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 mkp make_pair
#define rep(i,n) for(int i=0;i<(n);++i)
typedef long long ll;

const ll MOD=1e9+7;
const double EPS=1e-9;
const double PI=acos(-1.0);
//const long double PI=acos(-1.0L);

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

    Point operator +(const Point &b) const {return Point(x+b.x,y+b.y);}
    Point operator -(const Point &b) const {return Point(x-b.x,y-b.y);}
    Point operator *(const double b) const {return Point(x*b,y*b);}
    Point operator /(const double b) const {return Point(x/b,y/b);}
};

struct Line{
    Point a,b;
    Line(){}
    Line(Point a,Point b):a(a),b(b){}
};

int sgn(double a) {return (a>EPS)-(a<-EPS);}
int sgn(double a,double b) {return sgn(a-b);}

double dot(const Point &a,const Point &b) {return (a.x*b.x+a.y*b.y);}
double cross(const Point &a,const Point &b) {return (a.x*b.y-a.y*b.x);}
double norm(const Point &p) {return dot(p,p);}
double abs(const Point &p) {return sqrt(norm(p));}

//1:Counter_Clockwise -1:Clockwise
//2:a-b-c -2:c-a-b 0:a-c-b
int ccw(const Point &p,const Point &q){
    int s=sgn(cross(p,q));
    if(s!=0) return s;
    if(dot(p,q)<0) return -2;
    if(norm(p)<norm(q)) return 2;
    return 0;
}
int ccw(const Point &a,const Point &b,const Point &c){return ccw(b-a,c-a);}

bool isConvex(vector<Point> &g){
    int n=g.size();
    for(int i=0;i<n;i++){
        if(ccw(g[i],g[(i+1)%n],g[(i+2)%n])==-1) return false;
    }
    return true;
}

int main(){
    int N;
    cin>>N;
    vector<Point> g(N);
    rep(i,N) cin>>g[i].x>>g[i].y;

    if(isConvex(g)) cout<<"1"<<endl;
    else cout<<"0"<<endl;

    return 0;
}

