Picks

struct point{
    int x, y;
};

point P[mx];

int area(point a, point b){
    return (a.x * b.y - b.x * a.y);
}

int polyarea(int n){
    int ans = area(P[n - 1], P[0]);
    for(int i=1;i<n;i++){
        ans += area(P[i-1], P[i]);
    }
    return llabs(ans)/2;
}

int pointinline(int n){
    int ans = __gcd(llabs(P[0].x - P[n-1].x), llabs(P[0].y - P[n-1].y));
    for(int i=1;i<n;i++){
        ans += __gcd(llabs(P[i-1].x - P[i].x), llabs(P[i-1].y - P[i].y));
    }
    return ans;
}

int picks(int n){
    int B = pointinline(n);
    int A = polyarea(n);
    int I = A - B/2 + 1;
    return I;
}