from os.path import dirname,realpath,join

def profiler(method):
    from time import perf_counter_ns
    def wrapper_method(*args: any, **kwargs: any) -> any:
        start_time = perf_counter_ns()
        ret = method(*args, **kwargs)
        stop_time = perf_counter_ns() - start_time
        time_len = min(9, ((len(str(stop_time))-1)//3)*3)
        time_conversion = {9: 'seconds', 6: 'milliseconds', 3: 'microseconds', 0: 'nanoseconds'}
        print(f"Method {method.__name__} took : {stop_time / (10**time_len)} {time_conversion[time_len]}")
        return ret
    return wrapper_method

def binary_search(low_point, high_point, record_distance,record_time,min_or_max):
    if min_or_max == 'min':
        # custom binary search algorithm for minimum charge time to surpass the target distance
        while low_point < high_point:
            mid = (low_point + high_point)//2
            if ((record_time - mid) * mid) > record_distance:
                # if it is valid then we mark it as the high_point and continue searching
                high_point = mid
            else:
                # if it is not valid then we check if the next number up is valid and that should be the minimum time
                if ((record_time - mid + 1) * (mid + 1)) > record_distance:
                    return mid + 1
                # else we continue searching
                low_point = mid + 1
    elif min_or_max == 'max':
        # custom binary search algorithm for maximum charge time to surpass the target distance
        while low_point < high_point:
            mid = -((low_point + high_point)//-2) # math trick to do ceiling division
            if ((record_time - mid) * mid) > record_distance:
                low_point = mid
            else:
                # if it is not valid then we check if the next number down is valid and that should be the maximum time
                if ((record_time - mid + 1) * (mid + 1)) > record_distance:
                    return mid - 1
                # else we continue searching
                high_point = mid - 1

@profiler
def solver(input_str: str) -> tuple[int,int]:
    part_1_solve = 1
    for record_time,record_distance in zip( *[ [ int(number) for number in line.split()[1:] ] for line in input_str.split('\n') ] ):
        minimum_time = binary_search(0,record_time//2,record_distance,record_time,'min')
        # maximum_time = binary_search(record_time//2,record_time,record_distance,record_time,'max') # before I realized it was parabola lmao
        maximum_time = record_time - minimum_time
        part_1_solve *= maximum_time - minimum_time + 1

    # part 2
    # instead of splitting the numbers into multiple pairs, we will just remove the spaces and have one pair of numbers for time and distance.
    record_time,record_distance = [ int(line.replace(' ', '').split(':')[1]) for line in input_str.split('\n') ]
    minimum_time = binary_search(0,record_time//2,record_distance,record_time,'min')
    # maximum_time = binary_search(record_time//2,record_time,record_distance,record_time,'max') # before I realized it was parabola lmao
    maximum_time = record_time - minimum_time
    part_2_solve = maximum_time - minimum_time + 1

    return part_1_solve,part_2_solve

if __name__ == "__main__":
    BASE_DIR = dirname(realpath(__file__))
    with open(join(BASE_DIR, r'input'), 'r') as f:
        input_data = f.read().replace('\r', '').strip()
    result = solver(input_data)
    print("Part 1:", result[0], "\nPart 2:", result[1])