Найти прямоугольник, площадь которого максимальна

#include <iostream>
#include <vector>
#include <algorithm>
#include <random>
#include <iterator>
 
struct rect
{
    using coords_t = std::pair<std::pair<int, int>, std::pair<int, int>>;
    rect& operator= (const coords_t& coords)
    {
        mCoords = coords;
        return *this;
    }
    friend std::ostream& operator<< (std::ostream& os, const rect& r)
    {
        os << "x1: " << r.mCoords.first.first << " y1: " << r.mCoords.first.second <<
              " x2: " << r.mCoords.second.first << " y2: " << r.mCoords.second.second << std::endl;
        return os;
    }
    long long area() const
    {
        return std::abs((mCoords.first.first - mCoords.second.first) * (mCoords.first.second - mCoords.second.second));
    }
 
private:
    coords_t mCoords;
};
 
int main()
{
    std::cout << "Number of rectangles: ";
    std::size_t n;
    std::cin >> n;
 
    if (n < 1)
    {
        std::cerr << "Invalid input. Terminating..." << std::endl;
        return 1;
    }
 
    std::vector<rect> rects(n);
 
    std::mt19937 gen{ std::random_device{}() };
    std::normal_distribution<double> dist{ 0, 100 };
    std::generate(rects.begin(), rects.end(), [&dist, &gen]() {
        return std::make_pair( std::make_pair( static_cast<int>(dist(gen)), static_cast<int>(dist(gen)) ),
               std::make_pair( static_cast<int>(dist(gen)), static_cast<int>(dist(gen)) ) );
    });
 
    std::cout << "Generated rectangles:" << std::endl;
    std::copy(rects.begin(), rects.end(), std::ostream_iterator<rect>(std::cout, ""));
 
    auto max_area_rect = std::max_element(rects.begin(), rects.end(), [](auto& rect1, auto& rect2) { return rect1.area() < rect2.area(); });
    std::cout << "Maximum area rectangle: " << *max_area_rect;
    std::cout << "Its area is = " << max_area_rect->area() << std::endl;
 
    return 0;
}

struct Point
{
    double x,y;
}
 
struct Rect
{
    Point lb, rt; // lb - left_bottom, rt - right_top
}

[](auto& rect1, auto& rect2) { return rect1.area() < rect2.area(); }