Lower Triangular Matrix

Write a function make_lower_triangular_matrix(m) that returns an m x m matrix as a list of lists where row i (counting from 0) starts with the numbers 1, 2, ..., i + 1 and is padded with zeros. For m = 0 return the empty list. Use nested comprehensions rather than explicit loops.

Example

make_lower_triangular_matrix(5)
->  [[1, 0, 0, 0, 0],
     [1, 2, 0, 0, 0],
     [1, 2, 3, 0, 0],
     [1, 2, 3, 4, 0],
     [1, 2, 3, 4, 5]]

Your task

Implement this function:

def make_lower_triangular_matrix(m: int) -> list:

Write the function only — the arguments are read for you and the return value is printed automatically.

Arguments arrive as one Python literal per line, in this order: m.

Example

Input

5

Output

[[1, 0, 0, 0, 0], [1, 2, 0, 0, 0], [1, 2, 3, 0, 0], [1, 2, 3, 4, 0], [1, 2, 3, 4, 5]]