






from math import ceil, sqrt


def 				snake_case__							(							UpperCAmelCase							:  int = 1_0_0_0_0_0_0       ):
    lowerCAmelCase__   :Dict      							=				0

    for outer_width in range(3    ,			(limit // 4) + 2       ):
        if outer_width**2 > limit:
            lowerCAmelCase__   :Dict      							=				max(ceil(sqrt(outer_width**2 - limit       )       )    ,			1       )
        else:
            lowerCAmelCase__   :List[str]      							=				1
        if (outer_width - hole_width_lower_bound) % 2:
            hole_width_lower_bound += 1

        answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

    return answer


if __name__ == "__main__":
 print(f"""{solution() = }""")











def 				snake_case__							(							UpperCAmelCase							:  float    ,			UpperCAmelCase							:  list[float]       ):
    if discount_rate < 0:
        raise ValueError("Discount rate cannot be negative"       )
    if not cash_flows:
        raise ValueError("Cash flows list cannot be empty"       )
    lowerCAmelCase__   :List[Any]      							=				sum(
        cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(UpperCAmelCase       )       )
    return round(UpperCAmelCase    ,			ndigits=2       )


if __name__ == "__main__":
 import doctest

 doctest.testmod()



