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;
const double eps=1e-10;
int sign(double x)
{
    if(fabs(x)<=eps)return 0;
    if(x>0)return 1;
    return -1;
}
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 k){return Point(x*k,y*k);}
    Point operator / (double k){return Point(x/k,y/k);}
    double norm(){return x*x+y*y;}
    double abs(){return sqrt(norm());}
};
typedef Point Vector;
typedef vector<Point> polygon;
int n;
Point p;
polygon g;
double dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}
double cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
int ccw(Point a,Point b,Point c)
{
    if(sign(cross(b-a,c-a))==-1)return 1;
    return -1;
}
int main()
{
    scanf("%d",&n);
    while(n--){
        scanf("%lf%lf",&p.x,&p.y);
        g.push_back(p);
    }
    g.push_back(g[0]);
    for(int i=0;i<g.size()-2;i++){
        if(ccw(g[i],g[i+1],g[i+2])==1){
            printf("0\n");
            return 0;
        }
    }
    printf("1\n");
    return 0;
}

