import collections


def render(grid, brush=None):
    if brush is None:
        brush = {v: v for v in grid.values()}
    if isinstance(brush, str):
        brush = {i: c for i, c in enumerate(brush)}
    xmin, *_, xmax = sorted(int(p.real) for p in grid)
    ymin, *_, ymax = sorted(int(p.imag) for p in grid)
    brush[None] = ' '
    rendered = ''
    for y in range(ymin, ymax + 1):
        for x in range(xmin, xmax + 1):
            rendered += brush[grid.get(complex(x, y))]
        rendered += '\n'
    return rendered


def read_image(text):
    grid = collections.defaultdict(str)
    for y, line in enumerate(text.splitlines()):
        for x, cell in enumerate(line):
            grid[complex(x, y)] = cell
    return grid


def shortest_path(start, end, move):
    seen = {}
    edge = {start: None}
    while edge:
        seen.update(edge)
        edge = {
            adj: pos
            for pos in edge
            for adj in move(pos)
            if adj not in seen
        }
        if end in seen:
            break
    else:
        raise RuntimeError('Path not found', seen)
    path = []
    while end:
        path.append(end)
        end = seen[end]
    return path[::-1]