UFO

#include <iostream>
#include <cmath>

using namespace std;

struct Vector2{
    int x;
    int y;
    Vector2(int x = 0, int y = 0):x(x),y(y){}
};

int gcd(int a, int b){
    while(a > 0 && b > 0){
        if(a > b) a -= b;
        else b -= a;
    }
    return (max(a, b));
}

int main(){
    Vector2 A, B, C;

    /* cout << "Ax:";
    cin >> A.x;
    cout << "Ay:";
    cin >> A.y;
    cout << "Bx:";
    cin >> B.x;
    cout << "By:";
    cin >> B.y;
    cout << "Cx:";
    cin >> C.x;
    cout << "Cy:";
    cin >> C.y;*/

    A = Vector2(3, 1);
    B = Vector2(1, 5);
    C = Vector2(5, 4);

    float area, AB, BC, CA, interior, exterior, s, total;
    Vector2 distAB, distBC, distCA, temp;

    distAB.x = abs(B.x - A.x);
    distAB.y = abs(B.y - A.y);
    distBC.x = abs(C.x - B.x);
    distBC.y = abs(C.y - B.y);
    distCA.x = abs(A.x - C.x);
    distCA.y = abs(A.y - C.y);

    exterior = gcd(distAB.x, distAB.y) + gcd(distBC.x, distBC.y) + gcd(distCA.x, distCA.y);

    AB = sqrt(distAB.x * distAB.x + distAB.y * distAB.y);
    BC = sqrt(distBC.x * distBC.x + distBC.y * distBC.y);
    CA = sqrt(distCA.x * distCA.x + distCA.y * distCA.y);

    s = (AB + BC + CA) / 2;
    area = sqrt(s * (s - AB) * (s - BC) * (s - CA));
    interior = area + 1 - exterior / 2;

    total = exterior + interior;

    cout << total;
}