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vector<vector<int>> adj;
vector<int> sz, in, out, nxt, par;
int counter;
void dfs_sz(int v = 0, int from = -1) {
for (auto& u : adj[v]) if (u != from) {
dfs_sz(u, v);
sz[v] += sz[u];
if (adj[v][0] == from || sz[u] > sz[adj[v][0]]) {
swap(u, adj[v][0]); //changes adj!
}}}
void dfs_hld(int v = 0, int from = -1) {
par[v] = from;
in[v] = counter++;
for (int u : adj[v]) if (u != from) {
nxt[u] = (u == adj[v][0]) ? nxt[v] : u;
dfs_hld(u, v);
}
out[v] = counter;
}
void init(int root = 0) {
int n = ssize(adj);
sz.assign(n, 1), nxt.assign(n, root), par.assign(n, -1);
in.resize(n), out.resize(n);
counter = 0;
dfs_sz(root);
dfs_hld(root);
}
template<typename F>
void for_intervals(int u, int v, F&& f) {
for (;; v = par[nxt[v]]) {
if (in[v] < in[u]) swap(u, v);
f(max(in[u], in[nxt[v]]), in[v] + 1);
if (in[nxt[v]] <= in[u]) return;
}}
int get_lca(int u, int v) {
for (;; v = par[nxt[v]]) {
if (in[v] < in[u]) swap(u, v);
if (in[nxt[v]] <= in[u]) return u;
}}
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