Diagonal Matrices

Write a function that diagonally orders numbers in a n x n matrix, depending on which of the four corners you originate from: upper-left (ul), upper-right (ur), lower-left (ll), lower-right (lr).

Examples

diagonalize(3, "ul") ➞ [
  [0, 1, 2],
  [1, 2, 3],
  [2, 3, 4]
]

diagonalize(4, "ur") ➞ [
  [3, 2, 1, 0],
  [4, 3, 2, 1],
  [5, 4, 3, 2],
  [6, 5, 4, 3]
]

diagonalize(3, "ll") ➞ [
  [2, 3, 4],
  [1, 2, 3],
  [0, 1, 2]
]

diagonalize(5, "lr") ➞ [
  [8, 7, 6, 5, 4],
  [7, 6, 5, 4, 3],
  [6, 5, 4, 3, 2],
  [5, 4, 3, 2, 1],
  [4, 3, 2, 1, 0]
]

Notes

N/A