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 <bits/stdc++.h>
using namespace std;

#define dump(n) cout<<"# "<<#n<<'='<<(n)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define all(c) begin(c),end(c)
#define mp make_pair
#define mt make_tuple

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;

const int INF=1e9;
const int MOD=1e9+7;
const double EPS=1e-9;

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}
template<typename T>
ostream& operator<<(ostream& os,const vector<T>& a){
	os<<'[';
	rep(i,a.size()) os<<(i?" ":"")<<a[i];
	return os<<']';
}

int Signum(double x){
	return x<-EPS?-1:x>EPS?1:0;
}

struct Point{
	double x,y;
	Point(){}
	Point(double x,double y):x(x),y(y){}
	Point& operator+=(Point p){
		x+=p.x,y+=p.y;
		return *this;
	}
	Point& operator-=(Point p){
		x-=p.x,y-=p.y;
		return *this;
	}
	Point& operator*=(double c){
		x*=c,y*=c;
		return *this;
	}
	Point& operator/=(double c){
		x/=c,y/=c;
		return *this;
	}
};
Point operator+(Point a,Point b){
	return a+=b;
}
Point operator-(Point a,Point b){
	return a-=b;
}
Point operator*(Point a,double c){
	return a*=c;
}
Point operator*(double c,Point a){
	return a*=c;
}
Point operator/(Point a,double c){
	return a/=c;
}
bool operator==(Point a,Point b){
	return abs(a.x-b.x)<EPS && abs(a.y-b.y)<EPS;
}
bool operator!=(Point a,Point b){
	return !(a==b);
}

double Abs(Point p){
	return sqrt(p.x*p.x+p.y*p.y);
}
double Abs2(Point p){
	return p.x*p.x+p.y*p.y;
}
double Arg(Point p){
	return atan2(p.y,p.x);
}
double Dot(Point a,Point b){
	return a.x*b.x+a.y*b.y;
}
double Cross(Point a,Point b){
	return a.x*b.y-a.y*b.x;
}
Point Rot(Point p,double t){
	return Point(cos(t)*p.x-sin(t)*p.y,sin(t)*p.x+cos(t)*p.y);
}

int CCW(Point a,Point b,Point c){
	b-=a,c-=a;
	if(int sign=Signum(Cross(b,c)))
		return sign; // 1:ccw,-1:cw
	if(Dot(b,c)<-EPS)
		return -2;   // c-a-b
	if(Abs2(b)<Abs2(c)-EPS)
		return 2;    // a-b-c
	return 0;        // a-c-b (inclusive)
}

bool IsConvex(const vector<Point>& ps)
{
	int n=ps.size(),res=true;
	rep(i,n) res&=CCW(ps[i],ps[(i+1)%n],ps[(i+2)%n])!=-1;
	return res;
}

int main()
{
	for(int n;cin>>n && n;){
		vector<Point> ps(n);
		for(auto& p:ps) cin>>p.x>>p.y;
		cout<<IsConvex(ps)<<endl;
	}
}