#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{
protected:
  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];}
  };
public:
  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];
    }
  }
  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));
  }
};
struct ContourQuery{
private:
  std::vector<std::pair<int,int>>ptr;
  std::vector<std::vector<int>>dst;
  std::vector<int>stt_par,dep,lr;
  int vsc;
public:
  ContourQuery(){}
  template<typename T>
  ContourQuery(Tree<T>t){
    assert(!t.is_directed());
    int n=t.size();
    t.remove_parent();
    StaticTopTree stt(t);
    dep.resize(n*2-1);
    for(int i=n*2-1;i-->n;){
      dep[stt.left[i]]=dep[stt.right[i]]=dep[i]+1;
    }
    dst.resize(*std::max_element(dep.begin(),dep.begin()+n),std::vector<int>(n,-1));
    ptr.resize(n*2-1);
    std::vector<int>que(n+dst.size());
    int p=0,q=0;
    vsc=n;
    auto dfs=[&](auto self,int v)->std::vector<int> {
      if(v<n){
        return std::vector<int>{v};
      }
      const int d=dep[v];
      int lv=stt.left[v],rv=stt.right[v];
      std::vector<int>lch=self(self,lv);
      p=q=0;
      if(stt.A[lv]==stt.A[rv]){
        for(int x:lch){
          dst[d][x]=1;
          que[q++]=x;
        }
        while(p<q){
          int x=que[p++];
          if(x==stt.B[lv])continue;
          for(const Edge<T>&e:t[x]){
            dst[d][e.to]=dst[d][x]+1;
            que[q++]=e.to;
          }
        }
        int len=dst[d][que[q-1]]+1;
        ptr[lv]=std::make_pair(vsc,len);
        vsc+=len;
      }
      else{
        dst[d][stt.B[lv]]=0;
        bool boundaryA=false;
        if(t.parent(stt.B[lv])==stt.A[lv])que[q++]=~stt.B[lv],boundaryA=true;
        else{
          que[q++]=t.parent(stt.B[lv]);
          dst[d][stt.B[lv]]=0,dst[d][que[0]]=1;
        }
        while(p<q){
          int x=que[p++];
          if(x<0){
            x=~x;
            for(int y:lch)if(x!=y){
              dst[d][y]=dst[d][x]+2;
              que[q++]=y;
            }
          }
          else{
            for(const Edge<T>&e:t[x])if(dst[d][e.to]==-1){
              dst[d][e.to]=dst[d][x]+1;
              que[q++]=e.to;
            }
            int par=t.parent(x);
            if(par==stt.A[lv]){
              if(!boundaryA){
                que[q++]=~x;
                boundaryA=true;
              }
            }
            else if(dst[d][par]==-1){
              dst[d][par]=dst[d][x]+1;
              que[q++]=par;
            }
          }
        }
        int len;
        if(que[q-1]<0)len=q>=2?dst[d][que[q-2]]+1:1;
        else len=dst[d][que[q-1]]+1;
        ptr[lv]=std::make_pair(vsc,len);
        vsc+=len;
      }
      std::vector<int>rch=self(self,rv);
      p=q=0;
      for(int x:rch){
        dst[d][x]=1;
        que[q++]=x;
      }
      while(p<q){
        int x=que[p++];
        if(x==stt.B[rv])continue;
        for(const Edge<T>&e:t[x]){
          dst[d][e.to]=dst[d][x]+1;
          que[q++]=e.to;
        }
      }
      ptr[rv]=std::make_pair(vsc,dst[d][que[q-1]]+1);
      vsc+=dst[d][que[q-1]]+1;
      if(stt.A[lv]==stt.A[rv]){
        if(std::ssize(lch)<std::ssize(rch))std::swap(lch,rch);
        lch.insert(lch.end(),rch.begin(),rch.end());
      }
      return std::move(lch);
    };
    dfs(dfs,n*2-2);
    stt_par=std::move(stt.par);
    lr.resize(n-1);
    for(int i=0;i<n-1;i++)lr[i]=stt.left[i+n]^stt.right[i+n];
  }
  std::vector<int>get_vs(int v)const{
    std::vector<int>res;
    res.reserve(dep[v]+1);
    res.push_back(v);
    int d=dep[v]-1;
    int x=v;
    while(d>=0){
      res.push_back(ptr[v].first+dst[d][x]);
      v=stt_par[v];
      d--;
    }
    return res;
  }
  std::vector<std::pair<int,int>>get_range(int v,int l,int r)const{
    std::vector<std::pair<int,int>>res;
    if(l>=r)return res;
    if(l<=0&&1<=r){
      res.reserve(dep[v]+1);
      res.emplace_back(v,v+1);
    }
    else res.reserve(dep[v]);
    int x=v;
    while(true){
      int par=stt_par[v];
      if(par==-1)break;
      int another=lr[par-std::ssize(lr)-1]^v;
      int d=dep[par];
      int rtov=dst[d][x];
      int nl=std::clamp(l-rtov,0,ptr[another].second);
      int nr=std::clamp(r-rtov,0,ptr[another].second);
      if(nl!=nr)res.emplace_back(ptr[another].first+nl,ptr[another].first+nr);
      v=par;
    }
    return res;
  }
  inline int size()const{return vsc;}
};
#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;
  }
};
template<typename M>
struct DualSegmentTree{
  using S=typename M::S;
  using F=typename M::F;
private:
  int n,z,log2n;
  std::vector<S>dat;
  std::vector<F>lazy;
  inline void push(int i){
    lazy[i*2]=M::composition(lazy[i],lazy[i*2]);
    lazy[i*2+1]=M::composition(lazy[i],lazy[i*2+1]);
    lazy[i]=M::id();
  }
  void path_push(int i){
    int l=lsb(i);
    for(int j=log2n;j>l;j--)push(i>>j);
  }
public:
  DualSegmentTree():n(0),log2n(0),z(0){}
  DualSegmentTree(int n_):n(n_),z(ceil_pow2(n_)){
    log2n=msb(z);
    dat.resize(n,M::e());
    lazy.resize(z*2,M::id());
  }
  DualSegmentTree(const std::vector<S>&init):n(init.size()),z(ceil_pow2((int)init.size())),dat(init){
    log2n=msb(z);
    lazy.resize(z*2,M::id());
  }
  void apply(int l,int r,const F&f){
    l+=z,r+=z;
    path_push(l),path_push(r);
    while(l<r){
      if(l&1)lazy[l]=M::composition(f,lazy[l]),l++;
      if(r&1)--r,lazy[r]=M::composition(f,lazy[r]);
      l>>=1,r>>=1;
    }
  }
  S get(int i){
    i+=z;
    for(int j=log2n;j>=1;j--)push(i>>j);
    return M::mapping(lazy[i],dat[i-z],1);
  }
  void set(int i,const S&x){
    i+=z;
    for(int j=log2n;j>=1;j--)push(i>>j);
    lazy[i]=M::id();
    dat[i-z]=x;
  }
  std::vector<S>get_all(){
    for(int i=1;i<z;i++)push(i);
    std::vector<S>res(n);
    for(int i=0;i<n;i++)res[i]=M::mapping(lazy[i+z],dat[i],1);
    return res;
  }
};
//bbstは壊れる
template<typename T>
struct RangeLinearAddRangeSum{
  using S=std::pair<int,T>;
  using F=std::pair<T,T>;
  static inline S op(const S&x,const S&y){return x.first==-1?y:std::make_pair(x.first,x.second+y.second);}
  static inline S e(){return std::make_pair(-1,T());}
  static inline S mapping(const F&f,const S&x,long long k){return std::make_pair(x.first,x.second+f.first*(x.first*k+(((k-1)|1)*((k&-2)>>1)))+f.second*k);}
  static inline F composition(const F&f,const F&g){return std::make_pair(f.first+g.first,f.second+g.second);}
  static inline F id(){return std::make_pair(T(),T());}
};
/*
偶数:k-1
奇数:k
*/
void SOLVE(){
  int n;
  cin>>n;
  Tree t(n);
  t.read();
  ContourQuery cq(t);
  t.remove_parent();
  LowestCommonAncestor lca(t);
  vector<int>dst(n);
  for(int x:t.bfs_order()){
    for(auto e:t[x])dst[e.to]=dst[e.from]+1;
  }
  auto dist=[&](int u,int v)->int {
    int l=lca.query(u,v);
    return dst[u]+dst[v]-dst[l]*2;
  };
  ll base=0;
  rep(i,n-1)base+=dist(i,i+1);
  vector<ll>ans(n,base);
  using M=RangeLinearAddRangeSum<ll>;
  vector<M::S>init(cq.size());
  rep(i,cq.size())init[i]={i,0};
  DualSegmentTree<RangeLinearAddRangeSum<ll>>seg(init);
  vector<int>leader(cq.size(),-1);
  rep(i,n){
    for(int v:cq.get_vs(i))leader[v]=i;
  }
  debug(leader);
  for(int i=n-2;i>=0;i--){
    for(int v:cq.get_vs(i)){
      ans[i]+=seg.get(v).second;
    }
    ll d=dist(i,i+1);
    for(auto [l,r]:cq.get_range(i+1,0,d)){
      int v=leader[l];
      if(v==-1){
        l++;
        v=leader[l];
      }
      assert(v!=-1);
      int blank=dist(v,i+1);
      seg.apply(l,r,{0,-d});
      seg.apply(l,r,{1,-l+1+blank});
    }
    // rep(k,i)if(dist(k,i+1)<d-1)ans[k]+=-d+dist(k,i+1)+1;
  }
  // for(int i=n-2;i>=0;i--){
  //   rep(k,i){
  //     ll d=1+dist(k,i+1);
  //     if(dist(i,i+1)>d)ans[k]+=d-dist(i,i+1);
  //   }
  // }
  rep(i,n)cout<<ans[i]<<'\n';
}