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<cmath>
#include<vector>
#include<iomanip>
using namespace std;
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;
 
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
 
class Point{
	public:
		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 a){ return Point(a * x, a * y);}
		Point operator / (double a){ return Point(x / a, y / a);}
 
		double abs(){ return sqrt(norm());}
		double norm(){ return x * x + y * y;}
 
		bool operator < (const Point &p) const{
			return x != p.x ? x < p.x : y < p.y;
		}
 
		bool operator == (const Point &p) const{
			return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
		}
};
typedef Point Vector;
typedef vector<Point> Polygon;
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 p0, Point p1, Point p2){
	Vector a = p1 - p0;
	Vector b = p2 - p0;
	if(cross(a, b) > EPS) return COUNTER_CLOCKWISE;
	if(cross(a, b) < -EPS) return CLOCKWISE;
	if(dot(a, b) < -EPS) return ONLINE_BACK;
	if(a.norm() < b.norm()) return ONLINE_FRONT;
 
	return ON_SEGMENT;
}

int main(){
	int n;
	cin >> n;
	Polygon p(n);
	for(int i = 0; i < n; i++) cin >> p[i].x >> p[i].y;
	for(int i = 0; i < n; i++){
		int num = ccw(p[(i + 1) % n], p[i], p[(i + 2) % n]);
		if(num == COUNTER_CLOCKWISE){
			cout << 0 << endl;
			return 0;
		}
	}
	cout << 1 << endl;
	return 0;
}

