#include <iostream>
using namespace std;

int main() {

    int n;
    bool isIncorrect;

    do {
        isIncorrect = false;

        cout << "Enter the number of sides of the polygon:";
        cin >> n;

        if (cin.fail()) {
            cin.clear();
            cout << "Invalid input." << endl;
            isIncorrect = true;
        }

        if (!isIncorrect && n > 1000) {
                cout << "Number of sides is too big. Please, choose different value that is less than 1000." << endl;
                isIncorrect = true;
            }

        if (!isIncorrect && n < 3) {
            cout << "Polygon must have at least 3 sides." << endl;
            isIncorrect = true;
        }

        while (cin.get() != '\n');
    } while (isIncorrect);

    int* xValues = new int[n];
    int* yValues = new int[n];

    for (int i = 0; i < n; i++)
    {
        do {
            isIncorrect = false;

            cout << "Enter x value for " << i+1 << " point :" << endl;
            cin >> xValues[i];

            cout << "Enter y value for " << i+1 << " point :" << endl;
            cin >> yValues[i];

            if (cin.fail()) {
                cin.clear();
                cout << "Invalid input!" << endl;
                isIncorrect = true;
            }

            if (!isIncorrect && (xValues[i] < -1000 || xValues[i] > 1000)) {
                cout << "X value is out of range [-1000; 1000]. Please, choose different value." << endl;
                isIncorrect = true;
            }

            if (!isIncorrect && (yValues[i] < -1000 || yValues[i] > 1000)) {
                cout << "Y value is out of range [-1000; 1000]. Please, choose different value." << endl;
                isIncorrect = true;
            }

            while (cin.get() != '\n');
        } while (isIncorrect);
    }

    bool hasPositive = false;
    bool hasNegative = false;

    for (int i = 0; i < n; ++i) {
        double result = (xValues[(i + 1) % n] - xValues[i]) * (yValues[(i + 2) % n] - yValues[(i + 1) % n]) -
                        (yValues[(i + 1) % n] - yValues[i]) * (xValues[(i + 2) % n] - xValues[(i + 1) % n]);

        if (result > 0) {
            hasPositive = true;
        } else if (result < 0) {
            hasNegative = true;
        }

        // If both positive and negative results are encountered, the polygon is not convex
        // If no positive or no negative results are encountered, the polygon is not convex
        if ((hasPositive && hasNegative) || !(hasPositive && hasNegative)) {
            cout << "The polygon is not convex." << endl;
            return 0;
        }
    }

    // If the code reaches this point, the polygon is convex
    cout << "The polygon is convex." << endl;

    delete[] xValues;
    delete[] yValues;

    return 0;
}