On the circumference of a circle are two red points. One is allowed to perform the following operations:

1. Add a RED point to the circumference and change the color of its two neighboring points (red to blue, or blue to red).
2. Remove a RED point from the circumference and change the color of its two neighboring points, again from red to blue or blue to red.

If one starts with two red points, show that one cannot achieve a configuration with two blue points.