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
/*
判断是否是凸包
*/
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstdio>
#include <cstring>
using namespace std;
int num;
double x,yy1,yy2,yy3,yy4;
const double eps = 1e-8;
const double inf = 1e20;
const double pi = acos(-1.0);
const int maxp = 110;
int sgn(double x){
    if(fabs(x)<eps){
        return 0;
    }
    if(x<0){
        return -1;
    }else{
        return 1;
    }
}
struct Point{
    double x,y;
    Point(){}
    void input(){
        scanf("%lf%lf",&x,&y);
    }
    Point(double _x,double _y){
        x = _x;y = _y;
    }
    bool operator < (Point b)const{
        return sgn(x-b.x)==0?sgn(y-b.y)<0:x<b.x;
    }
    Point operator - (const Point &b)const{
        return Point(x-b.x,y-b.y);
    }
    double operator *(const Point &b)const{
        return x*b.x+y*b.y;
    }
    double operator ^(const Point &b)const{
        return x*b.y-y*b.x;
    }
    double distance(Point p){
        return hypot(x-p.x,y-p.y);
    }
};
struct Line{
    Point s,e;
    Line(){}
    Line(Point _s,Point _e){
        s  = _s;
        e = _e;
    }
};
struct polygon{
    int n;
    Point p[maxp];
    Line l[maxp];
    void input(int _n){
        n = _n;
        for(int i = 0;i < n;++i ){
            p[i].input();
        }
    }
    bool isconvex(){
        bool s[3];
        memset(s,false,sizeof(s));
        for(int i = 0;i < n;++i ){
            int j = (i+1)%n;
            int k = (j+1)%n;
            s[sgn((p[j]-p[i])^(p[k]-p[i]))+1] = true;
            if(s[0]&&s[2]){
                return false;
            }
        }
        return true;
    }
};
int main(){
    int N;
    scanf("%d",&N);
    polygon pp;
    pp.input(N);
    if(pp.isconvex()){
        printf("1\n");
    }else{
        printf("0\n");
    }

    return 0;
}
