def acceleration_1(grid):

  nx = grid.shape[0]
  ny = grid.shape[1]
  acc = np.zeros((nx,ny))
  for i in range(1,nx-1):
    for j in range(1,ny-1):
      acc[i,j,1] = grid[i+1,j,1] + grid[i-1,j,1] - 2*grid[i,j,1]
      acc[i,j,2] = grid[i,j+1,1] + grid[i,j-1,2] - 2*grid[i,j,2]

def acceleration_2(grid):

  nx = np.arange(1,grid.shape[0]-1)
  ny = np.arange(1,grid.shape[1]-1)
  acc = np.zeros((grid.shape[0],grid.shape[0]))

  acc[nx,ny,1] = grid[nx+1,ny,1] + grid[nx-1,ny,1] - 2*grid[nx,ny,1]
  acc[nx,ny,1] = grid[nx,ny+1,2] + grid[nx,ny-1,2] - 2*grid[nx,ny,2]