Consider that you have a set of N Christmas lights, which can turn red or green. The lights are numbered from 1 to N. Initially at time step 1 they are all red. The mechanism is set such that at time t, all lights whose id is divisible by t will change color (i.e. red to green, or green to red). For example, given 6 lights, numbered 1,2,3,4,5,6 at time step 1 R R R R R R at time step 2 R G R G R G at time step 3 R G G G R R

How many lights will be red at the end of N time steps ? Give a pseudocode of your algorithm and its complexity. If the algorithm complexity is O(n2) then you get 5 points If the algorithm complexity is O(n) then you get 10 points If the algorithm complexity is less than O(n) then you get 15 points