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
import java.util.Scanner;

public class Main{
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		long[][]p = new long[n + 1][2];
		for(int i = 0; i < n; i++) {
			long x = scan.nextLong();
			long y = scan.nextLong();
			long[]t = {x, y};
			p[i] = t;
		}
		p[n] = p[0];
		scan.close();
		for(int i = 0; i < n; i++) {
			long s = area(p[(i - 1 + n) % n], p[i], p[i + 1]);
			long t = area(p[i], p[i + 1], p[(i + 2) % n]);
			if(s * t < 0) {
				System.out.println(0);
				System.exit(0);
			}
		}
		System.out.println(1);
	}
	static long area(long[]x, long[]y, long[]z) {
		return (cross(vec(z, x), vec(z, y)));
	}
	static long cross(long[]u, long[]v) {
		return u[0] * v[1] - u[1] * v[0];
	}
	static long[] vec(long[]p1, long[]p2) {
		long[]u = {p2[0] - p1[0], p2[1] - p1[1]};
		return u;
	}
}
