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.