Matrix Trace

Return sum of diagonal elements of a square matrix. Example: [[1,2],[3,4]] => 5

Your task

Implement this function:

def trace(matrix: list) -> int:

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: matrix.

Example

Input

[[1, 2], [3, 4]]

Output

5