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 <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#include <vector>
#include <utility>
#define EPS 1e-10
using namespace std;
typedef long long ll;
struct Point{
	double x,y;
	Point(double x = 0.0,double y = 0.0): 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 lambda){
		return Point(x * lambda,y * lambda);
	}
	Point operator / (double lambda){
		return Point(x / lambda,y / lambda);
	}
	double norm(){
		return x * x + y * y;
	}
	double abs_(){
		return sqrt(norm());
	}
	bool operator == (const Point &p)const
	{
		return abs(x - p.x) < EPS && abs(y - p.y) < EPS;
	}
	bool operator < (const Point &p)const
	{
		if(abs(x - p.x) < EPS) return y - p.y < -EPS;
		else return x - p.x < EPS;
	}
};
typedef Point Vector;
struct Segment{
	Point p1,p2;
	Segment(Point p1 = Point(),Point p2 = Point()): p1(p1),p2(p2) {}
};
typedef Segment Line;
struct Circle{
	Point c;
	double r;
	Circle(Point c = Point(),double r = 0.0): c(c),r(r) {}
};
typedef vector<Point> Polygon;
double dot(Vector a,Vector b){
	return a.x * b.x + a.y * b.y;
}
double det(Vector a,Vector b){
	return a.x * b.y - b.x * a.y;
}
bool IsConvex(Polygon p){
	int n = p.size();
	for(int i=0;i<n;i++){
		Point p1 = p[(i - 1 + n) % n],p2 = p[(i + 1) % n];
		if(det(p2 - p[i],p1 - p[i]) < -EPS) return false;
	}
	return true;
}
Polygon p;
int n;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		Point p1;
		scanf("%lf%lf",&p1.x,&p1.y);
		p.push_back(p1);
	}
	printf("%d\n",(int)IsConvex(p));
	return 0;
}

