
def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    int = 10)      ->					str:






       '''simple docstring'''





       if not isinstance(UpperCamelCase__		,						UpperCamelCase__) or n < 0:
              raise ValueError("Invalid input")
       __UpperCamelCase			:     Optional[Any]         =      10**n
       __UpperCamelCase			:     str         =      28_433 * (pow(2		,						7_830_457		,						UpperCamelCase__)) + 1
       return str(number % modulus)


if __name__ == "__main__":
  from doctest import testmod

  testmod()
  print(f"{solution(10) = }")

from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Sequence[float]		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int)      ->					tuple[int | None, int | None, float]:






							'''simple docstring'''





							if not arr:
														return None, None, 0
							if low == high:
														return low, high, arr[low]

							__UpperCamelCase			:     Tuple         =      (low + high) // 2
							__UpperCamelCase     ,		__UpperCamelCase     ,		__UpperCamelCase			:     Dict         =      max_subarray(_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase)
							__UpperCamelCase     ,		__UpperCamelCase     ,		__UpperCamelCase			:     Optional[int]         =      max_subarray(_lowerCamelCase		,						mid + 1		,						_lowerCamelCase)
							__UpperCamelCase     ,		__UpperCamelCase     ,		__UpperCamelCase			:     Dict         =      max_cross_sum(_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase)
							if left_sum >= right_sum and left_sum >= cross_sum:
														return left_low, left_high, left_sum
							elif right_sum >= left_sum and right_sum >= cross_sum:
														return right_low, right_high, right_sum
							return cross_left, cross_right, cross_sum




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Sequence[float]		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int)      ->					tuple[int, int, float]:






							'''simple docstring'''





							__UpperCamelCase     ,		__UpperCamelCase			:     Union[str, Any]         =      float("-inf"), -1
							__UpperCamelCase     ,		__UpperCamelCase			:     Optional[int]         =      float("-inf"), -1

							__UpperCamelCase			:     int | float         =      0
							for i in range(_lowerCamelCase		,						low - 1		,						-1):
														summ += arr[i]
														if summ > left_sum:
																					__UpperCamelCase			:     Tuple         =      summ
																					__UpperCamelCase			:     Optional[int]         =      i

							__UpperCamelCase			:     Union[str, Any]         =      0
							for i in range(mid + 1		,						high + 1):
														summ += arr[i]
														if summ > right_sum:
																					__UpperCamelCase			:     Union[str, Any]         =      summ
																					__UpperCamelCase			:     Optional[int]         =      i

							return max_left, max_right, (left_sum + right_sum)




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    int)      ->					float:






							'''simple docstring'''





							__UpperCamelCase			:     Tuple         =      [randint(1		,						_lowerCamelCase) for _ in range(_lowerCamelCase)]
							__UpperCamelCase			:     Optional[Any]         =      time.time()
							max_subarray(_lowerCamelCase		,						0		,						input_size - 1)
							__UpperCamelCase			:     Any         =      time.time()
							return end - start




def 			_SCREAMING_SNAKE_CASE      (	)      ->					None:






							'''simple docstring'''





							__UpperCamelCase			:     Dict         =      [10, 100, 1_000, 10_000, 50_000, 100_000, 200_000, 300_000, 400_000, 500_000]
							__UpperCamelCase			:     Union[str, Any]         =      [time_max_subarray(_lowerCamelCase) for input_size in input_sizes]
							print("No of Inputs\t\tTime Taken")
							for input_size, runtime in zip(_lowerCamelCase		,						_lowerCamelCase):
														print(_lowerCamelCase		,						"\t\t"		,						_lowerCamelCase)
							plt.plot(_lowerCamelCase		,						_lowerCamelCase)
							plt.xlabel("Number of Inputs")
							plt.ylabel("Time taken in seconds")
							plt.show()


if __name__ == "__main__":
		from doctest import testmod

		testmod()