2768 - Number of Black Blocks\.

Medium

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:

Input: m = 3, n = 3, coordinates = \[\[0,0]]

Output: 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:

Input: m = 3, n = 3, coordinates = \[\[0,0],1,1,0,2]

Output: 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.

Constraints:

• <code>2 <= m <= 10⁵</code>

• <code>2 <= n <= 10⁵</code>

• <code>0 <= coordinates.length <= 10⁴</code>

• coordinates[i].length == 2

• 0 <= coordinates[i][0] < m

• 0 <= coordinates[i][1] < n

• It is guaranteed that coordinates contains pairwise distinct coordinates.