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>
using namespace std;

int main()
{
	int n, d;
	int x[102], y[102];
	bool s = 1;

	cin >> n;

	for (int i = 0; i < n; i++)
		cin >> x[i] >> y[i];

	x[n] = x[0];
	y[n] = y[0];
	x[n + 1] = x[1];
	y[n + 1] = y[1];

	for (int i = 0; i < n; i++) {
		d = (x[i + 1] - x[i]) * (y[i + 2] - y[i]) - (x[i + 2] - x[i]) * (y[i + 1] - y[i]);
		if (d < 0) {
			s = 0;
			break;
		}
	}

	cout << s << endl;

	return 0;
}
