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;

typedef complex<double>Point;

struct Segment{
    Point p1,p2;
    Segment(const Point &p1=Point(),const Point &p2=Point()):p1(p1),p2(p2){}
};

struct Circle{
    Point p;
    double r;
    Circle(const Point &p=Point(),double r=0.0):p(p),r(r){}
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point>Polygon;

const double PI=acos(-1);
const double EPS=1e-8;
const double INF=1e16;
const int COUNTER_CLOCKWISE=1;
const int CLOCKWISE=-1;
const int ONLINE_BACK=2;
const int ONLINE_FRONT=-2;
const int ON_SEGMENT=0;

inline double square(double a){return a*a;}
inline double norm(const Point &a){return square(a.real())+square(a.imag());}
inline double dot(const Point &a,const Point &b){return (conj(a)*b).real();}
inline double cross(const Point &a,const Point &b){return (conj(a)*b).imag();}
inline double toDeg(double t){return t/PI*180.0;}
inline double toRad(double t){return t/180.0*t;}
#define equals(a,b) (fabs((a)-(b))<EPS)
#define curr(P,i) P[(i)%P.size()]
#define next(P,i) P[(i+1)%P.size()]
#define prev(P,i) P[(i-1+P.size())%P.size()]


void getPoint(Point &p){
    double x,y;
    scanf("%lf%lf",&x,&y);
    p=Point(x,y);
}

void getSegment(Segment &s){
    getPoint(s.p1);
    getPoint(s.p2);
}

bool isOrthogonal(Vector a,Vector b){
    return equals(dot(a,b),0.0);
}

bool isOrthogonal(Point a1,Point a2,Point b1,Point b2){
    return isOrthogonal(a1-a2,b1-b2);
}

bool isOrthogonal(Segment s1,Segment s2){
    return isOrthogonal(s1.p1-s1.p2,s2.p1-s2.p2);
}

bool isParallel(Vector a,Vector b){
    return equals(cross(a,b),0.0);
}

bool isParallel(Point a1,Point a2,Point b1,Point b2){
    return isParallel(a1-a2,b1-b2);
}

bool isParallel(Segment s1,Segment s2){
    return isParallel(s1.p1-s1.p2,s2.p1-s2.p2);
}

Point project(Segment s,Point p){
    Vector base=s.p2-s.p1;
    double r=dot(p-s.p1,base)/norm(base);
    return s.p1+base*r;
}

Point reflection(Segment s,Point p){
    return p+(project(s,p)-p)*2.0;
}

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

bool isIntersectSS(Point p1,Point p2,Point p3,Point p4){
    return ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0&&
            ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0;
}

bool isIntersectSS(Segment s1,Segment s2){
    return isIntersectSS(s1.p1,s1.p2,s2.p1,s2.p2);
}

Point getCrossPointSS(Segment s1,Segment s2){
    Vector base=s2.p2-s2.p1;
    double d1=abs(cross(base,s1.p1-s2.p1));
    double d2=abs(cross(base,s1.p2-s2.p1));

    double t=d1/(d1+d2);
    return s1.p1+(s1.p2-s1.p1)*t;
}

double getDistancePP(Point a,Point b){
    return abs(a-b);
}

double getDistanceLP(Line l,Point p){
    return fabs(cross(l.p2-l.p1,p-l.p1)/abs(l.p2-l.p1));
}

double getDistanceLL(Line l,Line m){
    if(isParallel(l,m))return getDistanceLP(l,m.p1);
    return 0.0;
}

double getDistanceSP(Segment s,Point p){
    if(dot(s.p2-s.p1,p-s.p1)<0.0)return abs(p-s.p1);
    if(dot(s.p1-s.p2,p-s.p2)<0.0)return abs(p-s.p2);
    return getDistanceLP(s,p);
}

double getDistanceSS(Segment s1,Segment s2){
    if(isIntersectSS(s1,s2))return 0;
    return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
               min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}

double area(Polygon g){
    double res=0.0;
    for(int i=0;i<g.size();i++){
        res+=cross(curr(g,i),next(g,i));
    }
    return res/2.0;
}

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

int main(){
    int n;
    scanf("%d",&n);

    Polygon g;

    for(int i=0;i<n;i++){
        Point a;
        getPoint(a);
        g.push_back(a);
    }

    printf("%d\n",isConvex(g));
    return 0;
}