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 rep(i, a, b) for(int i = (a); i <= (b); ++i)
#define per(i, a, b) for(int i = (a); i >= (b); --i)
#define debug(x) cerr << #x << ' ' << x << endl;
using namespace std;

typedef long long ll;
const int mod = 1e9+7;
const int MAXN = 2e5 + 7;
const double EPS=1e-8;
inline int sign(double a){return a<-EPS?-1:a>EPS;}
inline int cmp(double a,double b){return sign(a-b);}
//点
struct P{
    double x,y;
    P(){}
    P(double _x,double _y):x(_x),y(_y){}
    P operator + (P p){return P(x+p.x,y+p.y);}
    P operator - (P p){return P(x-p.x,y-p.y);}
    P operator * (double k){return P(x*k,y*k);}
    P operator / (double k){return P(x/k,y/k);}
    double dot(P p){return x*p.x+y*p.y;}
    double det(P p){return x*p.y-y*p.x;}
    double distTo(P p){return (*this-p).abs();}
    double alpha(){return atan2(y,x);}
    void read(){scanf("%lf%lf", &x, &y);}
    void write(){printf("%.10lf %.10lf\n", x, y);}
    double abs(){return sqrt(abs2());}
    double abs2(){return x*x+y*y;}
    P rot90(){return P(-y,x);}
    P unit(){return *this/abs();}
    int quad(){return sign(y)==1||(sign(y)==0&&sign(x)>=0);}
    P rot(double an){return P(x*cos(an)-y*sin(an),x*sin(an)+y*cos(an));}
    bool operator < (P p)const{int c=cmp(x,p.x);if(c)return c==-1;return cmp(y,p.y)==-1;}
    bool operator == (P o)const{return cmp(x,o.x)==0&&cmp(y,o.y)==0;}
}s[105];

int main(int argc, char const *argv[])
{
    int n;
    scanf("%d", &n);
    rep(i, 0, n-1) s[i].read();
    bool flag = 1;
    rep(i, 0, n-1) if((s[(i+2)%n]-s[(i+1)%n]).det((s[i]-s[(i+1)%n])) < -EPS) flag = 0;
    printf("%d\n", flag);
    return 0;
}

