main.cpp

#include <fstream>
#include <iostream>
#include <cmath>
#include <cstdlib>
#include <array>
using namespace std;

struct point {
    int64_t x, y;
};

struct rect {
    point p1, p2, p3, p4;
};

istream& operator>>(istream& stream, point& p) {
    return stream >> p.x >> p.y;
}

istream& operator>>(istream& stream, rect& r) {
    return stream >> r.p1 >> r.p2 >> r.p3 >> r.p4;
}

// returns oriented double area of triangle
int64_t area(point p1, point p2, point p3) {
    return (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
}

// retruns true if point belongs to rectangle
bool belongs_to_rect(point p, rect r) {
    int64_t s_area = 0 ;

    // the idea is that if the point is inside, the sum of the areas of
    // triangles it makes with the sides of rectangle will add up to the area of
    // the rectangle
    s_area += abs(area(p, r.p1, r.p2));
    s_area += abs(area(p, r.p2, r.p3));
    s_area += abs(area(p, r.p3, r.p4));
    s_area += abs(area(p, r.p4, r.p1));

    int64_t r_area = abs(area(r.p1, r.p2, r.p3)) + abs(area(r.p1, r.p3, r.p4));
    return r_area == s_area;
}

int main() {
    ifstream in("input.txt");
    ofstream out("output.txt");
    int n;
    in >> n;
    int result = 0;
    for (int i = 0; i < n; i++) {
        point p; rect r;
        in >> p >> r;
        if (belongs_to_rect(p, r)) {
            result++;
        }
    }
    out << result << endl;
}