//#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--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 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({a,b,c})-min({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;}
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;
}
template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
  }
  friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
  }
  friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
  }
  friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
  }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

template< typename T >
struct Combination {
  vector< T > _fact, _rfact, _inv;

  Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(ll k) const { return _fact[k]; }

  inline T rfact(ll k) const { return _rfact[k]; }

  inline T inv(ll k) const { return _inv[k]; }

  T P(ll n, ll r) const {
    if(r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }

  T C(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }
  
  T RC(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return rfact(p) * fact(q) * fact(p - q);
  }

  T H(ll n, ll r) const {
    if(n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
  //+1がm個、-1がn個で prefix sumが常にk以上
  T catalan(ll m,ll n,ll k){
    if(n>m-k)return 0;
    else return C(n+m,m)-C(n+m,n+k-1);
  }
};
using modint = ModInt< MOD9 >;modint mpow(ll n, ll x){return modint(n).pow(x);}modint mpow(modint n, ll x){return n.pow(x);}
//using modint=ld;modint mpow(ll n, ll x){return pow(n,x);}modint mpow(modint n, ll x){return pow(n,x);}
using Comb=Combination<modint>;
template<typename T>
struct BIT{
  ll n;
  ll k=1;
  vector<T>data;
  BIT() = default;
  BIT(ll size):n(size){
    data.assign(n,0);
    while(k*2<=n)k*=2;
  }
  void add(ll a,T w){
    for(ll i=a+1;i<=n;i+=i&-i)data[i-1]+=w;
  }
  T sum(ll a){//[0,a)
	  if(a<=0)return 0;
    T ret = 0;
    for(ll i=a;i>0;i-=i&-i)ret+=data[i-1];
    return ret;
  }
  //[a,b)
  T sum(ll a,ll b){return a>=b?0:sum(b)-sum(a);}
  T operator[](ll pos){
    return sum(pos,pos+1);
  }
  ll lower_bound(ll x){
    ll ret=0;    
    for(ll i=k;i>0;i/=2){
      if(ret+i<=n&&data[ret+i-1]<x){
        x-=data[ret+i-1];
        ret+=i;
      }
    }
    return ret;
  }
  ll lower_first(ll x){
    return lower_bound(sum(n)-x+1);
  }
  void print(){
    for(ll i=0;i<n;i++){
      if(i!=0)cout<<" ";
      cout<<(*this)[i];
    }
    cout<<endl;
  }
};
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){
	//非可換クエリ用、配列0を順番を反転したデータ構造に、配列1を通常のデータ構造に
    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]){
          if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[r]+(isEdge?1:i)));
          else ret[i].emplace_back(in[r]+(isEdge?1:i),in[p]+1);
          break;
        }
        if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[head[p]]));
        else 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); 
  }
  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;
  }
};
template<typename T>
struct BIT2{
  ll n;
  ll k=1;
  vector<T>data;
  BIT2() = default;
  BIT2(ll size):n(size){
    n++;
    data.assign(n,0);
    while(k*2<=n)k*=2;
  }
  void add(ll a,T w){
    for(ll i=a+1;i<=n;i+=i&-i)data[i-1]+=w;
  }
  //[l,r)
  void add(ll l,ll r,T w){
	if(l>=r)return;
    add(l,w);add(r,-w);
  }
  T sum(ll a){//[0,a)
	  if(a<=0)return 0;
    T ret = 0;
    for(ll i=a;i>0;i-=i&-i)ret+=data[i-1];
    return ret;
  }
  //[a,b)
  T sum(ll a,ll b){return a>=b?0:sum(b)-sum(a);}
  T operator[](ll pos){
    return sum(0,pos+1);
  }
  ll lower_bound(ll x){
    ll ret=0;    
    for(ll i=k;i>0;i/=2){
      if(ret+i<=n&&data[ret+i-1]<x){
        x-=data[ret+i-1];
        ret+=i;
      }
    }
    return ret;
  }
  void print(){
    for(ll i=0;i<n-1;i++){
      if(i!=0)cout<<" ";
      cout<<(*this)[i];
    }
    cout<<endl;
  }
};
template< typename Monoid, typename OperatorMonoid,typename F, typename G, typename H>
struct LazySegmentTree {
  ll sz, height, n;
  vector< Monoid > data;
  vector< OperatorMonoid > lazy;
  const F f;
  const G g;
  const H h;
  Monoid M1;
  OperatorMonoid OM0;
  LazySegmentTree(int n, const F &f,const G &g, const H &h, Monoid M1, OperatorMonoid OM0):n(n),f(f),g(g),h(h),M1(M1),OM0(OM0){
    sz = 1;
    height = 0;
    while(sz < n) sz <<= 1, height++;
    data.assign(2 * sz, M1);
    lazy.assign(2 * sz, OM0);
  }

  void set(ll k, const Monoid &x) {
    data[k + sz] = x;
  }

  void build() {
    for(ll k = sz - 1; k > 0; k--) {
      data[k] = f(data[2 * k + 0], data[2 * k + 1]);
    }
  }

  inline void propagate(int k) {
    if(lazy[k] != OM0) {
      lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
      lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
      data[k] = reflect(k);
      lazy[k] = OM0;
    }
  }

  inline Monoid reflect(int k) {
    return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
  }

  inline void recalc(int k) {
    while(k >>= 1) data[k] = f(reflect(2 * k + 0), reflect(2 * k + 1));
  }

  inline void thrust(int k) {
    for(ll i = height; i > 0; i--) propagate(k >> i);
  }

  void update(int a, int b, const OperatorMonoid &x) {
	if(a>=b)return;
    thrust(a += sz);
    thrust(b += sz - 1);
    for(ll l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if(l & 1) lazy[l] = h(lazy[l], x), ++l;
      if(r & 1) --r, lazy[r] = h(lazy[r], x);
    }
    recalc(a);
    recalc(b);
  }
  
  void update(int a,const Monoid &x){
    thrust(a += sz);
    data[a] = x;
    lazy[a] = OM0;
    recalc(a);
  }

  Monoid query(int a, int b) {
	if(a>=b)return M1;
    thrust(a += sz);
    thrust(b += sz - 1);
    Monoid L = M1, R = M1;
    for(ll l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if(l & 1) L = f(L, reflect(l++));
      if(r & 1) R = f(reflect(--r), R);
    }
    return f(L, R);
  }

  Monoid operator[](const int &k) {
    return query(k, k + 1);
  }
  Monoid all_prod(){
    return reflect(1);
  }

  template< typename C >
  ll find_subtree(int a, const C &check, Monoid &M, bool type) {
    while(a < sz) {
      propagate(a);
      Monoid nxt = type ? f(reflect(2 * a + type), M) : f(M, reflect(2 * a + type));
      if(check(nxt)) a = 2 * a + type;
      else M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }

  template< typename C >
  ll find_first(int a, const C &check) {
    Monoid L = M1;
    if(a <= 0) {
      if(check(f(L, reflect(1)))) return find_subtree(1, check, L, false);
      return n;
    }
    thrust(a + sz);
    ll b = sz;
    for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if(a & 1) {
        Monoid nxt = f(L, reflect(a));
        if(check(nxt)) return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return n;
  }


  template< typename C >
  ll find_last(int b, const C &check) {
    Monoid R = M1;
    if(b >= sz) {
      if(check(f(reflect(1), R))) return find_subtree(1, check, R, true);
      return -1;
    }
    thrust(b + sz - 1);
    ll a = sz;
    for(b += sz; a < b; a >>= 1, b >>= 1) {
      if(b & 1) {
        Monoid nxt = f(reflect(--b), R);
        if(check(nxt)) return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
  void print(){
    for(ll i=0;i<n;i++)if((*this)[i]==M1)cout<<"x|";else cout<<(*this)[i]<<"|";
    cout<<endl;
  }
};
namespace affine_sum{
  using M=pair<modint,modint>;
  auto f=[](M x,M y)->M{
    return {x.fi+y.fi,x.se+y.se};
  };
  auto g=[](M x,M y)->M{
    return {y.fi*x.fi+x.se*y.se,x.se};
  };
  auto h=[](M x,M y)->M{
    return {x.fi*y.fi,y.fi*x.se+y.se};
  };
  LazySegmentTree<M,M,decltype(f),decltype(g),decltype(h)>make(int n){
    return {n,f,g,h,{0,0},{1,0}};
  }
}
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n;cin>>n;
  auto g=readGraph<int>(n,n-1);
  ll q;cin>>q;
  HLD hld(g);
  vector<modint>two(n+q+1,1);
  rep(i,0,two.size()-1)two[i+1]=two[i]*2;
  auto power=affine_sum::make(n);
  rep(i,0,n){
    power.set(i,{0,1});
  }
  power.build();
  vector<ll>cnt(n);
  BIT2<ll>num(n);
  modint ret=0;
  auto get=[&](ll x,ll y){
    //power.print();
    modint ret=0;
    ll k=hld.lca(x,y);
    auto tmp=hld.query_path(x,y,false);
    for(auto z:tmp){
        ret+=power.query(z.fi,z.se).fi;
    }
    OUT(x,y,ret);
    ret+=two[num[hld.in[k]]];
    OUT(x,y,ret);
    return ret;
  };
  auto add=[&](ll x,ll y,ll ch){
    if(ch==1){
        ret+=get(x,y);
    }
    ll k=hld.lca(x,y);
    cnt[k]+=ch;
    power.update(hld.in[k],{(two[cnt[k]]-1)*two[num[hld.in[k]]],1});
    auto tmp=hld.query_path(x,y,true);
    for(auto z:tmp){
        num.add(z.fi,z.se,ch);
        power.update(z.fi,z.se,{2,0});
    }
    //num.add(hld.in[k],-1);
    if(ch==-1){
        ret-=get(x,y);
    }
  };
  while(q--){
    char c;cin>>c;
    ll ch=1;if(c=='-')ch=-1;
    ll x,y;cin>>x>>y;x--;y--;
    add(x,y,ch);
    cout<<ret<<endl;
  }
  return 0;
}