class Grid():
    def __init__(self, x, y, initial):
        self.x = x
        self.y = y
        self.initial = initial
        self.data = [initial] * x * y

    def get(self, x, y):
        return self.data[self.x * y + x]

    def set(self, x, y, v):
        self.data[self.x * y + x] = v

    def in_bounds(self, x, y):
        return x < self.x and x >= 0 and y < self.y and y >= 0

    def __getitem__(self, coord):
        (x, y) = coord
        return self.get(x, y)

    def __setitem__(self, coord, value):
        (x, y) = coord
        self.set(x, y, value)

    def neighbors(self, x, y):
        r = []
        for direction in [(-1, -1), (0, -1), (1, -1), (1, 0), (1, 1), (0, 1), (-1, 1), (-1, 0)]:
            xc, yc = direction
            tx, ty = x + xc, y + yc
            if self.in_bounds(tx, ty):
                r.append((tx, ty))
        return r

def bresenhams(x1, y1, x2, y2):
    r = []
    dx = abs(x2 - x1)
    dy = abs(y2 - y1)
    x, y = x1, y1
    sx = -1 if x1 > x2 else 1
    sy = -1 if y1 > y2 else 1
    if dx > dy:
        err = dx / 2.0
        while x != x2:
            r.append((x, y))
            err -= dy
            if err < 0:
                y += sy
                err += dx
            x += sx
    else:
        err = dy / 2.0
        while y != y2:
            r.append((x, y))
            err -= dx
            if err < 0:
                x += sx
                err += dy
            y += sy
    r.append((x, y))
    return r