from collections import Counter


class Grid():
    dim = 12
    
    def __init__(self):
        self.cells = [(x, y) for x in range(Grid.dim) for y in range(Grid.dim)]

    def neighbors(self, x, y, diags=False):
        neighs = [(x, y - 1), (x - 1, y), (x + 1, y), (x, y + 1)]
        if diags:
            neighs += [(x - 1, y - 1), (x + 1, y - 1), (x - 1, y + 1), (x + 1, y + 1)]
        return [(x, y) for x, y in neighs if 0 <= x < Grid.dim and 0 <= y < Grid.dim]
    
    def _active_owned(self, pos):
        return pos in [(9, 9), (8, 9), (10, 9), (10, 10), (7, 9), 
                       (9, 11), (11, 10), (10, 11), (11, 9), (11, 11), 
                       (8, 11), (7, 11), (6, 11), (5, 11)]
        

    def update_pivot_for(self):
        start = (11,11)
        buffer = [start]
        visited_from = {start: []}

        while buffer:
            new_buffer = []
            for p in buffer:
                for n in self.neighbors(*p):
                    if self._active_owned(n):
                        if not n in visited_from:
                            new_buffer.append(n)
                        if not n in visited_from:
                            visited_from[n] = [p]
                        else:
                            visited_from[n].append(p)
            buffer = new_buffer
            
        
            
        return visited_from
        
grid = Grid()
c = grid.update_pivot_for()

print("\n".join([f"{k}: {v}" for k, v in c.items()]))