Code the "russian missile" example using dynamic programming techniques.

The input to your program should be a simple numeric list, giving the altitudes
of all the missiles as they appear from left to right. The output should be the
maximum number of missiles the catcher can intercept.

The input for the example we did in class would be:
97 379 350 268 250 318 130 229 170 362 301 192 41 215 60 147

Include a short description of how your solution works.