A10088 | Pasha and Stick

Pasha has a wooden stick of some positive integer length $n$ . He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be $n$ .

Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.

Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer $x$ , such that the number of parts of length $x$ in the first way differ from the number of parts of length $x$ in the second way.

The first line of the input contains a positive integer $n$ ( $1<=n<=2·10^{9}$ ) — the length of Pasha's stick.

The output should contain a single integer — the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square.