There is a regular convex polygon with n vertices. Each vertex is occupied by exactly $1$ monkey. The vertices are numbered from $0$ to n $- 1$ in clockwise order.

Every monkey chooses to move to an adjacent vertex simultaneously. Each monkey independently chooses to move either in a clockwise direction or in a counterclockwise direction.

A collision takes place if at least $2$ monkeys cross each other while moving along an edge or end up at the same vertex.

Return the number of movement configurations in which at least $1$ collision occurs. Since the answer can be very large, return it modulo $10^9 + 7$.

Note: Each monkey moves at the same speed and only moves once.

Constraints:

• $3 \leq$ n $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.