Minimum And Maximum I

*This problem is worth 50 points.* Let $A$ denote a permutation of length $N$. Define $f(A) = \sum_{i = 1}^{N} \min(A_i, A_{i + 1})$, where $A_{N + 1} = A_1$. Find the **minimum** value of $f(A)$ over all permutations of length $N$. Note that a permutation of length $N$ consists of all integers from $1$ to $N$ exactly once. ### Input - The first line of input will contain a single integer $