Write a function that takes in three parameters: r, c, i, where:

• r and c are the number of rows and columns to initialize a zero matrix.
• i represents the array of incrementing operations (+1).

And returns the resulting matrix after applying all the increment operations. Each increment operation will add 1 to the rows or columns specified in the incrementing array.

To illustrate:

final(3, 3, ["2r", "2c", "1r", "0c"])

// Initialize a 3 x 3 matrix of zeroes.

[
  [0, 0, 0],
  [0, 0, 0],
  [0, 0, 0]
]

// Apply "2r" (increment index 2 row).

[
  [0, 0, 0],
  [0, 0, 0],
  [1, 1, 1]
]

// Apply "2c" (increment index 2 column).

[
  [0, 0, 1],
  [0, 0, 1],
  [1, 1, 2]
]

# Apply "1r" (increment index 1 row).

[
  [0, 0, 1],
  [1, 1, 2],
  [1, 1, 2]
]

// Apply "0c" (increment index 0 column).
// This is the result you should return.

[
  [1, 0, 1],
  [2, 1, 2],
  [2, 1, 2]
]

Examples

final(2, 2, ["0r", "0r", "0r", "1c"]) ➞ [
  [3, 4],
  [0, 1]
]

final(2, 2, ["0c"]) ➞ [
  [1, 0],
  [1, 0]
]

final(3, 3, ["1c", "2c", "2c", "3c", "3c", "3c"]) ➞ [
    [1, 2, 3],
    [1, 2, 3],
    [1, 2, 3]
]

final(3, 3, []) ➞ [
  [0, 0, 0],
  [0, 0, 0],
  [0, 0, 0]
]

Notes

• The 2D matrix is 0-indexed.
• The matrix created will have at least one row and one column.
• All increment operations will be exactly +1.