#pragma region template
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
 
using ll=long long;
using ld=long double;
using vi=vector<int>;
using vll=vector<ll>;
using pi=pair<int,int>;
using pll=pair<ll,ll>;
 
#define overload2(a,b,c,...) c
#define overload3(a,b,c,d,...) d
#define overload4(a,b,c,d,e,...) e
#define overload5(a,b,c,d,e,f,...) f
 
#define TYPE1(T) template<typename T>
#define TYPE2(T,U) template<typename T,typename U>
#define TYPE(...) overload2(__VA_ARGS__,TYPE2,TYPE1)(__VA_ARGS__)
#define TYPES1(T) template<typename... T>
#define TYPES2(H,T) template<typename H,typename... T>
#define TYPES(...) overload2(__VA_ARGS__,TYPES2,TYPES1)(__VA_ARGS__)
 
#define REP4(i,s,n,d) for(int i=(s);i<(n);i+=(d))
#define REP3(i,s,n) REP4(i,s,n,1)
#define REP2(i,n) REP3(i,0,n)
#define REP1(n) REP2(tomato,n)
#define REP(...) overload4(__VA_ARGS__,REP4,REP3,REP2,REP1)(__VA_ARGS__)
 
#define RREP4(i,n,s,d) for(int i=(n)-1;i>=s;i-=d)
#define RREP3(i,n,s) RREP4(i,n,s,1)
#define RREP2(i,n) RREP3(i,n,0)
#define RREP1(n) RREP2(tomato,n)
#define RREP(...) overload4(__VA_ARGS__,RREP4,RREP3,RREP2,RREP1)(__VA_ARGS__)

#define FOR4(a,b,c,d,v) for(auto [a,b,c,d]:v)
#define FOR3(a,b,c,v) for(auto [a,b,c]:v)
#define FOR2(a,b,v) for(auto [a,b]:v)
#define FOR1(a,v) for(auto a:v)
#define FOR(...) overload5(__VA_ARGS__,FOR4,FOR3,FOR2,FOR1)(__VA_ARGS__)

#define AFOR4(a,b,c,d,v) for(auto&[a,b,c,d]:v)
#define AFOR3(a,b,c,v) for(auto&[a,b,c]:v)
#define AFOR2(a,b,v) for(auto&[a,b]:v)
#define AFOR1(a,v) for(auto&a:v)
#define AFOR(...) overload5(__VA_ARGS__,AFOR4,AFOR3,AFOR2,AFOR1)(__VA_ARGS__)

#define CFOR4(a,b,c,d,v) for(const auto&[a,b,c,d]:v)
#define CFOR3(a,b,c,v) for(const auto&[a,b,c]:v)
#define CFOR2(a,b,v) for(const auto&[a,b]:v)
#define CFOR1(a,v) for(const auto&a:v)
#define CFOR(...) overload5(__VA_ARGS__,CFOR4,CFOR3,CFOR2,CFOR1)(__VA_ARGS__)
 
#define ALL(v) v.begin(),v.end()
#define RALL(v) v.rbegin(),v.rend()
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define REVERSE(v) reverse(ALL(v))
#define UNIQUE(v) SORT(v),v.erase(unique(ALL(v)),v.end())
 
TYPES(T) void input(T&... a){ (cin>>...>>a); }
#define DECLARE(T,...) T __VA_ARGS__;input(__VA_ARGS__);
#define INT(...) DECLARE(int,__VA_ARGS__)
#define STR(...) DECLARE(string,__VA_ARGS__)
#define LL(...) DECLARE(long long,__VA_ARGS__)
#define CHR(...) DECLARE(char,__VA_ARGS__)
#define DBL(...) DECLARE(double,__VA_ARGS__)
#define VI(n,v) vi v(n);cin>>v;
#define VLL(n,v) vll v(n);cin>>v;
 
TYPE(T) istream&operator>>(istream&is,vector<T>&v){
  for(auto&a:v)cin>>a;
  return is;
}
TYPE(T) ostream&operator<<(ostream&os,const vector<T>&v){
  if(&os==&cerr)os<<"[";
  REP(i,v.size()){
    os<<v[i];
    if(i+1<v.size())os<<(&os==&cerr?",":" ");
  }
  if(&os==&cerr)os<<"]";
  return os;
}
TYPE(T,S) istream&operator>>(istream&is,pair<T,S>&p){
  cin>>p.first>>p.second;
  return is;
}

#ifdef __LOCAL
 #include <debug>
#else
 #define debug(...) void(0)
#endif

void print(){ cout << '\n'; }
TYPES(T,Ts) void print(const T& a,const Ts&... b){
  cout<<a;
  (cout<<...<<(cout<< ' ',b));
  cout << '\n';
}
 
TYPE(T) using pq=priority_queue<T>;
TYPE(T) using pqg=priority_queue<T,vector<T>,greater<T>>;
TYPE(T) T pick(queue<T>& que){assert(que.size()); T a=que.front();que.pop();return a;}
TYPE(T) T pick(pq<T>& que){assert(que.size()); T a=que.top();que.pop();return a;}
TYPE(T) T pick(pqg<T>& que){assert(que.size()); T a=que.top();que.pop();return a;}
TYPE(T) T pick(stack<T>& sta){assert(sta.size()); T a=sta.top();sta.pop();return a;}
 
string YES(bool f=true){return (f?"YES":"NO");}
string Yes(bool f=true){return (f?"Yes":"No");}
string yes(bool f=true){return (f?"yes":"no");}
 
constexpr int INF=1e9+7;
constexpr ll LINF=ll(1e18)+7;
constexpr ld EPS=1e-10;
 
vi iota(int n){vi a(n);iota(ALL(a),0);return a;}
TYPE(T) vector<pair<T,int>> query_sort(const vector<T>&v){
  vector<pair<T,int>> res(v.size());
  REP(i,v.size())res[i]={v[i],i};
  SORT(res);
  return res;
}
TYPE(T) T rev(T a){ REVERSE(a);return a; }
TYPE(T) void fin(T a){cout<<a<<endl;exit(0);}
TYPE(T) bool chmax(T &a,T b){return (a<b&&(a=b,true));}
TYPE(T) bool chmin(T &a,T b){return (a>b&&(a=b,true));}
TYPES(T,Ns) auto make_vector(T x,int n,Ns ...ns){
  if constexpr(sizeof...(ns)==0)return vector<T>(n,x);
  else return vector(n,make_vector<T>(x,ns...));
}
bool in(const ll S,const int a){return (S>>a)&1;}
int popcount(const ll S){return __builtin_popcountll(S);}
int digit(char c){ return (c>='0' and c<='9' ? c-'0' : -1);}
#pragma endregion template

#include <atcoder/modint>
using namespace atcoder;
using mint=modint1000000007;
ostream& operator<<(ostream &os,mint a){os<<a.val();return os;}
istream& operator>>(istream &is,mint &a){
  long long b;is>>b;a=b;
  return is;
}

struct Edge{
  int from,to;
  Edge()=default;
  Edge(int from,int to):from(from),to(to){}
};

struct Graph{
  int n;
  using edge_type=Edge;
  vector<edge_type> edges;
protected:
  vector<int> in_deg;
  bool prepared;
  class OutgoingEdges{
    Graph* g;
    int l,r;
  public:
    OutgoingEdges(Graph* g,int l,int r):g(g),l(l),r(r){}
    edge_type* begin(){ return &(g->edges[l]); }
    edge_type* end(){ return &(g->edges[r]); }
    edge_type& operator[](int i){ return g->edges[l+i]; }
    int size()const{ return r-l; }
  };
  class ConstOutgoingEdges{
    const Graph* g;
    int l,r;
  public:
    ConstOutgoingEdges(const Graph* g,int l,int r):g(g),l(l),r(r){}
    const edge_type* begin()const{ return &(g->edges[l]); }
    const edge_type* end()const{ return &(g->edges[r]); }
    const edge_type& operator[](int i)const{ return g->edges[l+i]; }
    int size()const{ return r-l; }
  };
public:
  OutgoingEdges operator[](int v){
    assert(prepared);
    return { this,in_deg[v],in_deg[v+1] };
  }
  const ConstOutgoingEdges operator[](int v)const{
    assert(prepared);
    return { this,in_deg[v],in_deg[v+1] };
  }

  bool is_prepared()const{ return prepared; }

  Graph():n(0),in_deg(1,0),prepared(false){}
  Graph(int n):n(n),in_deg(n+1,0),prepared(false){}
  Graph(int n,int m,bool directed=false,int indexed=1):
    n(n),in_deg(n+1,0),prepared(false){ scan(m,directed,indexed); }

  void resize(int n){n=n;}

  void add_arc(int from,int to){
    assert(!prepared);
    assert(0<=from and from<n and 0<=to and to<n);
    edges.emplace_back(from,to);
    in_deg[from+1]++;
  }
  void add_edge(int u,int v){
    add_arc(u,v);
    add_arc(v,u);
  }
  void add_arc(const edge_type&e){
    add_arc(e.from,e.to);
  }
  void add_edge(const edge_type&e){
    add_edge(e.from,e.to);
  }

  void scan(int m,bool directed=false,int indexed=1){
    edges.reserve(directed?m:2*m);
    while(m--){
      int u,v;cin>>u>>v;u-=indexed;v-=indexed;
      if(directed)add_arc(u,v);
      else add_edge(u,v);
    }
    build();
  }

  void build(){
    assert(!prepared);prepared=true;
    for(int v=0;v<n;v++)in_deg[v+1]+=in_deg[v];
    vector<edge_type> new_edges(in_deg.back());
    auto counter=in_deg;
    for(auto&&e:edges)new_edges[ counter[e.from]++ ]=e;
    edges=new_edges;
  }

  void graph_debug()const{
  #ifndef __LOCAL
    return;
  #endif
    assert(prepared);
    for(int from=0;from<n;from++){
      cerr<<from<<";";
      for(int i=in_deg[from];i<in_deg[from+1];i++)
        cerr<<edges[i].to<<" ";
      cerr<<"\n";
    }
  }
};
struct Tree:Graph{
  using Graph::Graph;
  int root=-1;
  vector<int> DFS,BFS,depth;

  void scan_root(int indexed=1){
    for(int i=1;i<n;i++){
      int p;cin>>p;
      add_edge(p-indexed,i);
    }
    build();
  }
  void scan(int indexed=1){
    Graph::scan(n-1,false,indexed);
    build();
  }

  edge_type& parent(int v){
    assert(~root and root!=v);
    return (*this)[v][0];
  }
  OutgoingEdges son(int v){
    assert(~root);
    if(v==root)return {this,in_deg[v],in_deg[v+1]};
    return {this,in_deg[v]+1,in_deg[v+1]};
  }

private:
  void dfs(int v,int pre=-1){
    for(auto&e:(*this)[v]){
      if(e.to==pre)swap((*this)[v][0],e);
      else{
        depth[e.to]=depth[v]+1;
        dfs(e.to,v);
      }
    }
    DFS.push_back(v);
  }
public:
  void build(int r=0){
    if(!is_prepared())Graph::build();
    if(~root){
      assert(r==root);
      return;
    }
    root=r;
    depth=vector<int>(n,0);
    DFS.reserve(n);BFS.reserve(n);
    dfs(root);
    queue<int> que;
    que.push(root);
    while(que.size()){
      int p=que.front();que.pop();
      BFS.push_back(p);
      for(const auto&e:son(p))que.push(e.to);
    }
  }
};
class EdgeVertex{
  int n;
  vector<pair<int,int>> edges;
public:
  EdgeVertex(int n):n(n){
    edges.reserve(n-1);
  }
  int add_edge(int u,int v){
    assert(0<=u and u<n);
    assert(0<=v and v<n);
    edges.emplace_back(u,v);
    return n+int(edges.size())-1;
  }

  Tree build(int root=0){
    assert(edges.size()==n-1);
    Tree T(n*2-1);
    for(int i=0;i<edges.size();i++){
      const auto&[u,v]=edges[i];
      int w=n+i;
      T.add_edge(u,w);
      T.add_edge(v,w);
    }
    T.build(root);
    return T;
  }
};
template<class Monoid>
class SegmentTree{
  using X=typename Monoid::value_type;
  vector<X> dat;
  int n,log,size;

  void update(int i){ dat[i]=Monoid::op(dat[2*i],dat[2*i+1]); }
public:
  SegmentTree():SegmentTree(0){}
  SegmentTree(int n):SegmentTree(vector<X>(n, Monoid::unit())){}
  SegmentTree(vector<X> v):n(v.size()){
    for(log=1;(1<<log)<n;log++){}
    size=1<<log;
    dat.assign(size<<1,Monoid::unit());
    for (int i=0;i<n;++i)dat[size+i]=v[i];
    for (int i=size-1;i>=1;--i) update(i);
  }

  X operator[](int i)const{ return dat[size+i]; }

  void set(int i,const X&x){
    assert(0<=i and i<n);
    dat[i+=size]=x;
    while(i>>=1)update(i);
  }
  void multiply(int i,const X&x){ set(i,Monoid::op(dat[i+size],x));}

  X prod(int L,int R)const{
    assert(0<=L and L<=R and R<=n);
    X vl=Monoid::unit(),vr=Monoid::unit();
    L+=size, R+=size;
    while(L<R){
      if(L&1)Monoid::Rchop(vl,dat[L++]);
      if(R&1)Monoid::Lchop(dat[--R],vr);
      L>>=1,R>>=1;
    }
    return Monoid::op(vl,vr);
  }
  X prod_all()const{ return dat[1]; }

  template <class F>
  int max_right(F& check,int L){
    assert(0<=L && L<=n && check(Monoid::unit()));
    if(L == n) return n;
    L += size;
    X sm = Monoid::unit();
    do {
      while (L % 2 == 0) L >>= 1;
      if (!check(Monoid::op(sm, dat[L]))) {
        while (L < size) {
          L <<= 1;
          if (check(Monoid::op(sm, dat[L])))
            Monoid::Rchop(sm, dat[L++]);
        }
        return L - size;
      }
      Monoid::Rchop(sm, dat[L++]);
    } while ((L & -L) != L);
    return n;
  }

  template <class F>
  int min_left(F& check, int R) {
    assert(0 <= R && R <= n && check(Monoid::unit()));
    if (R == 0) return 0;
    R += size;
    X sm = Monoid::unit();
    do {
      --R;
      while (R > 1 && (R % 2)) R >>= 1;
      if (!check(Monoid::op(dat[R], sm))) {
        while (R < size) {
          ( R <<= 1 )++;
          if (check(Monoid::op(dat[R], sm)))
            Monoid::Lchop(dat[R--], sm);
        }
        return R + 1 - size;
      }
      Monoid::Lchop(dat[R], sm);
    } while ((R & -R) != R);
    return 0;
  }

  X Xor_prod(int l, int r, int xor_val) {
    assert(Monoid::commute);
    X x = Monoid::unit();
    for (int k = 0; k < log + 1; ++k) {
      if (l >= r) break;
      if (l & 1) { Monoid::Rchop(x, dat[(size >> k) + ((l++) ^ xor_val)]); }
      if (r & 1) { Monoid::Rchop(x, dat[(size >> k) + ((--r) ^ xor_val)]); }
      l /= 2, r /= 2, xor_val /= 2;
    }
    return x;
  }

  ostream& operator<<(ostream&os)const{
    os<<"(";
    for(int L=1;L<=size;L<<=1){
      os<<"[";
      for(int j=L;j<(L<<1);j++){
        os<<dat[j];
        if(j+1<(L<<1))os<<",";
      }
      os<<"]";
    }
    os<<")";
    return os;
  }
};
template<typename Algebra>
struct AlgebraReverse:Algebra{
  using X=typename Algebra::value_type;
  static constexpr X op(const X& x, const X& y){ return Algebra::op(y,x); }
  static constexpr void Rchop(X&x,const X&y){ Algebra::Lchop(y,x); }
  static constexpr void Lchop(const X&x,X&y){ Algebra::Rchop(y,x); }
};
template<typename TREE>
struct HLD{
  int n;
  TREE T;
  vector<int> sz,head,id,id2;
  bool prepared;
  HLD(TREE T_):T(T_),n(T_.n),sz(n),head(n),id(n),id2(n),prepared(false){}
private:
  void dfs_sz(int v){
    sz[v]=1;
    for(auto&e:T.son(v)){
      sz[v]+=sz[e.to];
      if(sz[e.to]>sz[T.son(v)[0].to])swap(e,T.son(v)[0]);
    }
  }
  void dfs_hld(int v,int& k){
    id[v]=k++;
    for(int i=0;i<T.son(v).size();i++){
      const auto&e=T.son(v)[i];
      head[e.to]=(i?e.to:head[v]);
      dfs_hld(e.to,k);
    }
    id2[v]=k;
  }
public:
  vector<int> build(int r=0){
    assert(!prepared);prepared=true;
    if(~T.root)assert(T.root==r);
    else T.build(r);
    head[r]=r;
    dfs_sz(r);
    int k=0;
    dfs_hld(r,k);
    return id;
  }

  int lca(int u,int v){
    assert(prepared);
    while(head[u]!=head[v]){
      if(T.depth[head[u]]>T.depth[head[v]])u=T.parent(head[u]).to;
      else v=T.parent(head[v]).to;
    }
    return (T.depth[u]<T.depth[v]?u:v);
  }
  int distance(int u,int v){
    int w=lca(u,v);
    return T.depth[u]+T.depth[v]-T.depth[w]*2;
  }

  using path_t=vector<pair<int,int>>;
  pair<path_t,path_t> path(int u,int v){
    assert(prepared);
    path_t path_u,path_v;
    while(u!=v){
      if(head[u]==head[v]){
        if(T.depth[u]<T.depth[v])
          path_v.emplace_back(id[v],id[u]);
        else
          path_u.emplace_back(id[u],id[v]);
        break;
      }
      if(T.depth[head[u]]<T.depth[head[v]]){
        path_v.emplace_back(id[v],id[head[v]]);
        v=T.parent(head[v]).to;
      }
      else{
        path_u.emplace_back(id[u],id[head[u]]);
        u=T.parent(head[u]).to;
      }
    }
    if(u==v)path_u.emplace_back(id[u],id[u]);
    return {path_u,path_v};
  }

  pair<int,int> subtree(int v){
    assert(prepared);
    return {id[v],id2[v]}; 
  }
};
template<typename TREE,typename Monoid>
struct TreeMonoid{
  using X=typename Monoid::value_type;
  using Monoid_r=AlgebraReverse<Monoid>;
  int n;
  TREE T;
  HLD<Tree> hld;
  vector<int> hld_id,euler_in,euler_out;
  SegmentTree<Monoid> seg;
  SegmentTree<Monoid_r> seg_r; 
  
  TreeMonoid(TREE T,int r=0):T(T),hld(T),n(T.n),seg(n),seg_r(n){
    T.build(r);
    hld_id=hld.build(r);
  }
  TreeMonoid(TREE T,vector<X> a,int r=0):T(T),hld(T),n(T.n){
    T.build(r);
    hld_id=hld.build(r);
    vector<X> hld_a(n);
    for(int v=0;v<n;v++)hld_a[hld_id[v]]=a[v];
    seg=SegmentTree<Monoid>(hld_a);
    if(!Monoid::commute)seg_r=SegmentTree<Monoid_r>(hld_a);
  }

  void set(int v,X x){
    seg.set(hld_id[v],x);
    if(!Monoid::commute)seg_r.set(hld_id[v],x);
  }
  void multiply(int v,X x){
    seg.multiply(hld_id[v],x);
    if(!Monoid::commute)seg_r.multiply(hld_id[v],x);
  }
  X get(int v){ return seg.get(hld_id[v]); }
  
  X path_prod(int u,int v){
    auto [path_u,path_v]=hld.path(u,v);
    X prod_u=Monoid::unit(),prod_v=Monoid::unit();
    for(const auto&[l,r]:path_u){
      X val=(Monoid::commute?seg.prod(r,l+1):seg_r.prod(r,l+1));
      Monoid::Rchop(prod_u,val);
    }
    for(const auto&[l,r]:path_v){
      X val=seg.prod(r,l+1);
      Monoid::Lchop(val,prod_v);
    }
    return Monoid::op(prod_u,prod_v);
  }
  X path_root(int v){ return path(T.root,v); }

  X subtree_prod(int v){
    assert(Monoid::commute);
    auto [l,r]=hld.subtree(v);
    return seg.prod(l,r);
  }
};
#define REP_(i,n) for(int i=0;i<(n);i++)
#define REP2_(i,s,n) for(int i=(s);i<(n);i++)
template<typename K,size_t N>
struct SquareMatrix{
  using value_type=K;
  using vec=array<K,N>;
  using mat=array<vec,N>;
  mat M;

  SquareMatrix(K a=0){ 
    for(vec& v:M)v.fill(0); 
    if(a!=0)REP_(i,N)M[i][i]=a;
  }
  SquareMatrix(const mat&A):M(A){}
  SquareMatrix(const vector<vector<K>>&v){
    assert(v.size()==N and v[0].size()==N);
    REP_(i,N)REP_(j,N)M[i][j]=v[i][j];
  }

  vec& operator[](size_t k){return M[k];}
  const vec& operator[](size_t k)const{return M[k];}
  
  SquareMatrix& operator+=(const SquareMatrix &A){
    REP_(i,N)REP_(j,N)M[i][j]+=A[i][j];
    return *this;
  }
  SquareMatrix& operator-=(const SquareMatrix &A){
    REP_(i,N)REP_(j,N)M[i][j]-=A[i][j];
    return *this;
  }
  SquareMatrix operator+(const SquareMatrix &A)const{ return SquareMatrix(M)+=A; }
  SquareMatrix operator-(const SquareMatrix &A)const{ return SquareMatrix(M)-=A; }

  friend SquareMatrix operator*(const SquareMatrix &A,const SquareMatrix &B){
    SquareMatrix res;
    REP_(i,N)REP_(k,N)REP_(j,N)res[i][j]+=A[i][k]*B[k][j];
    return res;
  }
  SquareMatrix& operator*=(const SquareMatrix &A){
    M=((*this)*A).M;
    return *this;
  }

  SquareMatrix& operator/=(const SquareMatrix&A){ return (*this) *= A.inv(); }
  SquareMatrix operator/(const SquareMatrix&A)const{ return SquareMatrix(M) /= A; }

  bool operator==(const SquareMatrix &A){
    REP_(i,N)REP_(j,N)if(M[i][j]!=A[i][j])return false;
    return true;
  }
  bool operator!=(const SquareMatrix &A){ return !((*this)==A); }
  
  static SquareMatrix I(){ return SquareMatrix(1); }
  
  SquareMatrix pow(long long n)const{
    assert(n>=0);
    SquareMatrix A(M),res(1);
    while(n){
      if(n&1)res*=A;
      A*=A;
      n>>=1;
    }
    return res;
  }

  pair<int,int> GaussJordan(){
    int rnk=0,cnt=0;
    REP_(k,N){
      if(M[rnk][k]==0)
        REP2_(i,rnk+1,N)
          if(M[i][k]!=0){
            swap(M[i],M[rnk]);
            cnt^=1;
            break;
          }
      if(M[rnk][k]==0)continue;
      REP_(i,N)if(i!=rnk){
        K x=M[i][k]/M[rnk][k];
        REP_(j,N)M[i][j]-=M[rnk][j]*x;
      }
      if(++rnk==N)break;
    }
    return {rnk,cnt};
  }

  K det()const{
    SquareMatrix A(M);
    const auto&[rnk,cnt]=A.GaussJordan();
    if(rnk!=N)return 0;
    K res=1;
    REP_(i,N)res*=A[i][i];
    return (cnt?-res:res);
  }

  SquareMatrix inv()const{
    SquareMatrix A(M),B(1);
    REP_(k,N){
      if(A[k][k]==0)
        REP2_(i,k+1,N)
          if(A[i][k]!=0){
            swap(A[i],A[k]);
            swap(B[i],B[k]);
          }
      assert(A[k][k]!=0);
      REP_(i,N)if(i!=k){
        K x=A[i][k]/A[k][k];
        REP_(j,N){
          A[i][j]-=A[k][j]*x;
          B[i][j]-=B[k][j]*x;
        }
      }
      K x=A[k][k];
      REP_(j,N){
        A[k][j]/=x;
        B[k][j]/=x;
      }
    }
    return B;
  }
  
  friend ostream& operator<<(ostream&os,const SquareMatrix &M){ os<<M.M; return os; }
  friend istream& operator>>(istream&is,SquareMatrix &M){ REP_(i,N)REP_(j,N)is>>M.M[i][j]; return is; }
};
#undef REP_
#undef REP2_
template<typename X,bool COMMUTE=true>
struct GroupMultiply{
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x * y; }
  static constexpr void Rchop(X&x, const X&y){ x*=y; }
  static constexpr void Lchop(const X&x, X&y){ 
    if constexpr(COMMUTE){ y*=x; }
    else{ y=x*y;} 
  }
  static constexpr X inverse(const X &x) noexcept { return X(1)/x; }
  static constexpr X power(const X &x, long long n) noexcept { return x.pow(n); }
  static constexpr X unit() { return X(1); }
  static constexpr bool commute = COMMUTE;
};

using MAT=SquareMatrix<mint,2>;

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  INT(n);
  EdgeVertex EV(n);
  REP(n-1){
    INT(u,v);
    EV.add_edge(u,v);
  }
  Tree T=EV.build();

  TreeMonoid<Tree,GroupMultiply<MAT,false>> TM(T);

  INT(q);
  REP(q){
    CHR(c);
    if(c=='x'){
      INT(idx);
      MAT M;
      REP(i,2)REP(j,2)cin>>M[i][j];
      TM.set(n+idx,M);
    }
    else{
      INT(l,r);
      MAT M=TM.path_prod(l,r);
      REP(i,2)REP(j,2)
        cout<<M[i][j]<<"\n "[i+j<2];
    }
  }
}