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// Usual Tree DP can be broken down in 4 steps:
// - Initialize dp[v] = identity
// - Iterate over all children w and take a value for w
// by looking at dp[w] and possibly the edge label of v -> w
// - combine the values of those children
// usually, this operation should be commutative and associative
// - finalize the value of dp[v] after iterating over all children
struct Reroot{
using T = ll;
// identity element
T E(){}
// x: dp value of child
// e: index of edge going to child
T takeChild(T x, int e){}
T combine(T x, T y){}
// called after combining all dp values of children
T finalize(T x, int v){}
vector<vector<pair<int, int>>> g;
vector<int> ord, pae;
vector<T> dp;
T dfs(int v){
ord.push_back(v);
for(auto [w, e] : g[v]){
g[w].erase(find(all(g[w]), pair(v, e^1)));
pae[w] = e^1;
dp[v] = combine(dp[v], takeChild(dfs(w), e));
}
return dp[v] = finalize(dp[v], v);
}
vector<T> solve(int n, vector<pair<int, int>> edges){
g.resize(n);
for(int i = 0; i < n-1; i++){
g[edges[i].first].emplace_back(edges[i].second, 2*i);
g[edges[i].second].emplace_back(edges[i].first, 2*i+1);
}
pae.assign(n, -1);
dp.assign(n, E());
dfs(0);
vector<T> updp(n, E()), res(n, E());
for(int v : ord){
vector<T> pref(sz(g[v])+1), suff(sz(g[v])+1);
if(v != 0) pref[0] = takeChild(updp[v], pae[v]);
for(int i = 0; i < sz(g[v]); i++){
pref[i+1] = suff[i] = takeChild(dp[g[v][i].first], g[v][i].second);
pref[i+1] = combine(pref[i], pref[i+1]);
}
for(int i = sz(g[v])-1; i >= 0; i--)
suff[i] = combine(suff[i], suff[i+1]);
for(int i = 0; i < sz(g[v]); i++)
updp[g[v][i].first] = finalize(combine(pref[i], suff[i+1]), v);
res[v] = finalize(pref.back(), v);
}
return res;
}
};
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