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>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<n;++i)

using namespace std;

const int MAX_N = 100005;

double add(double a,double b)
{
    if(abs(a+b) < EPS * (abs(a) + abs(b))){
        return 0;
    }
    return a + b;
}

struct P
{
    double x,y;
    P() {}
    P(double x,double y) : x(x),y(y) {}
    P operator + (P p){
        return P(add(x,p.x),add(y,p.y));
    }
    P operator - (P p){
        return P(add(x,-p.x),add(y,-p.y));
    }
    P operator * (double d){
        return P(x*d,y*d);
    }
    double dot(P p){
        return add(x*p.x,y*p.y);
    }
    double det(P p){
        return add(x*p.y,-y*p.x);
    }
};

int n;
P ps[MAX_N];

bool cmp_x(const P& p,const P& q)
{
    if(p.x != q.x){
        return p.x < q.x;
    }
    return p.y < q.y;
}

vector<P> convex_hull(P* ps,int n)
{
    sort(ps,ps+n,cmp_x);
    int k = 0;
    vector<P> qs(n*2);
    rep(i,n){
        while(k > 1 && (qs[k-1] - qs[k-2]).det(ps[i] - qs[k-1]) < 0){   //????????????=?????\????????¨?????????????????????
            k--;
        }
        qs[k++] = ps[i];
    }
    for(int i = n-2,t=k;i >= 0;i--){
        while(k > t && (qs[k-1] - qs[k-2]).det(ps[i] - qs[k-1]) < 0){
            k--;
        }
        qs[k++] = ps[i];
    }
    qs.resize(k-1);
    return qs;
}

double dist(P p,P q)
{
    return (p-q).dot(p-q);
}

int main()
{
    scanf("%d",&n);
    rep(i,n){
        int a,b;
        scanf("%d%d",&a,&b);
        ps[i] = P(a,b);
    }
	vector<P> qs = convex_hull(ps,n);
    if(n <= qs.size()){   //???????????°??????????????´????????????
        cout << "1\n";
    }else{
        cout << "0\n";
    }
	return 0;
}