JEE Advanced 2023 Physics question on Ray Optics

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 _______.