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struct LCA {
vector<ll> depth;
vector<int> visited, first;
int idx;
SparseTable st; //sparse table von oben
void init(vector<vector<int>>& adj, int root) {
depth.assign(2 * sz(adj), 0);
visited.assign(2 * sz(adj), -1);
first.assign(sz(adj), 2 * sz(adj));
idx = 0;
dfs(adj, root);
st.init(&depth);
}
void dfs(vector<vector<int>>& adj, int v, ll d=0) {
visited[idx] = v, depth[idx] = d;
first[v] = min(idx, first[v]), idx++;
for (int u : adj[v]) {
if (first[u] == 2 * sz(adj)) {
dfs(adj, u, d + 1);
visited[idx] = v, depth[idx] = d, idx++;
}}}
int getLCA(int u, int v) {
if (first[u] > first[v]) swap(u, v);
return visited[st.queryIdempotent(first[u], first[v] + 1)];
}
ll getDepth(int v) {return depth[first[v]];}
};
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