


from __future__ import annotations
def 				UpperCamelCase_	(					__snake_case      :    list[list[int]]						,      __snake_case      :    int						,      __snake_case      :    int						,      __snake_case      :    int | float  )->   None:




						'''simple docstring'''
						__magic_name__		,      __magic_name__					=      m - 1, 0
						while i >= 0 and j < n:
												if key == mat[i][j]:
																		print(F'''Key {key} found at row- {i + 1} column- {j + 1}'''  )
																		return
												if key < mat[i][j]:
																		i -= 1
												else:
																		j += 1
						print(F'''Key {key} not found'''  )
def 				UpperCamelCase_	(					)->   None:




						'''simple docstring'''
						__magic_name__					=      [[2, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]]
						__magic_name__					=      int(input('Enter the element to be searched:'  )  )
						print(__snake_case  )
						search_in_a_sorted_matrix(__snake_case						,      len(__snake_case  )						,      len(mat[0]  )						,      __snake_case  )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()





from itertools import count
from math import asin, pi, sqrt
def 				UpperCamelCase_	(					__snake_case      :    float  )->   float:




						'''simple docstring'''
						return (
						    (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
						) / 4
def 				UpperCamelCase_	(					__snake_case      :    int  )->   float:




						'''simple docstring'''
						__magic_name__					=      (circles_number + 1 - sqrt(2 * circles_number  )) / (
						    2 * (circles_number**2 + 1)
						)
						__magic_name__					=      circles_number * intersection_y

						__magic_name__					=      intersection_x * intersection_y / 2
						__magic_name__					=      circle_bottom_arc_integral(
						    1 / 2  ) - circle_bottom_arc_integral(__snake_case  )

						return triangle_area + concave_region_area
def 				UpperCamelCase_	(					__snake_case      :    float = 1 / 10_00  )->   int:




						'''simple docstring'''
						__magic_name__					=      (1 - pi / 4) / 4

						for n in count(1  ):
												if concave_triangle_area(__snake_case  ) / l_section_area < fraction:
																		return n

						return -1


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

