Verify a rectangle covering

# Verify a rectangle covering.

def main():
    domain, rects = input()
    domain = set(domain)

    for (x, y, w, h) in rects:
        if w <= 0 or h <= 0:
            return "Degenerate rectangle at %s."%((x,y),)
        for i in range(x, x+w):
            for j in range(y, y+h):
                if (i,j) in domain:
                    domain.remove((i,j))
                else:
                    return "Coordinate %s covered incorrectly."%((i,j),)
        for (x2, y2, w2, h2) in rects:
            if x == x2 and w == w2 and y + h == y2:
                return "Aligned rectangles at %s and %s."%((x,y),(x2,y2))
            if y == y2 and h == h2 and x + w == x2:
                return "Aligned rectangles at %s and %s."%((x,y),(x2,y2))
    if domain:
        return "Coordinate %s not covered."%(domain.pop(),)
    else:
        return "The covering is valid."

if __name__ == "__main__":
    print main()