#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T1,typename T2,typename T3>istream &operator>>(istream &is,tuple<T1,T2,T3>&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;}
template<typename T,size_t n>istream &operator>>(istream &is,array<T,n>&a){for(auto&i:a)is>>i;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define overload3(_1,_2,_3,name,...) name
#define rep1(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)
#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)
#define reps(i,l,r) rep2(i,l,r)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)
#define yn(x) cout<<((x)?"Yes\n":"No\n")
#define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end())
template<typename T>
inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();}
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
  if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
  else return init;
}
#ifdef LOCAL
#include<debug.h>
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
struct Timer{
  clock_t start;
  Timer(){
    start=clock();
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout<<fixed<<setprecision(16);
  }
  inline double now(){return (double)(clock()-start)/1000;}
  #ifdef LOCAL
  ~Timer(){
    cerr<<"time:";
    cerr<<now();
    cerr<<"ms\n";
  }
  #endif
}timer;
void SOLVE();
int main(){
  int testcase=1;
  //cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
}
template<typename T=int>
struct Edge{
  int from,to;
  T weight;
  int index;
  Edge(int from_,int to_,T weight_=T(),int index_=-1):from(from_),to(to_),weight(weight_),index(index_){}
  Edge():from(-1),to(-1),weight(),index(-1){}
  friend std::ostream &operator<<(std::ostream &os,const Edge&e){
    os<<'[';
    os<<"from:"<<e.from;
    os<<"to:"<<e.to;
    os<<"weight:"<<e.weight;
    os<<"index:"<<e.index;
    os<<']';
    return os;
  }
};
template<typename T=int>
struct Tree{
  int n,r;
  std::vector<Edge<T>>edge;
  std::vector<Edge<T>>g;
  std::vector<int>ptr;
  struct tree_range{
    using iterator=typename std::vector<Edge<T>>::iterator;
    iterator l,r;
    iterator begin()const{return l;}
    iterator end()const{return r;}
    int size()const{return r-l;}
    bool empty()const{return !size();}
    Edge<T> &operator[](int i)const{return l[i];}
  };
  struct const_tree_range{
    using iterator=typename std::vector<Edge<T>>::const_iterator;
    iterator l,r;
    iterator begin()const{return l;}
    iterator end()const{return r;}
    int size()const{return r-l;}
    bool empty()const{return !size();}
    const Edge<T> &operator[](int i)const{return l[i];}
  };
  explicit Tree(int n_):n(n_){
    edge.reserve(n-1);
  }
  Tree():n(0){}
  Tree(int n_,const std::vector<Edge<T>>&e,bool dir=false):n(n_),r(-1),edge(e){
    if(!dir)build();
    else{
      std::vector<bool>seen(n,false);
      ptr.resize(n+1);
      for(const Edge<T>&i:edge)ptr[i.from]++,ptr[i.to]++,seen[e.to]=true;
      for(int i=1;i<=n;i++)ptr[i]+=ptr[i-1];
      r=std::find(seen.begin(),seen.end(),false)-seen.begin();
      assert(ptr[n]==n*2-2);
      g.resize(ptr[n]);
      for(const Edge<T>&i:edge)g[--ptr[i.to]]=Edge<T>(i.to,i.from,i.weight,i.index);
      for(const Edge<T>&i:edge)g[--ptr[i.from]]=i;
    }
  }
  template<bool weighted=false,bool index=1>
  void read(){
    for(int i=0;i<n-1;i++){
      int u,v;
      T w=T();
      std::cin>>u>>v;
      if constexpr(index)u--,v--;
      if constexpr(weighted)std::cin>>w;
      else w=1;
      edge.emplace_back(u,v,w,i);
    }
    build();
  }
  template<bool index=1>
  void readp(){
    ptr.resize(n+1);
    for(int i=1;i<n;i++){
      int p;
      std::cin>>p;
      if constexpr(index)p--;
      edge.emplace_back(p,i,1,i-1);
      ptr[p]++;
      ptr[i]++;
    }
    for(int i=1;i<=n;i++)ptr[i]+=ptr[i-1];
    g.resize(n*2-2);
    for(auto&&[u,v,w,i]:edge)g[--ptr[v]]=Edge<T>(v,u,w,i);
    for(int i=0;i<n-1;i++){
      g[--ptr[edge[i].from]]=edge[i];
    }
    r=0;
  }
  void add_edge(int u,int v){edge.emplace_back(u,v,1,edge.size());}
  void add_edge(int u,int v,T w){edge.emplace_back(u,v,w,edge.size());}
  void add_edge(int u,int v,T w,int idx){edge.emplace_back(u,v,w,idx);}
  inline bool is_directed()const{return r!=-1;}
  void build(){
    r=-1;
    ptr.resize(n+1,0);
    for(auto&&[u,v,w,i]:edge)ptr[u]++,ptr[v]++;
    for(int i=1;i<=n;i++)ptr[i]+=ptr[i-1];
    assert(ptr[n]==n*2-2);
    g.resize(n*2-2);
    for(auto&&[u,v,w,i]:edge){
      g[--ptr[u]]=Edge(u,v,w,i);
      g[--ptr[v]]=Edge(v,u,w,i);
    }
  }
  void remove_parent(int root=0){
    edge.resize(n-1);
    std::vector<int>par(n,-1);
    par[root]=-1;
    std::queue<int>que;
    que.push(root);
    while(!que.empty()){
      int x=que.front();
      que.pop();
      for(int i=ptr[x];i<ptr[x+1];){
        const Edge<T>&e=g[i];
        if(e.to!=par[x]){
          par[e.to]=x;
          assert(e.index<n-1);
          edge[e.index]=e;
          que.push(e.to);
          i++;
        }
        else{
          if(i+1==ptr[x+1])break;
          std::swap(g[i],g[ptr[x+1]-1]);
        }
      }
    }
    r=root;
  }
  std::vector<int>bfs_order()const{
    assert(is_directed());
    std::vector<int>bfs(n);
    int p=0,q=0;
    bfs[q++]=root();
    while(p<q){
      int x=bfs[p++];
      for(const Edge<T>&e:(*this)[x])bfs[q++]=e.to;
    }
    return bfs;
  }
  std::vector<int>dfs_order()const{
    assert(is_directed());
    std::vector<int>res;
    res.reserve(n);
    std::vector<int>st(n);
    int p=0;
    st[p++]=root();
    while(p){
      int x=st[--p];
      res.push_back(x);
      p+=(*this)[x].size();
      for(const Edge<T>&e:(*this)[x])st[--p]=e.to;
      p+=(*this)[x].size();
    }
    return res;
  }
  std::vector<int>rbfs_order()const{
    std::vector<int>bfs=bfs_order();
    std::reverse(bfs.begin(),bfs.end());
    return bfs;
  }
  void hld(){
    assert(is_directed());
    std::vector<int>sub(n);
    for(int x:rbfs_order()){
      sub[x]=1;
      int mx=-1;
      for(Edge<T>&e:(*this)[x]){
        sub[x]+=sub[e.to];
        if(mx<sub[e.to]){
          mx=sub[e.to];
          std::swap((*this)[x][0],e);
        }
      }
    }
  }
  std::pair<std::vector<int>,std::vector<int>>in_out_order(){
    assert(is_directed());
    std::vector<int>in(n),out(n);
    int p=0;
    auto dfs=[&](auto self,int x)->void {
      in[x]=p++;
      for(const Edge<T>&e:(*this)[x]){
        self(self,e.to);
      }
      out[x]=p;
    };
    dfs(dfs,root());
    return std::make_pair(in,out);
  }
  std::pair<T,std::vector<int>>diameter()const{
    assert(!is_directed());
    static constexpr T inf=std::numeric_limits<T>::max();
    std::vector<T>dst(n,inf);
    dst[0]=0;
    std::vector<int>que(n);
    int p=0,q=1;
    que[0]=0;
    while(p<q){
      int x=que[p++];
      for(const Edge<T>&e:(*this)[x])if(dst[e.to]==inf){
        dst[e.to]=dst[x]+e.weight;
        que[q++]=e.to;
      }
    }
    int u=std::max_element(dst.begin(),dst.end())-dst.begin();
    std::fill(dst.begin(),dst.end(),inf);
    dst[u]=0;
    p=0,q=1;
    que[0]=u;
    while(p<q){
      int x=que[p++];
      for(const Edge<T>&e:(*this)[x])if(dst[e.to]==inf){
        dst[e.to]=dst[x]+e.weight;
        que[q++]=e.to;
      }
    }
    int v=std::max_element(dst.begin(),dst.end())-dst.begin();
    T weight=dst[v];
    std::vector<int>res;
    while(u!=v){
      res.push_back(v);
      for(const Edge<T>&e:(*this)[v])if(dst[e.to]<dst[v]){
        v=e.to;
        break;
      }
    }
    res.push_back(u);
    return std::make_pair(weight,res);
  }
  int size()const{return n;}
  tree_range operator[](int i){return tree_range{g.begin()+ptr[i],g.begin()+ptr[i+1]-(r!=-1&&r!=i)};}
  const_tree_range operator[](int i)const{return const_tree_range{g.begin()+ptr[i],g.begin()+ptr[i+1]-(r!=-1&&r!=i)};}
  const Edge<T>& get_edge(int i)const{return edge[i];}
  inline int parent(int i)const{return i==r?-1:g[ptr[i+1]-1].to;}
  inline int root()const{return r;}
  typename std::vector<Edge<T>>::iterator begin(){return edge.begin();}
  typename std::vector<Edge<T>>::iterator end(){return edge.end();}
  typename std::vector<Edge<T>>::const_iterator begin()const{return edge.begin();}
  typename std::vector<Edge<T>>::const_iterator end()const{return edge.end();}
};
struct StaticTopTree{
private:
  template<typename T>
  void build(Tree<T>t){
    int n=t.size();
    left.reserve(n*2-1),right.reserve(n*2-1),par.reserve(n*2-1),A.reserve(n*2-1),B.reserve(n*2-1);
    left.resize(n,-1),right.resize(n,-1),par.resize(n,-1),A.resize(n),B.resize(n);
    for(int i=0;i<n;i++){
      A[i]=t.parent(i);
      B[i]=i;
    }
    auto dfs=[&](auto self,int x)->std::pair<int,int> {
      std::vector<std::pair<int,int>>vs{{0,x}};
      while(t[x].size()>=1){
        std::priority_queue<std::pair<int,int>,std::vector<std::pair<int,int>>,std::greater<std::pair<int,int>>>que;
        int heavy=t[x][0].to;
        que.emplace(0,heavy);
        for(int i=1;i<t[x].size();i++)que.push(self(self,t[x][i].to));
        while((int)que.size()>=2){
          auto [d1,v1]=que.top();que.pop();
          auto [d2,v2]=que.top();que.pop();
          if(B[v2]==heavy)std::swap(d1,d2),std::swap(v1,v2);
          int nv=left.size();
          left.push_back(v1),right.push_back(v2),par.push_back(-1),A.push_back(x),B.push_back(B[v1]);
          par[v1]=par[v2]=nv;
          que.emplace(std::max(d1,d2)+1,nv);
        }
        vs.push_back(que.top());
        while(true){
          int sz=vs.size();
          if(sz>=3&&(vs[sz-3].first==vs[sz-2].first||vs[sz-3].first<=vs[sz-1].first)){
            int nv=left.size();
            left.push_back(vs[sz-3].second),right.push_back(vs[sz-2].second),par.push_back(-1),A.push_back(A[vs[sz-3].second]),B.push_back(B[vs[sz-2].second]);
            par[vs[sz-3].second]=par[vs[sz-2].second]=nv;
            vs[sz-3].first=std::max(vs[sz-3].first,vs[sz-2].first)+1;
            vs[sz-3].second=nv;
            vs[sz-2]=vs[sz-1];
            vs.pop_back();
          }
          else if(sz>=2&&vs[sz-2].first<=vs[sz-1].first){
            int nv=left.size();
            left.push_back(vs[sz-2].second),right.push_back(vs[sz-1].second),par.push_back(-1),A.push_back(A[vs[sz-2].second]),B.push_back(B[vs[sz-1].second]);
            par[vs[sz-2].second]=par[vs[sz-1].second]=nv;
            vs[sz-2].first=std::max(vs[sz-2].first,vs[sz-1].first)+1;
            vs[sz-2].second=nv;
            vs.pop_back();
          }
          else break;
        }
        x=heavy;
      }
      while((int)vs.size()>=2){
        int sz=vs.size();
        int nv=left.size();
        left.push_back(vs[sz-2].second),right.push_back(vs[sz-1].second),par.push_back(-1),A.push_back(A[vs[sz-2].second]),B.push_back(B[vs[sz-1].second]);
        par[vs[sz-2].second]=par[vs[sz-1].second]=nv;
        vs[sz-2].first=std::max(vs[sz-2].first,vs[sz-1].first)+1;
        vs[sz-2].second=nv;
        vs.pop_back();
      }
      return vs[0];
    };
    dfs(dfs,t.root());
  }
public:
  std::vector<int>left,right,par,A,B;
  StaticTopTree(){}
  template<typename T>
  explicit StaticTopTree(Tree<T>t,int){
    build(std::move(t));
  }
  template<typename T>
  explicit StaticTopTree(Tree<T>t){
    assert(t.is_directed());
    t.hld();
    build(std::move(t));
  }
};
template<typename T=int>
struct CentroidDecomposition:public Tree<T>{
private:
  using Tree<T>::Tree;
  using Tree<T>::g;
  using Tree<T>::ptr;
  using Tree<T>::remove_parent;
  using Tree<T>::hld;
  int boundaryA1,boundaryB1,boundaryA2,boundaryB2;
  std::vector<Edge<T>>adj1,adj2;
  bool prepared=false;
  StaticTopTree stt;
  void prepare(){
    if(prepared)return;
    remove_parent();
    hld();
    stt=StaticTopTree(*this,0);
    prepared=true;
  }
public:
  template<typename Func>
  void run(const Func&f){
    prepare();
    int n=this->size();
    auto dfs=[&](auto self,int nd)->std::vector<Edge<T>> {
      if(nd<n){
        std::vector<Edge<T>>res(1);
        if(nd==0)res[0]=Edge<T>(-1,0);
        else{
          res[0]=g[ptr[nd+1]-1];
          std::swap(res[0].from,res[0].to);
        }
        return res;
      }
      int lv=stt.left[nd],rv=stt.right[nd];
      std::vector<Edge<T>>lch=self(self,lv);
      std::vector<Edge<T>>rch=self(self,rv);
      boundaryA1=stt.A[lv];
      boundaryB1=stt.B[lv];
      boundaryA2=stt.A[rv];
      boundaryB2=stt.B[rv];
      std::swap(adj1,lch);
      std::swap(adj2,rch);
      f(boundaryA1,boundaryA2);
      std::swap(adj1,lch);
      std::swap(adj2,rch);
      if(boundaryA1==boundaryA2){
        if(std::ssize(lch)<std::ssize(rch))std::swap(lch,rch);
        lch.insert(lch.end(),rch.begin(),rch.end());
      }
      return lch;
    };
    dfs(dfs,n*2-2);
  }
  typename Tree<T>::tree_range get(int c,int x){
    if(c==0){
      if(x==boundaryA1)return typename Tree<T>::tree_range{adj1.begin(),adj1.end()};
      if(x==boundaryB1)return typename Tree<T>::tree_range{g.begin()+ptr[x+1]-(!!x),g.begin()+ptr[x+1]};
      return typename Tree<T>::tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else if(c==1){
      if(x==boundaryA2)return typename Tree<T>::tree_range{adj2.begin(),adj2.end()};
      if(x==boundaryB2)return typename Tree<T>::tree_range{g.begin()+ptr[x+1],g.begin()+ptr[x+1]};
      return typename Tree<T>::tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else std::abort();
  }
  typename Tree<T>::const_tree_range get(int c,int x)const{
    if(c==0){
      if(x==boundaryA1)return typename Tree<T>::const_tree_range{adj1.begin(),adj1.end()};
      if(x==boundaryB1)return typename Tree<T>::const_tree_range{g.begin()+ptr[x+1]-(!!x),g.begin()+ptr[x+1]};
      return typename Tree<T>::const_tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else if(c==1){
      if(x==boundaryA2)return typename Tree<T>::const_tree_range{adj2.begin(),adj2.end()};
      if(x==boundaryB2)return typename Tree<T>::const_tree_range{g.begin()+ptr[x+1],g.begin()+ptr[x+1]};
      return typename Tree<T>::const_tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else std::abort();
  }
  CentroidDecomposition(const Tree<T>&t){Tree<T>::operator=(t);}
};
#include<type_traits>
#include<concepts>
template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>msb(T n){return n==0?-1:31-__builtin_clz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>msb(T n){return n==0?-1:63-__builtin_clzll(n);}

template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>lsb(T n){return n==0?-1:__builtin_ctz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>lsb(T n){return n==0?-1:__builtin_ctzll(n);}

template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>floor_pow2(T n){return n==0?0:T(1)<<msb(n);}

template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>ceil_pow2(T n){return n<=1?1:T(1)<<(msb(n-1)+1);}

template<std::integral T>
constexpr T safe_div(T a,T b){return a/b-(a%b&&(a^b)<0);}
template<std::integral T>
constexpr T safe_ceil(T a,T b){return a/b+(a%b&&(a^b)>0);}
template<typename M,int L=5>
struct SparseTable{
  using S=typename M::S;
private:
  std::vector<S>dat,prefix,suffix;
  std::vector<std::vector<S>>sp;
public:
  SparseTable(){}
  SparseTable(std::vector<S>a):dat(a){
    int n=a.size();
    n=(n+(1<<L)-1)&~((1<<L)-1);
    a.resize(n,M::e());
    prefix=suffix=a;
    std::vector<S>d2(n>>L,M::e());
    for(int i=0;i<(int)d2.size();i++){
      for(int j=0;j<(1<<L);j++)d2[i]=M::op(d2[i],a[(i<<L)+j]);
    }
    for(int i=0;i<(n>>L);i++){
      for(int j=1;j<(1<<L);j++)prefix[(i<<L)+j]=M::op(prefix[(i<<L)+j-1],prefix[(i<<L)+j]);
    }
    for(int i=(n>>L)-1;i>=0;i--){
      for(int j=(1<<L)-1;j>=1;j--)suffix[(i<<L)+j-1]=M::op(suffix[(i<<L)+j-1],suffix[(i<<L)+j]);
    }
    int d=(d2.size()==1?1:32-__builtin_clz(d2.size()-1));
    sp.resize(d,d2);
    for(int i=1;i<d;i++){
      int w=1<<i;
      for(int j=w;j<=(int)d2.size();j+=w*2){
        for(int k=j-2;k>=j-w;k--)sp[i][k]=M::op(d2[k],sp[i][k+1]);
        int r=std::min<int>(d2.size(),j+w);
        for(int k=j+1;k<r;k++)sp[i][k]=M::op(sp[i][k-1],d2[k]);
      }
    }
  }
  S prod(int l,int r)const{
    if(l==r)return M::e();
    r--;
    int lid=l>>L,rid=r>>L;
    if(lid==rid){
      S ret=M::e();
      for(int i=l;i<=r;i++)ret=M::op(ret,dat[i]);
      return ret;
    }
    else{
      lid++;
      rid--;
      S mid=M::e();
      if(lid==rid)mid=sp[0][lid];
      else if(lid<rid){
        int s=msb(lid^rid);
        mid=M::op(sp[s][lid],sp[s][rid]);
      }
      return M::op(suffix[l],M::op(mid,prefix[r]));
    }
  }
};
struct LowestCommonAncestor{
private:
  struct p_min{
    using S=std::pair<int,int>;
    static S op(const S&x,const S&y){return x.first<y.first?x:y;}
    static S e(){return std::make_pair(std::numeric_limits<int>::max(),-1);}
  };
  SparseTable<p_min>sp;
  std::vector<int>idx;
public:
  template<typename T>
  LowestCommonAncestor(const Tree<T>&t):idx(t.size()){
    assert(t.is_directed());
    int r=t.root();
    int ord=0;
    std::vector<int>dep(t.size());
    dep[r]=0;
    std::vector<std::pair<int,int>>init(t.size()*2-1);
    auto dfs=[&](auto&&self,int x)->void {
      idx[x]=ord;
      init[ord++]=std::make_pair(dep[x],x);
      for(const auto&e:t[x]){
        dep[e.to]=dep[e.from]+1;
        self(self,e.to);
        init[ord++]=std::make_pair(dep[x],x);
      }
    };
    dfs(dfs,r);
    sp=SparseTable<p_min>(init);
  }
  LowestCommonAncestor(){}
  int query(int u,int v)const{
    if(u==v)return u;
    if(idx[u]>idx[v])std::swap(u,v);
    return sp.prod(idx[u],idx[v]+1).second;
  }
};
using namespace std;
template<typename T=int>
struct AuxiliaryTree{
private:
  vector<vector<Edge<T>>>g;
  LowestCommonAncestor lca;
  vector<int>in,out;
  vector<T>dep;
public:
  AuxiliaryTree(const Tree<T>&t):g(t.size()),in(t.size()),out(t.size()){
    assert(t.is_directed());
    lca=LowestCommonAncestor(t);
    int root=t.root();
    int i=0;
    dep.resize(t.size());
    auto dfs=[&](auto&&self,int x,int p)->void {
      in[x]=i++;
      for(const auto&e:t[x])if(e.to!=p){
        dep[e.to]=dep[e.from]+e.weight;
        self(self,e.to,e.from);
      }
      out[x]=i;
    };
    dep[root]=0;
    dfs(dfs,root,-1);
  }
  AuxiliaryTree(){}
  int build(vector<int>v){
    assert(!v.empty());
    auto comp=[&](int x,int y)->bool {return in[x]<in[y];};
    sort(v.begin(),v.end(),comp);
    v.reserve(v.size()*2-1);
    int vsize=v.size();
    for(int i=1;i<vsize;i++)v.push_back(lca.query(v[i-1],v[i]));
    sort(v.begin(),v.end(),comp);
    v.erase(unique(v.begin(),v.end()),v.end());
    for(int i=0;i<(int)v.size();i++)g[v[i]].clear();
    stack<int>st;
    for(int i=0;i<(int)v.size();i++){
      while(!st.empty()&&out[st.top()]<=in[v[i]])st.pop();
      if(!st.empty()){
        T w=dep[v[i]]-dep[st.top()];
        g[st.top()].push_back(Edge<T>(st.top(),v[i],w));
        g[v[i]].push_back(Edge<T>(v[i],st.top(),w));
      }
      st.push(v[i]);
    }
    while(st.size()>1)st.pop();
    return st.top();
  }
  vector<Edge<T>> &operator[](int i){return g[i];}
  const vector<Edge<T>> &operator[](int i)const{return g[i];}
};
void SOLVE(){
  int n;
  cin>>n;
  Tree t1(n),t2(n);
  t1.read(),t2.read();
  ull ans=0;
  CentroidDecomposition<int> cd(t1);
  t2.remove_parent();
  AuxiliaryTree aux(t2);
  LowestCommonAncestor lca(t2);
  vector<int>dep(n);
  for(int x:t2.bfs_order()){
    for(auto e:t2[x])dep[e.to]=dep[e.from]+1;
  }
  vector<int>vs;
  vector<int>type(n,-1);
  vector<int>dst(n);
  auto dfs=[&](auto self,int x,int p,int ban,int id)->void {
    if(x!=ban){
      type[x]=id;
      vs.push_back(x);
    }
    for(auto e:cd.get(id,x))if(e.to!=p){
      dst[e.to]=dst[x]+1;
      self(self,e.to,x,ban,id);
    }
  };
  cd.run([&](int a1,int a2){
    vs.clear();
    dst[a2]=0;
    dfs(dfs,a2,-1,a1,0);
    int p=vs.size();
    dfs(dfs,a2,-1,a2,1);
    ull dstsum1=0,depsum1=0;
    ull dstsum2=0,depsum2=0;
    rep(i,p){
      dstsum1+=dst[vs[i]];
      depsum1+=dep[vs[i]];
      ans+=ull(dst[vs[i]])*dep[vs[i]]*(vs.size()-p);
    }
    rep(i,p,vs.size()){
      dstsum2+=dst[vs[i]];
      depsum2+=dep[vs[i]];
      ans+=ull(dst[vs[i]])*dep[vs[i]]*p;
    }
    ans+=dstsum1*depsum2;
    ans+=dstsum2*depsum1;
    int root=aux.build(vs);
    auto dfs2=[&](auto self2,int x,int p)->tuple<ull,ull,ull,ull> {
      ull sum1=0,cnt1=0;
      ull sum2=0,cnt2=0;
      for(auto e:aux[x])if(e.to!=p){
        auto [sum11,cnt11,sum22,cnt22]=self2(self2,e.to,x);
        ans-=(sum1*cnt22+sum2*cnt11+sum11*cnt2+sum22*cnt1)*dep[x]*2;
        sum1+=sum11;
        cnt1+=cnt11;
        sum2+=sum22;
        cnt2+=cnt22;
      }
      if(type[x]!=-1){
        if(type[x]==0){
          ans-=(sum2+dst[x]*cnt2)*dep[x]*2;
          sum1+=dst[x];
          cnt1++;
        }
        else{
          ans-=(sum1+dst[x]*cnt1)*dep[x]*2;
          sum2+=dst[x];
          cnt2++;
        }
      }
      return {sum1,cnt1,sum2,cnt2};
    };
    dfs2(dfs2,root,-1);
    for(int v:vs)type[v]=-1;
  });
  ans*=2;
  cout<<ans<<endl;
}