#include <iostream>
#include <cmath>
using namespace std;

// Define a structure to represent a point
struct Point {
    double x, y;
};

// Calculate the cross product of two vectors
double crossProduct(Point a, Point b, Point c) {
    return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}

// Check if two points are on the same side of a line passing through two other points
bool sameSide(Point a, Point b, Point c, Point d) {
    double cp1 = crossProduct(c, d, a);
    double cp2 = crossProduct(c, d, b);
    return cp1 * cp2 >= 0;
}

// Check if there exists a point that all the other thirteen points lie on the same side of the line passing through these points
bool hasSameSidePoint(Point points[], int n) {
    for (int i = 0; i < n; i++) {
        int count1 = 0, count2 = 0;
        for (int j = 0; j < n; j++) {
            if (i != j) {
                if (sameSide(points[i], points[j], points[i+1], points[(i+2)%n])) {
                    count1++;
                }
                if (sameSide(points[i], points[j], points[i+1], points[(i+n-1)%n])) {
                    count2++;
                }
            }
        }
        if (count1 == n-2 || count2 == n-2) {
            return true;
        }
    }
    return false;
}

int main() {
    // Define the set of points
    Point points[15] = {{0, 0}, {1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, {6, 6}, {7, 7}, {8, 8}, {9, 9}, {10, 10}, {11, 11}, {12, 12}, {13, 13}, {14, 14}};
    int n = 15;

    // Check if there exists a point that all the other thirteen points lie on the same side of the line passing through these points
    bool result = hasSameSidePoint(points, n);

    // Output the result
    if (result) {
        cout << "There exists a point that all the other thirteen points lie on the same side of the line passing through these points." << endl;
    } else {
        cout << "There does not exist a point that all the other thirteen points lie on the same side of the line passing through these points." << endl;
    }

    return 0;
}