"""
Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101 .

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
"""

import time
from functools import lru_cache


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        print(f"{func.__name__} time: {end_time - start_time:.8f} seconds")
        return result

    return wrapper


def sum_right(length: int) -> int:
    sumo = 0
    last = 1
    for i in range(1, length + 1):
        sumo += last + 2 * (i - 1)
        last += 2 * (i - 1)
    return sumo


@lru_cache(maxsize=None)
def sum_left(length: int) -> tuple[list[int], int]:
    if length == 1:
        return [1], 1
    else:
        two, sum_o = sum_left(length - 2)
        i = length // 2
        max_two = max(two)
        new_two = [max_two + i * 4, max_two + i * 8]
        return new_two, sum_o + sum(new_two)


def sum_of_diagonals(length: int) -> int:
    if length % 2 == 0:
        raise ValueError("Input must be an odd number")
    return sum_left(length)[1] + sum_right(length) - 1


@timer
def main_pro(length: int) -> None:
    sum_o = sum_of_diagonals(length)
    print(sum_o)


@timer
def main_math(length: int) -> None:
    if length % 2 == 0:
        raise ValueError("Input must be an odd number")
    n = length // 2
    sum_o = 1 + 10 * n**2 + (16 * n**3 + 26 * n) / 3
    print(int(sum_o))


@timer
def main_math_pro(length: int) -> None:
    if length % 2 == 0:
        raise ValueError("Input must be an odd number")
    n = length // 2
    maxnum = int(length**2)
    sumo = 1
    for i in range(n, 0, -1):
        delta = 2 * i
        sumo += 4 * maxnum - 6 * delta
        maxnum -= delta * 4
    print(int(sumo))


if __name__ == "__main__":
    length = 1001
    main_math(length)
    main_pro(length)
    main_math_pro(length)