//#define _GLIBCXX_DEBUG

//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

#include<bits/stdc++.h>
using namespace std;


#ifdef LOCAL
#include <debug_print.hpp>
#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define OUT(...) (static_cast<void>(0))
#endif

#define endl '\n'
#define lfs cout<<fixed<<setprecision(15)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)

namespace template_tute{
  using ll = long long;
  using ld = long double;
  const ll MOD1 = 1e9+7;
  const ll MOD9 = 998244353;
  const ll INF = 4.1e18;
  using P = pair<ll, ll>;
  template<typename T> using PQ = priority_queue<T>;
  template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
  template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
  template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
  ll median(ll a,ll b, ll c){return a+b+c-max<ll>({a,b,c})-min<ll>({a,b,c});}
  void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
  void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
  void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
  template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
  template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
  template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
  template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
  template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
  template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
  template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
  template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
  template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
  template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
  template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
  template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
  vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
  template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
  template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
  template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << "(" << p.first << "," << p.second << ")";}
  template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;}
  template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
    auto tmp = v;
    for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
  }
  template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
    rearrange(ord, head);
    rearrange(ord, tail...);
  }
  template<typename T> vector<int> ascend(const vector<T>&v){
    vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
    sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});
    return ord;
  }
  template<typename T> vector<int> descend(const vector<T>&v){
    vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
    sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});
    return ord;
  }
  template<typename T> vector<T> inv_perm(const vector<T>&ord){
    vector<T>inv(ord.size());
    for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
    return inv;
  }
  ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
  ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
  ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
  ll modulo(ll n,ll d){return (n%d+d)%d;};
  template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
  template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
  template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
  template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
  //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
  int popcount(ll x){return __builtin_popcountll(x);};
  int poplow(ll x){return __builtin_ctzll(x);};
  int pophigh(ll x){return 63 - __builtin_clzll(x);};
  template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
  template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
  template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
  template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
  ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
  ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
  ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
  std::ostream &operator<<(std::ostream &dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
      __uint128_t tmp = value < 0 ? -value : value;
      char buffer[128];
      char *d = std::end(buffer);
      do {
        --d;
        *d = "0123456789"[tmp % 10];
        tmp /= 10;
      } while (tmp != 0);
      if (value < 0) {
        --d;
        *d = '-';
      }
      int len = std::end(buffer) - d;
      if (dest.rdbuf()->sputn(d, len) != len) {
        dest.setstate(std::ios_base::badbit);
      }
    }
    return dest;
  }
  namespace converter{
    int dict[500];
    const string lower="abcdefghijklmnopqrstuvwxyz";
    const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    const string digit="0123456789";
    const string digit1="123456789";
    void regi_str(const string &t){
      for(int i=0;i<t.size();i++){
        dict[t[i]]=i;
      }
    }
    void regi_int(const string &t){
      for(int i=0;i<t.size();i++){
        dict[i]=t[i];
      }
    }
    vector<int>to_int(const string &s,const string &t){
      regi_str(t);
      vector<int>ret(s.size());
      for(int i=0;i<s.size();i++){
        ret[i]=dict[s[i]];
      }
      return ret;
    }
    vector<int>to_int(const string &s){
      auto t=s;
      sort(t.begin(),t.end());
      t.erase(unique(t.begin(),t.end()),t.end());
      return to_int(s,t);
    }
    
    vector<vector<int>>to_int(const vector<string>&s,const string &t){
      regi_str(t);
      vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));
      for(int i=0;i<s.size();i++){
        for(int j=0;j<s[0].size();j++){
          ret[i][j]=dict[s[i][j]];
        }
      }
      return ret;
    }
    vector<vector<int>>to_int(const vector<string>&s){
      string t;
      for(int i=0;i<s.size();i++){
        t+=s[i];
      }
      sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());
      return to_int(s,t);
    }
    string to_str(const vector<int>&s,const string &t){
      regi_int(t);
      string ret;
      for(auto z:s)ret+=dict[z];
      return ret;
    }
    vector<string> to_str(const vector<vector<int>>&s,const string &t){
      regi_int(t);
      vector<string>ret(s.size());
      for(int i=0;i<s.size();i++){
        for(auto z:s[i])ret[i]+=dict[z];
      }
      return ret;
    }
  }
  template< typename T = int >
  struct edge {
    int to;
    T cost;
    int id;
    edge():to(-1),id(-1){};
    edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
    operator int() const { return to; }
  };

  template<typename T>
  using Graph = vector<vector<edge<T>>>;
  template<typename T>
  Graph<T>revgraph(const Graph<T> &g){
    Graph<T>ret(g.size());
    for(int i=0;i<g.size();i++){
      for(auto e:g[i]){
        int to = e.to;
        e.to = i;
        ret[to].push_back(e);
      }
    }
    return ret;
  }
  template<typename T>
  Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
    Graph<T> ret(n);
    for(int es = 0; es < m; es++){
      int u,v;
      T w=1;
      cin>>u>>v;u-=indexed,v-=indexed;
      if(weighted)cin>>w;
      ret[u].emplace_back(v,w,es);
      if(!directed)ret[v].emplace_back(u,w,es);
    }
    return ret;
  }
  template<typename T>
  Graph<T> readParent(int n,int indexed=1,bool directed=true){
    Graph<T>ret(n);
    for(int i=1;i<n;i++){
      int p;cin>>p;
      p-=indexed;
      ret[p].emplace_back(i);
      if(!directed)ret[i].emplace_back(p);
    }
    return ret;
  }
}
using namespace template_tute;
template<typename T>
struct TreeDistanceQuery{
  int n;
  const Graph<T> &g;
  vector<bool> used;//既に重心として選ばれたか
  vector<int> sub;//部分木のサイズ
  bool weighted;
  TreeDistanceQuery(const Graph<T> &g, bool weighted = false):n(g.size()),g(g),weighted(weighted){
    sub.assign(g.size(), 0);
    used.assign(g.size(), false);
    build();
  }
  int search_centroid(int root){
    return dfs_search(root, -1, dfs_sz(root, -1) / 2 );
  }
  int dfs_sz(int k, int par){
    sub[k] = 1;
    for(auto e:g[k]){
      if(e.to == par || used[e.to])continue;
      sub[k] += dfs_sz(e.to, k);
    }
    return sub[k];
  }
  int dfs_search(int k,int par, int mid){
    for(auto e:g[k]){
      if(e.to == par || used[e.to])continue;
      if(sub[e.to] > mid)return dfs_search(e.to, k, mid);
    }
    return k;
  }
  vector<vector<pair<int,int>>>belong;
  //所属position, index 区間系の場合最初だけ無視
  vector<vector<T>>dist;
  //dist[i][j]:=position i, index jの重心からの距離
  vector<vector<T>>border;
  int ass_position = 0;
  void build(){
    belong.resize(n);
    dist.resize(4*n);
    run(0);
    if(!weighted){
      border.resize(4*n);
      for(int i=0;i<4*n;i++){
        if(dist[i].empty())continue;
        border[i].resize(max(dist[i])+2);
        border[i].back() = dist[i].size();
        for(int j=dist[i].size()-1;j>=0;j--){
          border[i][dist[i][j]]=j;
        }
      }
    }
  }
  void run(int v){
    int cent = search_centroid(v);
    used[cent] = true;
    using pi = pair<int, int>;
    priority_queue<pi, vector<pi>, greater<pi>>pq;
    vector<vector<pair<T,int>>>childs;
    for(auto e:g[cent]){
      if(used[e.to])continue;
      run(e.to);
      queue<tuple<T, int, int>>que;
      childs.emplace_back();
      que.emplace(e.cost, e.to, cent);
      while(!que.empty()){
        auto [d, k, par] = que.front();
        childs.back().emplace_back(d, k);
        que.pop();
        for(auto e:g[k]){
          if(e.to == par || used[e.to])continue;
          que.emplace(d + e.cost, e.to, k);
        }
      }
      if(weighted)sort(childs.back().begin(), childs.back().end());
      pq.emplace(childs.back().size(), childs.size() - 1);
    }
    while(pq.size() > 1){
      auto [sz1, idx1] = pq.top();
      pq.pop();
      auto [sz2, idx2] = pq.top();
      pq.pop();
      dist[ass_position].reserve(childs[idx1].size());
      for(auto [d, vi]: childs[idx1]){
        belong[vi].emplace_back(ass_position, dist[ass_position].size());
        dist[ass_position].push_back(d);
      }
      ass_position++;
      dist[ass_position].reserve(childs[idx2].size());
      for(auto [d, vi]: childs[idx2]){
        belong[vi].emplace_back(ass_position, dist[ass_position].size());
        dist[ass_position].push_back(d);
      }
      ass_position++;
      vector<pair<T,int>>tmp;
      merge(childs[idx1].begin(),childs[idx1].end(),childs[idx2].begin(),childs[idx2].end(),back_inserter(tmp));
      childs[idx2] = tmp;
      pq.emplace(tmp.size(), idx2);
    }
    if(pq.empty()){
      pq.emplace(0, 0);
      childs.emplace_back();
    }
    int idx = pq.top().second;
    dist[ass_position].reserve(childs[idx].size() + 1);
    belong[cent].insert(belong[cent].begin(), make_pair(ass_position, dist[ass_position].size()));
    dist[ass_position].push_back(0);
    for(auto [d, vi]: childs[idx]){
      belong[vi].emplace_back(ass_position, dist[ass_position].size());
      dist[ass_position].push_back(d);
    }
    ass_position++;
    belong[cent].emplace_back(ass_position,0);
    dist[ass_position].push_back(0);
    ass_position++;
    used[cent] = false;
  }
  //[l,r)
  vector<tuple<int,int,int>>query(int v,T l,T r){
    vector<tuple<int,int,int>>ret;
    for(int i = 1; i < belong[v].size(); i++){
      auto [pos, idx] = belong[v][i];
      T vd = dist[pos][idx];
      int li, ri;
      if(weighted){
        li = lower_bound(dist[pos^1].begin(), dist[pos^1].end(), l - vd) - dist[pos^1].begin();
        ri = lower_bound(dist[pos^1].begin(), dist[pos^1].end(), r - vd) - dist[pos^1].begin();
      }
      else{
        li = border[pos^1][clamp<T>(l - vd, 0, T(border[pos^1].size()) - 1)];
        ri = border[pos^1][clamp<T>(r - vd, 0, T(border[pos^1].size()) - 1)];
      }
      ret.emplace_back(pos^1, li, ri);
    }
    return ret;
  }
};

template< typename sum_t, typename key_t >
struct ReRooting {
  struct Edge {
    int to;
    key_t data;
    sum_t dp, ndp;
  };

  using F = function< sum_t(sum_t, sum_t) >;
  using G = function< sum_t(sum_t, key_t) >;

  vector< vector< Edge > > g;
  vector< sum_t > subdp, dp;
  vector< sum_t > init;
  const sum_t ident;
  const F f;
  const G gg;

  ReRooting(int V, const F f, const G g, const sum_t &ident)
      : g(V), f(f), gg(g), ident(ident), subdp(V, ident), dp(V, ident), init(V, ident) {}

  void add_edge(int u, int v, const key_t &d) {
    g[u].emplace_back((Edge) {v, d, ident, ident});
    g[v].emplace_back((Edge) {u, d, ident, ident});
  }

  void add_edge_bi(int u, int v, const key_t &d, const key_t &e) {
    g[u].emplace_back((Edge) {v, d, ident, ident});
    g[v].emplace_back((Edge) {u, e, ident, ident});
  }

  void set(int idx, sum_t s){
    subdp[idx] = s;
    init[idx] = s;
  }
  void dfs_sub(int idx, int par) {
    for(auto &e : g[idx]) {
      if(e.to == par) continue;
      dfs_sub(e.to, idx);
      subdp[idx] = f(subdp[idx], gg(subdp[e.to], e.data));
    }
  }

  void dfs_all(int idx, int par, const sum_t &top) {
    sum_t buff{init[idx]};
    for(int i = 0; i < (int) g[idx].size(); i++) {
      auto &e = g[idx][i];
      e.ndp = buff;
      e.dp = gg(par == e.to ? top : subdp[e.to], e.data);
      buff = f(buff, e.dp);
    }
    dp[idx] = buff;
    buff = ident;
    for(int i = (int) g[idx].size() - 1; i >= 0; i--) {
      auto &e = g[idx][i];
      if(e.to != par) dfs_all(e.to, idx, f(e.ndp, buff));
      e.ndp = f(e.ndp, buff);
      buff = f(buff, e.dp);
    }
  }

  vector< sum_t > build() {
    dfs_sub(0, -1);
    dfs_all(0, -1, ident);
    return dp;
  }
};
template<typename T>
struct HLD{
  using D=long long;
  int n;
  vector<int>sz;//部分木サイズ
  vector<D>dep;
  vector<int>par;
  vector<int>head;
  Graph<T> &g;//隣接リスト
  vector<edge<T>>edges;//データ構造に乗せるedge列
  vector<int>in,out;//[in,out)で部分木、[ina,inb]でa~bのパス(aが上)
  vector<int>comp;//連結成分の根
  //inは頂点のindexを表す。また、edge列の下側の頂点である
  HLD(Graph<T> &g,int r=-1):g(g),n(g.size()){
    hld_build(r);
  }
  void hld_build(int root = -1){
    in.assign(n,-1);out.assign(n,-1);dep.assign(n,0);
    par.assign(n,-1);head.assign(n,-1);sz.assign(n,-1);comp.assign(n,-1);
    edges.assign(n,edge<T>());
    if(root == -1){//根がどこでも良い場合(森でも可)
      for(int i=0;i<n;i++){
        if(sz[i] == -1){
          head[i] = i;
          dfs_sz(i, 0, i);
          dfs_hld(i);
        }
      }
    }
    else{
      head[root] = root;
      dfs_sz(root, 0, root);
      dfs_hld(root);
    }
  }
  void dfs_sz(int k, D d,int r){
    sz[k] = 1;
    comp[k] = r;
  dep[k] = d;
    for(auto &e: g[k]){
      if(e.to == par[k])continue;
      par[e.to] = k;
      dfs_sz(e.to, d+e.cost, r);
      sz[k] += sz[e.to];
      if(g[k][0].to==par[k]||sz[e.to] > sz[g[k][0].to])swap(e, g[k][0]);
    }
  }
  int time = 0;
  void dfs_hld(int k){
    in[k] = time++;
    for(auto e:g[k]){
      if(e.to == par[k])continue;
      head[e.to] = (e.to == g[k][0].to ? head[k]: e.to);
      edges[time] = e;
      dfs_hld(e.to);
    }
    out[k] = time;
  }
  int lca(int p,int q){
    while(1){
      if(in[p] < in[q])swap(p,q);
      if(head[p] == head[q])return q;
      p = par[head[p]];
    }
  }
  vector<pair<int,int>>query_path(int p,int q,bool isEdge){
    int r=lca(p,q);
    vector<pair<int,int>>ret;
    for(int i=0;i<2;i++){
      if(i == 1)swap(p,q);
      while(1){
        if(isEdge&&p==r)break;
        if(head[p]==head[r]){
          ret.emplace_back(in[r]+(isEdge?1:i),in[p]+1);
          break;
        }
        ret.emplace_back(in[head[p]],in[p]+1);
        p = par[head[p]];
      }
    }
    return ret;
  }
  vector<vector<pair<int,int>>>query_order_path(int p,int q,bool isEdge){
  //配列0:反転 配列1:通常
    vector<vector<pair<int,int>>>ret(2);
    int r=lca(p,q);
    for(int i=0;i<2;i++){
      if(i == 1)swap(p,q);
      while(1){
        if(isEdge&&p==r)break;
        if(head[p]==head[r]){
          ret[i].emplace_back(in[r]+(isEdge?1:i),in[p]+1);
          break;
        }
        ret[i].emplace_back(in[head[p]],in[p]+1);
        p = par[head[p]];
      }
    }
    reverse(ret[1].begin(), ret[1].end());
    return ret;
  }
  pair<int,int>query_subtree(int p,bool isEdge){
    return make_pair(in[p]+isEdge,out[p]);
  }
  //uのv方向の子 子孫関係は前もって確認すること(in,outを見る)
  int child(int u,int v)const{
    while(1){
      if(head[u]==head[v]){
        v=g[u][0].to;
        break;
      }
      v=head[v];
      if(par[v]==u)break;
      v=par[v];
    }
    return v;
  }
  //uをv方向に一つ進めた頂点
  int move(int u,int v)const{
    assert(u!=v);
    if(in[u]<in[v]&&in[v]<out[u])return child(u,v);
    else return par[u];
  }
  D dist(int u,int v){
    return dep[u]+dep[v]-2*dep[lca(u,v)];
  }
  vector<int>rev_in;
  int climb(int u,int k){
    if(rev_in.empty()){
      rev_in.resize(n);
      for(int i=0;i<n;i++)rev_in[in[i]]=i;
    }
    int nd=max<int>(dep[u]-k, 0);
    while(dep[u]>nd){
      if(dep[head[u]]>nd){
        u=par[head[u]];
      }
      else{
        u=rev_in[in[head[u]]+nd-dep[head[u]]];
      }
    }
    return u;
  }
  int jump(int from,int to, int k){
    int r = lca(from, to);
    int d1 = dep[from] - dep[r];
    int d2 = dep[to] - dep[r];
    if(d1 + d2 < k)return -1;
    else if(k <= d1)return climb(from, k);
    else return climb(to, d1 + d2 - k);
  }
  //from,to,c  from->to辺をc進んだところに到着 重み0は進めるだけ進む
  //根に到達する場合は(根,根,0)を返す
  vector<T>dep_in;
  tuple<int,int,T>climb_weighted(int u,T k){
    if(rev_in.empty()){
      rev_in.resize(n);
      for(int i=0;i<n;i++)rev_in[in[i]]=i;
    }
    if(dep_in.empty()){
      dep_in.resize(n);
      for(int i=0;i<n;i++)dep_in[in[i]]=dep[i];
    }
    if(dep[u]<=k)return make_tuple(rev_in[0],rev_in[0],0);
    T nd=max<T>(dep[u]-k, 0);
    while(1){
      if(dep[head[u]]>=nd){
        u=head[u];
        if(dep[par[u]]<nd){
          return make_tuple(u,par[u],dep[u]-nd);
        }
        u=par[u];
      }
      else{
        int l=in[head[u]],r=in[u];
        int idx=lower_bound(dep_in.begin()+l,dep_in.begin()+r+1,nd)-dep_in.begin();
        return make_tuple(rev_in[idx],rev_in[idx-1],dep[rev_in[idx-1]]-nd);
      }
    }
    assert(false);
  }
  template<typename I>
  Graph<T>lca_tree(vector<I>&v){
    auto compare=[&](int x,int y){return in[x]<in[y];};
    sort(v.begin(),v.end(),compare);
    int sz1=v.size();
    for(int i=0;i<sz1-1;i++)v.push_back(lca(v[i],v[i+1]));
    sort(v.begin(),v.end(),compare);
    v.erase(unique(v.begin(),v.end()),v.end());
    int sz2=v.size();
    Graph<T>ret(sz2);
    stack<int>st;
    for(int i=0;i<sz2;i++){
      while(!st.empty()&&out[v[st.top()]]<=in[v[i]])st.pop();
      if(!st.empty()){
        ret[st.top()].emplace_back(i,dep[v[i]]-dep[v[st.top()]]);
        ret[i].emplace_back(st.top(),dep[v[i]]-dep[v[st.top()]]);
      }
      st.push(i);
    }
    return ret;
  }
};
void solve(){
	ll res=0,buf=0;
  bool judge = true;

  int n;cin>>n;
  auto g1=readGraph<int>(n,n-1);
  auto g2=readGraph<int>(n,n-1);
  TreeDistanceQuery<int>tdq(g1);
  HLD hld(g2);
  vector<vector<int>>tdv(tdq.dist.size());
  rep(i,0,tdq.dist.size())tdv[i].resize(tdq.dist[i].size(),-1);
  rep(i,0,n){
    for(auto [pos,idx]:tdq.belong[i]){
      tdv[pos][idx]=i;
    }
  }
  using ull=unsigned long long;
  ull ret=0;
  vector<pair<int,int>>td(n,MP(-1,-1));
  for(int i=0;i<tdq.dist.size();i+=2){
    if(tdq.dist[i].empty())continue;
    vector<int>ver;
    rep(j,i,i+2){
      rep(o,0,tdq.dist[j].size()){
        if(tdv[j][o]!=-1){
          ver.push_back(tdv[j][o]);
          td[tdv[j][o]]=MP(j-i,tdq.dist[j][o]);
        }
      }
    }
    auto tree=hld.lca_tree(ver);
    using pi=pair<ull,ull>;
    auto f1=[&](pi x,pi y){return MP(x.fi+y.fi,x.se+y.se);};
    auto f2=[&](pi x,ull y){return MP(x.fi+x.se*y,x.se);};
    OUT("-----");
    OUT(td);
    rep(tt,0,2){
    ReRooting<pi,ull>rr(tree.size(),f1,f2,MP(0,0));
      rep(j,0,tree.size()){
        for(auto e:tree[j]){
          if(e.to<j)continue;
          OUT(j,e.to,e.cost);
          rr.add_edge(j,e.to,e.cost);
        }
      }
      rep(j,0,ver.size()){
        if(td[ver[j]].fi==-1)continue;
        OUT(td[ver[j]],tt);
        if(td[ver[j]].fi==tt){
          rr.set(j,MP(0,1));
          OUT(j);
        }
      }
      auto dp=rr.build();
      OUT(ver,dp);
      OUT(td,tt);
      rep(j,0,ver.size()){
        if(td[ver[j]].fi==-1)continue;
        if(td[ver[j]].fi==(tt^1)){
          OUT(j,dp[j],td[ver[j]]);
          ret+=dp[j].fi*td[ver[j]].se;
        }
      }
    }

    rep(j,i,i+2){
      rep(o,0,tdq.dist[j].size()){
        if(tdv[j][o]!=-1){
          td[tdv[j][o]]=MP(-1,-1);
        }
      }
    }
  }
  cout<<ret*2<<endl;
}

int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  int T = 1;
  //cin>>T;
  while(T--){
    solve();
  }
  return 0;
}