Inner Vertices

There is an infinite square grid. Some vertices of the grid are black and other vertices are white.

A vertex $V$ is called inner if it is both vertical-inner and horizontal-inner. A vertex $V$ is horizontal-inner if there are two black vertices in the same row such that $V$ is between them. Similarly, a vertex $V$ is vertical-inner if there are two black vertices in the same column such that $V$ is between them.

On each step, all white inner vertices become black, while black vertices keep their color. The process stops when all inner vertices are black.

Write a program that determines the number of black vertices on the grid after the process stops.

Output

Print the number of black vertices after the process stops. If the process never stops, output -1.