2016NEFU集训第n+3场 D - Bicycle Race

Description

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 (x_i, y_i) ( - 10 000 ≤ x_i, y_i ≤ 10 000). The first of these points is the starting position. The i-th straight section of the track begins at the point (x_i, y_i) and ends at the point (x_i + 1, y_i + 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.

Sample Input

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

//想明白后就回发现这是一道水题，只怪自己英语不好，读题太费劲
//题意：一个数n，然后给出n+1个点，围成一个水池，每次都是只能往东南西北走，并且刚开始的方向一定是往北面走。其中有一些点若是不拐弯就一定会
//掉入水池，问有几个这样的点。选择比赛赛道的最南端为起始位置（如果有多个这样的点，选择最西的）
//有了以上的限定条件，可以知道左拐的点若一直走就会调入水中，所以看有几个左拐点就可以

#include <iostream>

using namespace std;

struct node
{
    int x,y;
}data[];

int main()
{
    int n,ans;
    while(cin>>n)
    {
        ans=;
        for(int i=;i<=n;i++)
        cin>>data[i].x>>data[i].y;
        for(int i=;i<=n;i++)
        {
            int fx,fy,xx,yy;
            fx=data[i-].x-data[i-].x;
            fy=data[i-].y-data[i-].y;
            xx=data[i].x-data[i-].x;
            yy=data[i].y-data[i-].y;
            if(fx==&&fy>&&xx<&&yy==)
            ans++;
            else if(fx<&&fy==&&xx==&&yy<)
            ans++;
            else if(fx>&&fy==&&xx==&&yy>)
            ans++;
            else if(fx==&&fy<&&yy==&&xx>)
            ans++;
        }
        cout<<ans<<endl;
    }
    return ;
}