Problem: 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:

<image>

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.

Solution (in JAVA):

Solution:


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;


public class BicycleRace {
    static final double EPS =1e-9;
	public static void main(String[] args) throws IOException {
	Scanner sc = new Scanner(System.in);
	
	int n =sc.nextInt();
	int c=0;
	
	Point st = new Point(sc.nextInt(), sc.nextInt());
	Point mid = new Point(sc.nextInt(), sc.nextInt());
	Point last = new Point(sc.nextInt(), sc.nextInt());
	
	if(ccw(st,mid,last))
		c++;
	
	for(int i=0;i<n-3;i++) {
		st = mid;
		mid =last;
		last =new Point(sc.nextInt(), sc.nextInt());
		
		if(ccw(st,mid,last))
			c++;
		
	}
	System.out.println(c);
	
   }
   static double distToLine(Point p, Point a,Point b) {
		  if(a.compareTo(b)==0)
			  return p.dist(a);
	      Vector ap = new Vector(a, p), ab = new Vector(a, b);
	      double u =ap.dot(ab)/ab.norm2();
	      Point c = a.translate(ab.scale(u));
	      return p.dist(c);
	  }
	  
	  public static class Vector {

			double x, y; 
	        
			Vector(Point a, Point b)
			{
				x = b.x - a.x;
				y = b.y - a.y;
			}
			
			Vector(double a, double b) { x = a; y = b; }

//			Vector(Point a, Point b) { this(b.x - a.x, b.y - a.y); }

			Vector scale(double s) { return new Vector(x * s, y * s); }              //s is a non-negative value

			double dot(Vector v) { return (x * v.x + y * v.y); }

			double cross(Vector v) { return x * v.y - y * v.x; }

			double norm2() { return x * x + y * y; }

			Vector reverse() { return new Vector(-x, -y); }

			
		}
	  
	  static double area ( Point[] x ) {
		   double tot=0;
		   
		   for(int i=0;i+1<x.length;i++) {
			   tot+=x[i].x*x[i+1].y-x[i+1].x*x[i].y;
		   }
		   return tot/2.0;
		   
	  }

	static Point [] convexHull (Point [] points) {
		 int n = points.length;
		 Arrays.sort(points);
		 
		 Point [] ans = new Point [n<<1];
		 int size=0; int start=0;
		 
		for(int i=0;i<n;i++) {
			 Point p = points[i];
			 while(size-start>=2&&!ccw(ans[size-2],ans[size-1],p))
				 size--;
			 ans[size++]=p;
		 }
		 start = --size;
		 for(int i=n-1;i>=0;i--) {
			 Point p = points[i];
			 while(size-start>=2&&!ccw(ans[size-2],ans[size-1],p))
				 size--;
			 ans[size++]=p;
		 }
		 
		 return Arrays.copyOf(ans,size);
		 
	}
	  
	static Point [] cutPolygon(Point [] pts , Point a, Point b) {
	  Point[] ans = new Point[pts.length<<1];
	  Line l = new Line(a, b);
	  Vector v = new Vector(a, b);
	  int size=0; 
	  
	  for(int i=0;i<pts.length;i++) {
		   double left1 = v.cross(new Vector(a, pts[i]));
		   double left2 =i ==pts.length-1?0:v.cross(new Vector(a, pts[i+1]));
		   
		   if(left1 + EPS>0) {
			   ans[size++]=pts[i];
		   }
		   
		   if(left1*left2+EPS<0)
			   ans[size++]=l.intersect(new Line(pts[i], pts[i+1]));
		  
	  }
	  if(size!=0&& ans[0]!=ans[size-1])
		   ans[size++]=ans[0];
	  
	  return Arrays.copyOf(ans, size);
	} 	

	static boolean ccw(Point a, Point b, Point c)
	{
		return new Vector(a, b).cross(new Vector(a, c)) > 0;
	}


	static class Point implements Comparable<Point>
	{
		double x, y;
		
		Point(double a, double b) { x = a; y = b; }
		
		public int compareTo(Point o) {
			if(o.x!=x)
				return (int)(x-o.x);
			return (int)(y-o.y);
		}
		public double dist(Point p) { return Math.sqrt((x - p.x)*(x - p.x) +(y - p.y)*(y - p.y)); }
		Point translate(Vector v) { return new Point(x + v.x , y + v.y); }
	}

	static class Line
	{
		double a, b, c;
		
		Line(Point p, Point q)
		{
			if(Math.abs(p.x - q.x) < EPS)
			{
				a = 1.0; b = 0.0; c = -p.x;
			}
			else
			{
				a = (q.y - p.y) / (p.x - q.x);
				b = 1.0;
				c = - a * p.x - p.y; 
			}
		}
		
		boolean parallel(Line l)
		{
			return Math.abs(l.a - a) < EPS && Math.abs(l.b - b) < EPS;
		}
		
		Point intersect(Line l)
		{
			if(parallel(l)) return null;
			
			double x = (b * l.c - c * l.b) /(a * l.b - b * l.a);
			double y;
			if(Math.abs(b) > EPS) y = - a * x - c;
			else 				  y = - l.a * x - l.c;
			return new Point(x, y);
		}
	}

	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}
		
		public long nextLong() throws IOException {return Long.parseLong(next());}

		public String nextLine() throws IOException {return br.readLine();}
		
		public double nextDouble() throws IOException
		{
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if(x.charAt(0) == '-')
			{
				neg = true;
				start++;
			}
			for(int i = start; i < x.length(); i++)
				if(x.charAt(i) == '.')
				{
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				}
				else
				{
					sb.append(x.charAt(i));
					if(dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg?-1:1);
		}
			
		public boolean ready() throws IOException {return br.ready();}


	}
}