import java.io.*;
import java.util.*;

import static java.awt.geom.Point2D.Double;

public class MaartenScanner {
    public static void main(String[] args) throws IOException {
        try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {
            new MaartenScanner().run(new Scanner(reader));
        }
    }

    public void run(Scanner sc) throws IOException {
        int n = sc.nextInt();
        Double[] points = new Double[n];
        for (int i = 0; i < n; i++) {
            points[i] = new Double(sc.nextDouble(), sc.nextDouble());
        }

        double A = 0;
        for (int i = 0; i < n - 1; i++) {
            A += (points[i + 1].x - points[i].x) * (points[i].y + points[i + 1].y) / 2;
        }

        double ans = Math.sqrt(3) / 4;
        if (n > 2) {
            double ratio = 0;
            for (int i = 0; i < n - 1; i++) {
                ratio += Math.pow(points[i + 1].x - points[i].x, 2) + Math.pow(points[i + 1].y - points[i].y, 2);
            }
            ans += 3 * A / (1 - ratio);
        }
        System.out.println(ans);
    }
}