Bicycle Race

Bicycle Race

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Maria participates in a bicycle race.

The speedway takes place on the shores of Lake Lucerne, just repeating its contour. As you know, the lake shore consists only of straight sections, directed to the north, south, east or west.

Let's introduce a system of coordinates, directing the Ox axis from west to east, and the Oy axis from south to north. As a starting position of the race the southernmost point of the track is selected (and if there are several such points, the most western among them). The participants start the race, moving to the north. At all straight sections of the track, the participants travel in one of the four directions (north, south, east or west) and change the direction of movement only in bends between the straight sections. The participants, of course, never turn back, that is, they do not change the direction of movement from north to south or from east to west (or vice versa).

Maria is still young, so she does not feel confident at some turns. Namely, Maria feels insecure if at a failed or untimely turn, she gets into the water. In other words, Maria considers the turn dangerous if she immediately gets into the water if it is ignored.

Help Maria get ready for the competition — determine the number of dangerous turns on the track.

Input

The first line of the input contains an integer n (4 ≤ n ≤ 1000) — the number of straight sections of the track.

The following (n + 1)-th line contains pairs of integers (xi, yi) ( - 10 000 ≤ xi, yi ≤ 10 000). The first of these points is the starting position. The i-th straight section of the track begins at the point (xi, yi) and ends at the point(xi + 1, yi + 1).

It is guaranteed that:

• the first straight section is directed to the north;
• the southernmost (and if there are several, then the most western of among them) point of the track is the first point;
• the last point coincides with the first one (i.e., the start position);
• any pair of straight sections of the track has no shared points (except for the neighboring ones, they share exactly one point);
• no pair of points (except for the first and last one) is the same;
• no two adjacent straight sections are directed in the same direction or in opposite directions.

Output

Print a single integer — the number of dangerous turns on the track.

Examples

input

6
0 0
0 1
1 1
1 2
2 2
2 0
0 0

output

1

input

16
1 1
1 5
3 5
3 7
2 7
2 9
6 9
6 7
5 7
5 3
4 3
4 4
3 4
3 2
5 2
5 1
1 1

output

6

Note

The first sample corresponds to the picture:

The picture shows that you can get in the water under unfortunate circumstances only at turn at the point (1, 1). Thus, the answer is 1.

题意：给出n个点的坐标，围成一个游泳池。绕着游泳池走的话，求危险的转弯点。（若该处不转弯会落到水里面的转弯点就成为危险转弯点）

思路：

我完全没有思路= =

看了别人的代码后发现代码异常简单只有一行。

（n-4）/2

这道题目根本和具体的点的坐标没有任何关系。

想了一下以后，我是这样理解这个公式：4代表4个顶点，矩形最边上的4个点，这四个点一定不会是危险点，而且由于给出数据的方式所限制（边必须是东南西北四个方向），所以至少有4个点。所以矩形是最基本的图形。下面考虑在矩形的基础上变化，

如图，左边基础上增加一个块，那么会增加2个点，4个转弯，其中只有1个A点是危险转弯。删除块也是一样，边上的两个点不会有影响，只有中间的两个点会有影响，依据行驶的方式AB中必有一个会掉到水里面为危险转弯点。