Maximum Number of Bridges

In a futuristic aerial city, there are many small islands (districts). Bridges can be built between two islands, but there is a rule: if there is a bridge between $A$ and $B$, and a bridge between $B$ and $C$, then a bridge between $A$ and $C$ is not allowed. In other words, for any three islands, it is forbidden to have bridges built between every pair (i.e. a triangle is not allowed). Under this constraint, your task is to build as many bridges as possible between the islands without considering any spatial issues.

Note: This problem is equivalent to finding the maximum number of edges in a triangle-free graph with $n$ vertices. By Mantel's theorem, the maximum number of edges is ( \lfloor \frac{n^2}{4} \rfloor ).

inputFormat

The input consists of a single integer $n$ ($1 \le n \le 10^9$) representing the number of islands.

outputFormat

Output a single integer denoting the maximum number of bridges that can be constructed under the given constraints.

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