Current check for a polygon order is incorrect, and it breaks on the following test:

Here's the code that generates this test:

vector<Point> pts = {{0,2}, {1,3}, {0,1}, {1,0}, {-1,0}, {-1,3}};vector<vector<size_t>>adj(pts.size());auto add_edge = [&](int u,int v) {    adj[u].push_back(v);    adj[v].push_back(u);};add_edge(0,1);add_edge(1,2);add_edge(2,3);add_edge(3,4);add_edge(4,5);add_edge(5,0);

For an outer face (1→2→3→4→5→0), the previous version of the algorithm would first check the triplet 1→2→3. Since this triplet is ordered in counter-clockwise order, it would incorrectly mark this face as inner.

So, instead we should use something different. I used the oriented area, however, since the coordinates are stored as int64_t, I had to use __int128, which doesn't feel that elegant.