An optical arrangement consists of two concave mirrors M$$_1$$ and M$$_2$$, and a convex lens L with a common principal axis, as shown in the figure. The focal length of L is 10 cm. The radii of curvature of M$$_1$$ and M$$_2$$ are 20 cm and 24 cm, respectively. The distance between L and M$$_2$$ is 20 cm. A point object S is placed at the mid-point between L and M$$_2$$ on the axis. When the distance between L and M$$_1$$ is $$n/7$$ cm, one of the images coincides with S. The value of $$n$$ is ______.