// LLP-Kruskal: edge-inclusion lattice driven by union-find.

class LLPKruskal {
  boolean[] LLPKruskal(int[] u, int[] v, int[] parent) {
    boolean[] C = false;
    forbidden (j) : !C[j] && find(u[j], parent) != find(v[j], parent)  =>
      advance : {
        C[j] = true;
        union(u[j], v[j], parent);
      };
    return C;
  }

  // Iterative find with path-halving.
  int find(int x, int[] parent) {
    while (parent[x] != x) {
      parent[x] = parent[parent[x]];
      x = parent[x];
    };
    return x;
  }

  // Union by simple link of the roots; idempotent on already-merged sets.
  void union(int a, int b, int[] parent) {
    int ra = find(a, parent);
    int rb = find(b, parent);
    if (ra != rb) {
      parent[ra] = rb;
    }
  }
}