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.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.List;
import java.util.ArrayList;

public class Main {
    public static double cross(double x1, double y1, double x2, double y2) {
        return x1 * y2 - x2 * y1;
    }
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        ArrayList<String[]> points = new ArrayList<String[]>();
        for (int i = 0; i < n; i++){
            String[] s = br.readLine().split(" ");
            points.add(s);
        }
        ArrayList<double[]> edges = new ArrayList<double[]>();
        for (int i = 0; i < n - 1; i++){
            double xi = Double.parseDouble(points.get(i)[0]);
            double yi = Double.parseDouble(points.get(i)[1]);
            double xi1 = Double.parseDouble(points.get(i+1)[0]);
            double yi1 = Double.parseDouble(points.get(i+1)[1]);
            double[] vector = new double[2];
            vector[0] = xi1 - xi;
            vector[1] = yi1 - yi;
            edges.add(vector);
        }
        // i == n -1
        double xn = Double.parseDouble(points.get(n-1)[0]);
        double yn = Double.parseDouble(points.get(n-1)[1]);
        double xn1 = Double.parseDouble(points.get(0)[0]);
        double yn1 = Double.parseDouble(points.get(0)[1]);
        double[] vector = new double[2];
        vector[0] = xn1 - xn;
        vector[1] = yn1 - yn;
        edges.add(vector);
        
        boolean flag = true;
        for (int i = 0; i < n - 1; i++){
            if (cross(edges.get(i)[0], edges.get(i)[1], edges.get(i+1)[0],edges.get(i+1)[1])< 0){
                System.out.println(0);
                flag = false;
                break;
            }
        }
        if (flag){
            System.out.println(1);
        }
    }
}