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<cstdio>
#include<vector>
#include<queue>
#include<map>
#include<string>
#include <math.h>
#include<algorithm>
#include<functional>
#define ll long long
#define inf  999999999
#define pa pair<int,int>
#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b))<EPS)

using namespace std;

class Point{
	public:
	double x,y;
	Point(double x=0,double y=0):x(x),y(y) {}
	Point operator + (Point p) {return Point(x+p.x,y+p.y);}
	Point operator - (Point p) {return Point(x-p.x,y-p.y);}
	Point operator * (double a) {return Point(x*a,y*a);}
	Point operator / (double a) {return Point(x/a,y/a);}
	double absv() {return sqrt(norm());}
	double norm() {return x*x+y*y;}
	bool operator < (const Point &p) const{
		return x != p.x ? x<p.x: y<p.y;
	}
	bool operator == (const Point &p) const{
		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
	}
};
typedef Point Vector;

struct Segment{
Point p1,p2;
};


double dot(Vector a,Vector b){
	return a.x*b.x+a.y*b.y;
}
double cross(Vector a,Vector b){
	return a.x*b.y-a.y*b.x;
}

//----------------kokomade temple------------
int zz(double a){
if(a>EPS) return 1;
else if(a<-EPS) return -1;
else return 0;
}


int main(){
int n,k=0;
double x,y;
cin>>n;
Point a[110];
Vector v[110];
for(int i=0;i<n;i++){
cin>>x>>y;
a[i].x=x;
a[i].y=y;
}
a[n]=a[0];
for(int i=0;i<n;i++){
v[i]=a[i]-a[i+1];
}
v[n]=v[0];
int ans=0;
for(int i=0;i<n;i++){
ans=ans+zz(cross(v[i],v[i+1]));
if(zz(cross(v[i],v[i+1]))==0) k++;
}
if(ans==n-k || ans==-n+k) cout<<"1"<<endl;
else cout<<"0"<<endl;


}