CF610A.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.

帕沙有一根长度为某个正整数 $ n $ 的木棍。他希望恰好进行三次切割，从而得到四段木棍。每一段的长度都必须是某个正整数，且这四段长度之和显然等于 $ n $。

帕沙喜欢矩形，但讨厌正方形，因此他想知道：有多少种方式可将木棍切成四段，使得能用这四段构成一个矩形，但无法构成正方形？

你的任务是帮助帕沙计算满足条件的方式数目。若存在某个整数 $ x $，使得第一种切法中长度为 $ x $ 的段数与第二种切法中长度为 $ x $ 的段数不同，则认为这两种切法是不同的。

The first line of the input contains a positive integer n (1 ≤ n ≤ 2·109) — the length of Pasha's stick.

输入的第一行包含一个正整数 $n$（$1 \leq n \leq 2\cdot10^9$）——即帕沙的木棍长度。

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.

输出应为一个整数——将帕沙的木棍分成四段正整数长度的方法数，使得这四段首尾相连可以构成一个矩形，但无法构成一个正方形。

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.

第一个样例中，将木棍划分的方式只有一种：{1, 1, 2, 2}。

第二个样例中有四种划分方式：{1, 1, 9, 9}、{2, 2, 8, 8}、{3, 3, 7, 7} 和 {4, 4, 6, 6}。注意，{5, 5, 5, 5} 不可行。