#213EasyMatrix· Index Mapping for Rotation

Rotate Tile Grid

A tiling robot lays a rectangular floor pattern described by a grid of tile codes: `grid[r][c]` is the code of the tile in row `r`, column `c`. The pattern was designed for a wall that is turned a quarter of a turn, so the whole pattern has to be rotated by 90 degrees clockwise before it is laid. Return the rotated pattern as a new grid. The pattern does not have to be square: a grid with `h` rows and `w` columns becomes a grid with `w` rows and `h` columns.

Input format

`grid`: a non-empty rectangular grid of integers.

Output format

A new grid with `grid[0].length` rows and `grid.length` columns holding the rotated pattern.

Examples

Input: grid = [[1, 2, 3], [4, 5, 6]]

Output: [[4, 1], [5, 2], [6, 3]]

The first column read from the bottom up (4, 1) becomes the first row, the second column becomes the second row, and so on. A 2 x 3 grid turns into a 3 x 2 grid.

Input: grid = [[1, 2], [3, 4]]

Output: [[3, 1], [4, 2]]

For a square grid the corners travel one step around: 1 moves to the top-right, 2 to the bottom-right, 4 to the bottom-left and 3 to the top-left.

Input: grid = [[9]]

Output: [[9]]

A single tile is unchanged.

Constraints

1 <= grid.length, grid[0].length <= 100
All rows have the same length.
-10^4 <= grid[r][c] <= 10^4

#matrix
#rotation
#index-mapping
#arrays