Fool's problem of the day,

$(1)$ There are $ N $ equidistant light poles around a circular garden. If every three light poles which form either an acute angled triangle or an obtuse angled triangle are fixed with same shape of light, find the number of different shapes of bulbs can be used.

**NOTE**: Please don't post the solution here, instead use this thread for clarification of problem statement discussing strategy and checking the answer. The reason for this is once a solution is posted it act as a spoiler for others. At-least wait for a day before posting a solution. And If you are

Question

Fool's problem of the day,

$(1)$ There are $ N $ equidistant light poles around a circular garden. If every three light poles which form either an acute angled triangle or an obtuse angled triangle are fixed with same shape of light, find the number of different shapes of bulbs can be used.

**NOTE**: Please don't post the solution here, instead use this thread for clarification of problem statement discussing strategy and checking the answer. The reason for this is once a solution is posted it act as a spoiler for others. At-least wait for a day before posting a solution. And If you are