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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <vector>
#include <cmath>
#include <queue>
#include <algorithm>
using namespace std;
#define EPS (1E-10)
const int maxn=100000+10;
int n;

struct Point
{
    int x,y;
    Point() {}
    Point(int _x,int _y):x(_x),y(_y) {}
    Point operator -(Point p)
    {
        return Point(x-p.x,y-p.y);
    }
    bool operator <(Point p)
    {
        return x==p.x?y<p.y:x<p.x;
    }
    int cross(Point p)
    {
        return x*p.y-y*p.x;
    }
    int dot(Point p)
    {
        return x*p.x+y*p.y;
    }
    int norm()
    {
        return x*x+y*y;
    }

};
vector<Point> ps;

int ccw(Point p,Point p1,Point p2)
{
    #define COUNT_CLOCKWISE 1
    #define CLOCKWISE -1
    #define ONLINE_FRONT 2
    #define ONLINE_BACK -2
    #define ON_SEGMENT 0
    Point a=p1-p;
    Point b=p2-p;
    if(a.cross(b)<-EPS) return CLOCKWISE;
    if(fabs(a.cross(b)<EPS)) return CLOCKWISE;
    if(a.cross(b)>EPS) return COUNT_CLOCKWISE;
    if(a.dot(b)<-EPS) return ONLINE_BACK;
    if(a.norm()<b.norm()) return ONLINE_FRONT;
    return ON_SEGMENT;

}

vector<Point> convex_hull(vector<Point> ps)
{
    vector<Point> u,l;
    if(ps.size()<3) return ps;
    sort(ps.begin(),ps.end());
    u.push_back(ps[0]);
    u.push_back(ps[1]);
    l.push_back(ps[ps.size()-1]);
    l.push_back(ps[ps.size()-2]);
    for(int i=2;i<ps.size();i++)
    {
        for(int n=u.size();n>=2&&ccw(u[n-2],u[n-1],ps[i])!=CLOCKWISE;n--)
        {
            u.pop_back();
        }
        u.push_back(ps[i]);
    }
    for(int i=ps.size()-3;i>=0;i--)
    {
        for(int n=l.size();n>=2&&ccw(l[n-2],l[n-1],ps[i])!=CLOCKWISE;n--)
        {
            l.pop_back();
        }
        l.push_back(ps[i]);
    }
    reverse(l.begin(),l.end());
    for(int i=u.size()-2;i>=1;i--) l.push_back(u[i]);
    return l;
}
bool is_convex(vector<Point> ps)
{
    int n=(int)ps.size();
    for(int i=0;i<n;i++)
    {
        if(ccw(ps[(i+1)%n],ps[(i)%n],ps[(i+2)%n])==COUNT_CLOCKWISE) return false;
    }
    return true;
}
int main()
{
//    freopen("in.txt","r",stdin);
    scanf("%d",&n);
    int x,y;
    for(int i=0;i<n;i++)
    {
        scanf("%d%d",&x,&y);
        ps.push_back(Point(x,y));
    }
   vector<Point> qs=convex_hull(ps);
    if(qs.size()==n) printf("1\n");
    else printf("0\n");


    return 0;

}