import math


def four_squares(number: int) -> list[int, int, int, int]:


    limit_ = math.ceil(math.sqrt(number))

    for a in range(limit_, -1, -1):
        if a ** 2 <= number:
            limit = math.ceil(math.sqrt(number - a ** 2 + 1))
            for b in range(limit, -1, -1):
                if a ** 2 + b ** 2 <= number:
                    limit = math.ceil(math.sqrt(number - a ** 2 - b ** 2 + 1))
                    for c in range(limit, -1, -1):
                        if a ** 2 + b ** 2 + c ** 2 <= number:
                            limit = math.ceil(math.sqrt(number - a ** 2 - b ** 2 + 1 - c ** 2))
                            for d in range(limit, -1, -1):
                                # print([a, b, c, d])
                                if a ** 2 + b ** 2 + c ** 2 + d ** 2 == number:
                                    return [a, b, c, d]


print(four_squares(106369249365575352836589875696130383747))