class Solution {
public:
    size_t d2(int x1, int y1, int x2, int y2) {
      return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
    }
    
    double minAreaFreeRect(vector<vector<int>>& ps, size_t res = 0) {
        unordered_map<size_t, unordered_map<size_t, vector<vector<int>>>> m;
      
        for(auto i = 0; i < ps.size(); ++i)
        for(auto j = i + 1; j < ps.size(); ++j) {
          auto center = (size_t(ps[i][0] + ps[j][0]) << 16) + ps[i][1] + ps[j][1];
          auto len = d2(ps[i][0], ps[i][1], ps[j][0], ps[j][1]);
          m[center][len].push_back({ps[i][0], ps[i][1], ps[j][0], ps[j][1]});
        }
        
        for(auto it_c = begin(m); it_c != end(m); ++it_c)
            for(auto it_l = begin(it_c->second); it_l != end(it_c->second); ++it_l)
                for(auto i = 0; i < it_l->second.size(); ++i)
                    for(auto j = i + 1; j < it_l->second.size(); ++j) {
                        auto &p1 = it_l->second[i], &p2 = it_l->second[j];
                        auto area = d2(p1[0], p1[1], p2[0], p2[1]) * d2(p1[0], p1[1], p2[2], p2[3]);
                        if(res == 0 || res > area) res = area;
                    }
        return sqrt(res);
    }
};