



"""simple docstring"""





def      a__			(   lowerCAmelCase__ = 10**9   ):
      UpperCAmelCase_    				=							1
      UpperCAmelCase_    				=							2

      UpperCAmelCase_    				=							0
      UpperCAmelCase_    				=							0
      UpperCAmelCase_    				=							0
      while perimeter <= max_perimeter:
            perimeters_sum += perimeter

            prev_value += 2 * value
            value += prev_value

            UpperCAmelCase_    				=							2 * value + 2 if i % 2 == 0 else 2 * value - 2
            i += 1

      return perimeters_sum


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









"""simple docstring"""





from heapq import heappop, heappush

import numpy as np
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    ):
      UpperCAmelCase_				,					UpperCAmelCase_    				=							grid.shape
      UpperCAmelCase_    				=							[-1, 1, 0, 0]
      UpperCAmelCase_    				=							[0, 0, -1, 1]
      if allow_diagonal:
            dx += [-1, -1, 1, 1]
            dy += [-1, 1, -1, 1]

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

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

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

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

      return np.inf, []


if __name__ == "__main__":
  import doctest

  doctest.testmod()




