Maximum Humans on a Grid

You are given an integer m representing the size of a square grid with dimensions m \(\times\) m. Your task is to determine the maximum number of humans that can be placed on the grid such that no two humans can see each other vertically, horizontally, or diagonally.

Two humans are said to "see" each other if they share the same row, the same column, or lie on the same diagonal. It turns out that the optimal number of humans that can be safely placed on the grid is given by the following formula:

\( \left\lfloor \frac{m^2+1}{2} \right\rfloor \)

Use this formula to compute the desired maximum count.

inputFormat

The input is provided via stdin and consists of a single integer m (with a constraint of 1 ≤ m ≤ 10⁹), which represents the side length of the square grid.

outputFormat

Output a single integer to stdout: the maximum number of humans that can be placed on the grid following the given constraints.

## sample

1

1

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