Pasha and Stick

Pasha有一个正整数长度的木棍n。他想要完成三次切割以获得四个部分。每个部分必须有一些正整数长度，这些长度的总和显然是n。 Pasha喜欢长方形但讨厌正方形，所以他想知道，有多少种方法可以将棍子分成四个部分，这样就可以用这些部分形成一个矩形，但不可能形成正方形。 你的任务是帮助Pasha并计算这些方式的数量。

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.

6

1

20

4

There is only one way to divide the stick in the first sample {1, 1, 2, 2}. Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work.