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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// 入力
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		List<Vector2d> p = new ArrayList<>();
		for (int i=0; i<n; i++) {
			double x = sc.nextDouble();
			double y = sc.nextDouble();
			p.add(new Vector2d(x, y));
		}
		sc.close();
		System.out.println(solve(p));
	}

	static class Vector2d {
		Vector2d(Double x, Double y){
			this.x = x;
			this.y = y;
		}
		Double x;
		Double y;
		public String toString() {
			return String.format("%1$.10f %2$.10f", x, y);
		}
	}

	public static Vector2d sub(Vector2d v1, Vector2d v2){
		return new Vector2d(v2.x - v1.x, v2.y - v1.y);
	}

	public static int solve(List<Vector2d> p) {
		boolean ans = true;
		int s = p.size();
		for (int i=0; i<s; i++) {
			Vector2d a = sub(p.get(i), p.get((i+1)%s));
			Vector2d b = sub(p.get((i+1)%s), p.get((i+2)%s));
			ans = ans && ((a.x * b.y - a.y * b.x) >= 0);
		}
		return ans ? 1 : 0;
	}
}

