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<cmath>
#include<algorithm>
#include<iostream>
#include<vector>
#include<climits>
#include<cfloat>
#include<cstdio>
#define curr(P,i) P[(i)%P.size()]
#define next(P,i) P[(i+1)%P.size()]
#define prev(P,i) P[(i+P.size()-1)%P.size()]


using namespace std;

typedef double Real;

Real EPS = 1e-8;
const Real PI = acos(-1);

int sgn(Real a, Real b=0){return a<b-EPS?-1:a>b+EPS?1:0;}
Real sqr(Real a){return sqrt(max(a,(Real)0));}

struct Point{  
  Real add(Real a, Real b){
    if(abs(a+b) < EPS*(abs(a)+abs(b)))return 0;
    return a+b;
  }

  Real x, y;
  Point(){}
  Point(Real x,Real y) : x(x) , y(y){}

  Point operator + (Point p){return Point(add(x,p.x), add(y,p.y));}
  Point operator - (Point p){return Point(add(x,-p.x), add(y,-p.y));}
  Point operator * (Real d){return Point(x*d,y*d);}
  Point operator / (Real d){return Point(x/d,y/d);}
  bool operator == (Point p){return !sgn(dist(p));}
  bool operator < (Point p){return (p.x!=x)?p.x<x:p.y<y;}
  Real norm(){return sqr(x*x+y*y);}
  Real dist(Point a){return (*this-a).norm();}
  Real dot(Point a){return x*a.x+y*a.y;}
  Real cross(Point a){return x*a.y-y*a.x;}
  //点pを中心に角度r(radius)だけ半時計回りに回転する
  Point rotate(Real r,Point p = Point(0,0)){
    Real ta=cos(r)*(x-p.x)-sin(r)*(y-p.y)+p.x;
    Real tb=sin(r)*(x-p.x)+cos(r)*(y-p.y)+p.y;
    return Point(ta,tb);
  }
  Real arg(){
    if(sgn(x)>0)return atan(y/x);
    if(sgn(x)<0)return atan(y/x)+PI;
    if(sgn(y)>0)return PI/2;
    if(sgn(y)<0)return 3*PI/2;
    return 0;
  }
};

//a -> b -> c
int ccw(Point a, Point b, Point c) {
  b = b-a; c = c-a;

  if (b.cross(c) > 0)   return +1;       // counter clockwise
  if (b.cross(c) < 0)   return -1;       // clockwise
  if (b.dot(c) < 0)     return +2;       // c--a--b on line
  if (b.norm() < c.norm()) return -2;    // a--b--c on line
  return 0;                              // a--c--b on line
}

struct Polygon{
  vector<Point>v;
  
  Polygon(){}
  Polygon(int n){v.resize(n);}
  
  bool isConvex() {
    for (int i=0; i<v.size();i++){
      if (ccw(prev(v,i),curr(v,i),next(v,i))==-1)return false;
    }
    return true;
  }
};

int main(void){

  int n;
  cin >> n;
  Polygon p(n);

  for(int i=0;i<n;i++)
    cin >> p.v[i].x >> p.v[i].y;

  cout << p.isConvex() << endl;

  return 0;
}