You are given four integers, m, n, introvertsCount, and extrovertsCount. You have an m x n grid, and there are two types of people: introverts and extroverts. There are introvertsCount introverts and extrovertsCount extroverts.
You should decide how many people you want to live in the grid and assign each of them one grid cell. Note that you do not have to have all the people living in the grid.
\n\nThe happiness of each person is calculated as follows:
\n\n120 happiness and lose 30 happiness for each neighbor (introvert or extrovert).40 happiness and gain 20 happiness for each neighbor (introvert or extrovert).Neighbors live in the directly adjacent cells north, east, south, and west of a person's cell.
\n\nThe grid happiness is the sum of each person's happiness. Return the maximum possible grid happiness.
\n\n\n
Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2020/11/05/grid_happiness.png\")
\n\nInput: m = 2, n = 3, introvertsCount = 1, extrovertsCount = 2\nOutput: 240\nExplanation: Assume the grid is 1-indexed with coordinates (row, column).\nWe can put the introvert in cell (1,1) and put the extroverts in cells (1,3) and (2,3).\n- Introvert at (1,1) happiness: 120 (starting happiness) - (0 * 30) (0 neighbors) = 120\n- Extrovert at (1,3) happiness: 40 (starting happiness) + (1 * 20) (1 neighbor) = 60\n- Extrovert at (2,3) happiness: 40 (starting happiness) + (1 * 20) (1 neighbor) = 60\nThe grid happiness is 120 + 60 + 60 = 240.\nThe above figure shows the grid in this example with each person's happiness. The introvert stays in the light green cell while the extroverts live on the light purple cells.\n\n\n
Example 2:
\n\n\nInput: m = 3, n = 1, introvertsCount = 2, extrovertsCount = 1\nOutput: 260\nExplanation: Place the two introverts in (1,1) and (3,1) and the extrovert at (2,1).\n- Introvert at (1,1) happiness: 120 (starting happiness) - (1 * 30) (1 neighbor) = 90\n- Extrovert at (2,1) happiness: 40 (starting happiness) + (2 * 20) (2 neighbors) = 80\n- Introvert at (3,1) happiness: 120 (starting happiness) - (1 * 30) (1 neighbor) = 90\nThe grid happiness is 90 + 80 + 90 = 260.\n\n\n
Example 3:
\n\n\nInput: m = 2, n = 2, introvertsCount = 4, extrovertsCount = 0\nOutput: 240\n\n\n
\n
Constraints:
\n\n1 <= m, n <= 50 <= introvertsCount, extrovertsCount <= min(m * n, 6)给你四个整数 m、n、introvertsCount 和 extrovertsCount 。有一个 m x n 网格，和两种类型的人：内向的人和外向的人。总共有 introvertsCount 个内向的人和 extrovertsCount 个外向的人。
请你决定网格中应当居住多少人，并为每个人分配一个网格单元。 注意，不必 让所有人都生活在网格中。
\n\n每个人的 幸福感 计算如下：
\n\n120 个幸福感，但每存在一个邻居（内向的或外向的）他都会 失去 30 个幸福感。40 个幸福感，每存在一个邻居（内向的或外向的）他都会 得到 20 个幸福感。邻居是指居住在一个人所在单元的上、下、左、右四个直接相邻的单元中的其他人。
\n\n网格幸福感 是每个人幸福感的 总和 。 返回 最大可能的网格幸福感 。
\n\n\n\n
示例 1：
\n![\"\"](\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/11/15/grid_happiness.png\")
\n\n输入：m = 2, n = 3, introvertsCount = 1, extrovertsCount = 2\n输出：240\n解释：假设网格坐标 (row, column) 从 1 开始编号。\n将内向的人放置在单元 (1,1) ，将外向的人放置在单元 (1,3) 和 (2,3) 。\n- 位于 (1,1) 的内向的人的幸福感：120（初始幸福感）- (0 * 30)（0 位邻居）= 120\n- 位于 (1,3) 的外向的人的幸福感：40（初始幸福感）+ (1 * 20)（1 位邻居）= 60\n- 位于 (2,3) 的外向的人的幸福感：40（初始幸福感）+ (1 * 20)（1 位邻居）= 60\n网格幸福感为：120 + 60 + 60 = 240\n上图展示该示例对应网格中每个人的幸福感。内向的人在浅绿色单元中，而外向的人在浅紫色单元中。\n\n\n
示例 2：
\n\n\n输入：m = 3, n = 1, introvertsCount = 2, extrovertsCount = 1\n输出：260\n解释：将内向的人放置在单元 (1,1) 和 (3,1) ，将外向的人放置在单元 (2,1) 。\n- 位于 (1,1) 的内向的人的幸福感：120（初始幸福感）- (1 * 30)（1 位邻居）= 90\n- 位于 (2,1) 的外向的人的幸福感：40（初始幸福感）+ (2 * 20)（2 位邻居）= 80\n- 位于 (3,1) 的内向的人的幸福感：120（初始幸福感）- (1 * 30)（1 位邻居）= 90\n网格幸福感为 90 + 80 + 90 = 260\n\n\n
示例 3：
\n\n\n输入：m = 2, n = 2, introvertsCount = 4, extrovertsCount = 0\n输出：240\n\n\n
\n\n
提示：
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