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 eps = (1e-10);
//点
struct Point{
    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(a*x,a*y);}
    Point operator / (double a){return Point(x/a,y/a);}
    double norm(){return x*x+y*y;}//模的平方
    double ABS() {return sqrt(norm());}//模
};
//线段
struct Segment{
    Point p1,p2;
};
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;
}
vector<Point> polygon;
bool check(vector<Point> polygon){
    int n=(int)polygon.size();
    polygon.push_back(polygon[0]);
    polygon.push_back(polygon[2]);
    for(int i=0;i<n;i++){
        Point a=polygon[i+1]-polygon[i];
        Point b=polygon[i+2]-polygon[i+1];
        if(cross(a,b)<0) return 0;
    }
    return 1;
}
int main(){
    int n;
    scanf("%d",&n);
    double x,y;
    for(int i=1;i<=n;i++){
        scanf("%lf %lf",&x,&y);
        polygon.push_back({x,y});
    }
    if(check(polygon)) puts("1");
    else puts("0");
    return 0;
}
