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 <complex>
#include <vector>
using namespace std;

double cross(complex< double > a, complex< double > b){
	return a.real() * b.imag() - a.imag() * b.real();
}

int main() {
	int n,x,y,convex;
	vector< complex< double > > vertex;
	
	cin >> n;
	vertex.resize(n);
	for(int i=0;i<n;++i){
		cin >> x >> y;
		vertex[i] = complex< double >(x, y);
	}
	
	convex = 1;
	for(int i=0;i<n;++i){
		if(cross(vertex[(i+1)%n]-vertex[i], vertex[(i+2)%n]-vertex[(i+1)%n]) < 0){
			convex = 0;
			break;
		}
	}
	cout << (convex ? 1 : 0) << endl;
	
	return 0;
}