For a given polygon g, print "1" if g is a convex polygon, "0" otherwise. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.

g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n-1) are sides of the polygon. The line segment connecting pn and p1 is also a side of the polygon.

Constraints

* 3 ≤ n ≤ 100
* -10000 ≤ xi, yi ≤ 10000
* No point of the polygon will occur more than once.
* Two sides of the polygon can intersect only at a common endpoint.

Input

g is given by coordinates of the points p1,..., pn in the following format:


n
x1 y1
x2 y2
:
xn yn


The first integer n is the number of points. The coordinate of a point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them.

Output

Print "1" or "0" in a line.

Examples

Input

4
0 0
3 1
2 3
0 3


Output

1


Input

5
0 0
2 0
1 1
2 2
0 2


Output

0
#include <iostream>
#include <cmath>
#include <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

#define EPS 1e-10
#define equal(a,b) (fabs(a-b) < EPS)
#define PI acos(-1)

struct Point{
  double x,y;

  Point(){}
  Point(double x,double y) : x(x),y(y) {}

  Point operator + (const Point &p)const{
    return Point(x + p.x , y + p.y);
  }

  Point operator - (const Point &p)const{
    return Point(x - p.x , y - p.y);
  }

  Point operator * (const double &k)const{
    return Point(x * k , y * k);
  }

  Point operator / (const double &k)const{
    return Point(x / k , y / k);
  }

  double dot(const Point &p)const{
    return x*p.x + y*p.y;
  }

  double cross(const Point &p)const{
    return x*p.y - p.x*y;
  }

  double dist(const Point &p)const{
    return sqrt(pow(x-p.x,2) + pow(y-p.y,2));
  }

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

  double Abs(){
    return sqrt(norm());
  }
};

#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
typedef Point Vector;

int ccw(Point p0,Point p1,Point p2){
  Vector a = p1 - p0;
  Vector b = p2 - p0;
  if(a.cross(b) > EPS){ return COUNTER_CLOCKWISE; }
  if(a.cross(b) < -EPS){ return CLOCKWISE; }
  if(a.dot(b) < -EPS){ return ONLINE_BACK; }
  if(a.norm() < b.norm()){ return ONLINE_FRONT; }
  return ON_SEGMENT;
}

typedef vector<Point> Polygon;

#define prev(G,i) (G[(i-1+G.size())%G.size()])
#define curr(G,i) (G[(i)%G.size()])
#define next(G,i) (G[(i+1)%G.size()])

bool isConvex(const Polygon &p){
  for(int i = 0 ; i < (int)p.size() ; i++){
    if(ccw(prev(p,i),curr(p,i),next(p,i)) == CLOCKWISE){
      return false;
    }
  }
  return true;
}

int main(){
  int N;
  cin >> N;
  Polygon p(N);
  for(int i = 0 ; i < N ; i++){
    cin >> p[i].x >> p[i].y;
  }
  cout << isConvex(p) << endl;
  return 0;
}