
"""simple docstring"""







from maths.prime_factors import prime_factors
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     int:







							"""simple docstring"""


							if not isinstance(SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE ):
														__snake_case     			=       F'''Input value of [number={number}] must be an integer'''
														raise TypeError(SCREAMING_SNAKE_CASE )
							if number < 1:
														raise ValueError("Input must be a positive integer" )
							return -1 if len(prime_factors(SCREAMING_SNAKE_CASE ) ) % 2 else 1


if __name__ == "__main__":
		import doctest

		doctest.testmod()


"""simple docstring"""







from heapq import heappop, heappush

import numpy as np
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    )  ->     tuple[float | int, list[tuple[int, int]]]:







							"""simple docstring"""


							__snake_case			,   __snake_case     			=       grid.shape
							__snake_case     			=       [-1, 1, 0, 0]
							__snake_case     			=       [0, 0, -1, 1]
							if allow_diagonal:
														dx += [-1, -1, 1, 1]
														dy += [-1, 1, -1, 1]

							__snake_case			,   __snake_case     			=       [(0, source)], set()
							__snake_case     			=       np.full((rows, cols)							,    np.inf )
							__snake_case     			=       0
							__snake_case     			=       np.empty((rows, cols)							,    dtype=SCREAMING_SNAKE_CASE )
							__snake_case     			=       None

							while queue:
														((__snake_case)			,   (__snake_case))     			=       heappop(SCREAMING_SNAKE_CASE )
														if (x, y) in visited:
																					continue
														visited.add((x, y) )

														if (x, y) == destination:
																					__snake_case     			=       []
																					while (x, y) != source:
																												path.append((x, y) )
																												__snake_case			,   __snake_case     			=       predecessors[x, y]
																					path.append(SCREAMING_SNAKE_CASE )  # add the source manually
																					path.reverse()
																					return matrix[destination], path

														for i in range(len(SCREAMING_SNAKE_CASE ) ):
																					__snake_case			,   __snake_case     			=       x + dx[i], y + dy[i]
																					if 0 <= nx < rows and 0 <= ny < cols:
																												__snake_case     			=       grid[nx][ny]
																												if next_node == 1 and matrix[nx, ny] > dist + 1:
																																			heappush(SCREAMING_SNAKE_CASE							,    (dist + 1, (nx, ny)) )
																																			__snake_case     			=       dist + 1
																																			__snake_case     			=       (x, y)

							return np.inf, []


if __name__ == "__main__":
		import doctest

		doctest.testmod()
