。注意，(1, 2) 处的兵不会被吃掉。(1, 2) 处的兵，移动马吃掉它需要 1 步：(2, 4) -> (1, 2) 。\n\n
提示：
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