Problem: Write a program which manipulates a weighted rooted tree $T$ with the following operations:

* $add(v,w)$: add $w$ to all edges from the root to node $u$

* $getSum(u)$: report the sum of weights of all edges from the root to node $u$



The given tree $T$ consists of $n$ nodes and every node has a unique ID from $0$ to $n-1$ respectively where ID of the root is $0$. Note that all weights are initialized to zero.

Constraints

* All the inputs are given in integers
* $ 2 \leq n \leq 100000 $
* $ c_j < c_{j+1} $   $( 1 \leq j \leq k-1 )$
* $ 2 \leq q \leq 200000 $
* $ 1 \leq u,v \leq n-1 $
* $ 1 \leq w \leq 10000 $

Input

The input is given in the following format.

$n$
$node_0$
$node_1$
$node_2$
$:$
$node_{n-1}$
$q$
$query_1$
$query_2$
$:$
$query_{q}$


The first line of the input includes an integer $n$, the number of nodes in the tree.

In the next $n$ lines,the information of node $i$ is given in the following format:


ki c1 c2 ... ck


$k_i$ is the number of children of node $i$, and $c_1$ $c_2$ ... $c_{k_i}$ are node IDs of 1st, ... $k$th child of node $i$.

In the next line, the number of queries $q$ is given. In the next $q$ lines, $i$th query is given in the following format:


0 v w


or


1 u


The first integer represents the type of queries.'0' denotes $add(v, w)$ and '1' denotes $getSum(u)$.

Output

For each $getSum$ query, print the sum in a line.

Examples

Input

6
2 1 2
2 3 5
0
0
0
1 4
7
1 1
0 3 10
1 2
0 4 20
1 3
0 5 40
1 4


Output

0
0
40
150


Input

4
1 1
1 2
1 3
0
6
0 3 1000
0 2 1000
0 1 1000
1 1
1 2
1 3


Output

3000
5000
6000

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
using Int = long long;
//BEGIN CUT HERE
template<typename T,typename E>
struct LinkCutTree{
  struct Node{
    Node *l,*r,*p;
    int idx;
    bool rev;
    T val,dat;
    E laz;
    Node(){}
    Node(int idx,T val,E laz):
      idx(idx),rev(0),val(val),dat(val),laz(laz){l=r=p=nullptr;}
    bool is_root(){
      return !p||(p->l!=this&&p->r!=this);
    }
  };
  
  using F = function<T(T,T)>;
  using G = function<T(T,E)>;
  using H = function<E(E,E)>;
  using S = function<T(T)>;
  F f;
  G g;
  H h;
  S s;
  T ti;
  E ei;
  
  const size_t LIM = 1e6;
  vector<Node> pool;
  size_t ptr;
  
  
  LinkCutTree(F f,G g,H h,T ti,E ei):
    f(f),g(g),h(h),ti(ti),ei(ei),pool(LIM),ptr(0){
    s=[](T a){return a;};
  }
  
  LinkCutTree(F f,G g,H h,S s,T ti,E ei):
    f(f),g(g),h(h),s(s),ti(ti),ei(ei),pool(LIM),ptr(0){}
  
  inline Node* create(){
    return &pool[ptr++];
  }
  
  inline Node* create(int idx,T v){
    return &(pool[ptr++]=Node(idx,v,ei));
  }

  void propagate(Node *t,E v){
    t->laz=h(t->laz,v);
    t->val=g(t->val,v);
    t->dat=g(t->dat,v);
  }

  void toggle(Node *t){
    swap(t->l,t->r);
    t->dat=s(t->dat);
    t->rev^=1;
  }

  void eval(Node *t){
    if(t->laz!=ei){
      if(t->l) propagate(t->l,t->laz);
      if(t->r) propagate(t->r,t->laz);
      t->laz=ei;
    }
    if(t->rev){
      if(t->l) toggle(t->l);
      if(t->r) toggle(t->r);
      t->rev=false;
    }
  }

  void update(Node *t){
    t->dat=t->val;
    if(t->l) t->dat=f(t->l->dat,t->dat);
    if(t->r) t->dat=f(t->dat,t->r->dat);
  }

  void rotR(Node *t){
    Node *x=t->p,*y=x->p;
    if((x->l=t->r)) t->r->p=x;
    t->r=x;x->p=t;
    update(x);update(t);
    if((t->p=y)){
      if(y->l==x) y->l=t;
      if(y->r==x) y->r=t;
      update(y);
    }
  }
  
  void rotL(Node *t){
    Node *x=t->p,*y=x->p;
    if((x->r=t->l)) t->l->p=x;
    t->l=x;x->p=t;
    update(x);update(t);
    if((t->p=y)){
      if(y->l==x) y->l=t;
      if(y->r==x) y->r=t;
      update(y);
    }
  }

  void splay(Node *t){
    eval(t);
    while(!t->is_root()){
      Node *q=t->p;
      if(q->is_root()){
	eval(q);eval(t);
	if(q->l==t) rotR(t);
	else rotL(t);
      }else{
	auto *r=q->p;
	eval(r);eval(q);eval(t);
	if(r->l==q){
	  if(q->l==t) rotR(q),rotR(t);
	  else rotL(t),rotR(t);
	}else{	
	  if(q->r==t) rotL(q),rotL(t);
	  else rotR(t),rotL(t);
	}
      }
    }
  }

  Node* expose(Node *t){
    Node *rp=nullptr;
    for(Node *c=t;c;c=c->p){
      splay(c);
      c->r=rp;
      update(c);
      rp=c;
    }
    splay(t);
    return rp;
  }

  void link(Node *par,Node *c){
    expose(c);
    expose(par);
    c->p=par;
    par->r=c;
  }

  void cut(Node *c){
    expose(c);
    Node *par=c->l;
    c->l=nullptr;
    par->p=nullptr;
  }

  void evert(Node *t){
    expose(t);
    toggle(t);
    eval(t);
  }

  bool is_connected(Node *a,Node *b){
    expose(a);
    while(a->l) a=a->l;
    expose(b);
    while(b->l) b=b->l;
    return a==b;
  }

  Node *lca(Node *a,Node *b){
    expose(a);
    return expose(b);
  }

  void set_propagate(Node *t,E v){
    expose(t);
    propagate(t,v);
    eval(t);
  }
};

//END CUT HERE
//INSERT ABOVE HERE

signed GRL_5_C(){
  int n;
  cin>>n;
  using LCT = LinkCutTree<int,int>;
  LCT::F f=[](int a,int b){return min(a,b);};
  LCT lc(f,f,f,0,0);

  vector<LCT::Node*> v(n);
  for(int i=0;i<n;i++) v[i]=lc.create(i,0);
  for(int i=0;i<n;i++){
    int k;
    cin>>k;
    for(int j=0;j<k;j++){
      int c;
      cin>>c;
      lc.link(v[i],v[c]);
    }
  }
  
  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    int a,b;
    cin>>a>>b;
    cout<<lc.lca(v[a],v[b])->idx<<endl;
  }
  
  return 0;
}
/*
  verified on 2018/06/14
  https://onlinejudge.u-aizu.ac.jp/problems/GRL_5_C
*/

signed GRL_5_D(){
  int n;
  cin>>n;
  using LCT = LinkCutTree<int,int>;
  LCT::F f=[](int a,int b){return a+b;};
  LCT lc(f,f,f,0,0);

  vector<LCT::Node*> v(n);
  for(int i=0;i<n;i++) v[i]=lc.create(i,0);
  for(int i=0;i<n;i++){
    int k;
    cin>>k;
    for(int j=0;j<k;j++){
      int c;
      cin>>c;
      lc.link(v[i],v[c]);
    }
  }
  
  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    int t;
    cin>>t;
    if(t==0){
      int a,b;
      cin>>a>>b;
      lc.expose(v[a]);
      v[a]->val=f(v[a]->val,b);
    }
    if(t==1){
      int a;
      cin>>a;
      lc.expose(v[a]);
      cout<<v[a]->dat<<endl;
    }
  }
  
  return 0;
}
/*
  verified on 2018/06/14
  https://onlinejudge.u-aizu.ac.jp/problems/GRL_5_D
*/


signed GRL_5_E(){
  int n;
  cin>>n;
  using P = pair<Int, Int>;
  using LCT = LinkCutTree<P, Int>;
  auto f=[](P a,P b){return P(a.first+b.first,a.second+b.second);};
  auto g=[](P a,int b){return P(a.first+b*a.second,a.second);};
  auto h=[](Int a,Int b){return a+b;};
  
  LCT lc(f,g,h,P(0,0),0);

  vector<LCT::Node*> v(n);
  for(int i=0;i<n;i++) v[i]=lc.create(i,P(0,1));
  for(int i=0;i<n;i++){
    int k;
    cin>>k;
    for(int j=0;j<k;j++){
      int c;
      cin>>c;
      lc.link(v[i],v[c]);
    }
  }
  
  int q;
  cin>>q;
  Int c=0;
  for(int i=0;i<q;i++){
    int t;
    cin>>t;
    if(t==0){
      int a,b;
      cin>>a>>b;
      lc.set_propagate(v[a],b);
      c+=b;
    }
    if(t==1){
      int a;
      cin>>a;
      lc.expose(v[a]);
      cout<<(v[a]->dat).first-c<<endl;
    }
  }
  
  return 0;
}
/*
  verified on 2018/06/14
  https://onlinejudge.u-aizu.ac.jp/problems/GRL_5_E
*/

signed JOISC2013_DAY4_3(){
  int n,q;
  scanf("%d %d",&n,&q);
  
  using LCT = LinkCutTree<int, int>;
  auto f=[](int a,int b){return a+b;};
  LCT lct(f,f,f,0,0);
  vector<LCT::Node*> vs(n);
  for(int i=0;i<n;i++) vs[i]=lct.create(i,0);

  for(int i=0;i<q;i++){
    int t,a,b=0;
    scanf("%d %d",&t,&a);
    if(t!=2) scanf("%d",&b);
    a--;b--;
    if(t==1) lct.link(vs[b],vs[a]);
    if(t==2) lct.cut(vs[a]);
    if(t==3){
      if(!lct.is_connected(vs[a],vs[b])) puts("-1");
      else printf("%d\n",lct.lca(vs[a],vs[b])->idx+1);
    }
  }
  return 0;
}

/*
  verified on 2018/06/14
  https://beta.atcoder.jp/contests/joisc2013-day4/tasks/joisc2013_spaceships
*/

signed AOJ_2450(){
  int n,q;
  scanf("%d %d",&n,&q);

  using T = tuple<int,int,int,int,int,int,int>;
  using P = pair<int,int>;
  using LCT = LinkCutTree<T, P>;

  vector<vector<int> > G(n); 
  T d1(-1,-1,-1,-1,-1,-1,-1);
  P d0(-1,-114514);
  
  vector<LCT::Node* > vs(n);
  vector<int> ps(n,-1);
  
  auto f=[&](T a,T b){
    int al,ar,as,ava,avi,avl,avr;
    tie(al,ar,as,ava,avi,avl,avr)=a;
    int bl,br,bs,bva,bvi,bvl,bvr;
    tie(bl,br,bs,bva,bvi,bvl,bvr)=b;
    int cl=al,cr=br,cs=as+bs;
    int cva=ava+bva,cvi=max(avi,bvi),cvl=avl,cvr=bvr;
    cvi=max(cvi,avr+bvl);
    cvl=max(cvl,ava+bvl);
    cvr=max(cvr,avr+bva);
    return T(cl,cr,cs,cva,cvi,cvl,cvr);
  };
  
  auto g=[&](T a,P p){
    if(p==d0) return a;
    int al,ar,as,ava,avi,avl,avr;
    tie(al,ar,as,ava,avi,avl,avr)=a;
    int v=p.first,b=p.second;
    if(~v) al=ar=v,as=1;
    if(b>=0) return T(al,ar,as,b*as,b*as,b*as,b*as);
    return T(al,ar,as,b*as,b,b,b);
  };
  
  auto h=[&](P a,P b){a.first++;return b;};
  auto s=
    [&](T a){      
      int al,ar,as,ava,avi,avl,avr;
      tie(al,ar,as,ava,avi,avl,avr)=a;
      swap(al,ar);
      swap(avl,avr);
      return T(al,ar,as,ava,avi,avl,avr);
    };
  
  LCT lct(f,g,h,s,d1,d0);
  
  vector<int> w(n);
  for(int i=0;i<n;i++) scanf("%d",&w[i]);
  for(int i=0;i<n;i++) vs[i]=lct.create(i,g(d1,P(i,w[i])));
  
  for(int i=0;i<n-1;i++){
    int a,b;
    scanf("%d %d",&a,&b);
    a--;b--;
    G[a].emplace_back(b);
    G[b].emplace_back(a);
  }

  for(int i=0;i<n;i++)
    sort(G[i].begin(),G[i].end());

  {
    queue<P> q;
    q.emplace(0,-1);
    while(!q.empty()){
      int v,p;
      tie(v,p)=q.front();q.pop();
      if(~p) lct.link(vs[p],vs[v]);
      ps[v]=p;
      for(int u:G[v]){
	if(u==p) continue;
	q.emplace(u,v);
      }
    }
  }
  
  while(q--){
    int t,a,b,c;
    scanf("%d %d %d %d",&t,&a,&b,&c);
    a--;b--;
    if(t==1){
      lct.evert(vs[a]);
      lct.set_propagate(vs[b],P(-1,c));      
    }
    if(t==2){
      lct.evert(vs[a]);
      lct.expose(vs[b]);
      int vva,vvi,vvl,vvr;
      tie(ignore,ignore,ignore,vva,vvi,vvl,vvr)=vs[b]->dat;
      printf("%d\n",max({vva,vvi,vvl,vvr}));
    }
  }
  
  return 0;
}

/*
  verified on 2018/06/14
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2450
*/

signed AOJ_0367(){
  int n,k;
  cin>>n>>k;
  
  vector<vector<int> > G(n); 
  vector<map<Int, Int> > m(n);
  for(Int i=0;i<n-1;i++){
    Int a,b,c;
    cin>>a>>b>>c;
    G[a].emplace_back(b);
    G[b].emplace_back(a);
    m[a][b]=m[b][a]=c;
  }
  
  vector<Int> w(n,0);
  vector<int> ps(n,-1);
  using T = tuple<Int, Int, Int>;
  auto mget=[&](Int a,Int b){
	      if(ps[a]!=b&&ps[b]!=a) return 0LL;
	      Int res=w[a]+w[b]+m[a][b];
	      if(res%k) return res;
	      return 0LL;
	    };
  
  auto f=[&](T a,T b){
	   if(a>b) swap(a,b);
	   Int al,ar,av;
	   tie(al,ar,av)=a;
	   Int bl,br,bv;
	   tie(bl,br,bv)=b;
	   if(al<0||ar<0) return b;
	   Int cl,cr,cv=av+bv;
	   if(m[al].count(bl)){
	     cl=ar;cr=br;
	     cv+=mget(al,bl);
	   }else if(m[al].count(br)){
	     cl=ar;cr=bl;
	     cv+=mget(al,br);
	   }else if(m[ar].count(bl)){
	     cl=al;cr=br;
	     cv+=mget(ar,bl);
	   }else if(m[ar].count(br)){
	     cl=al;cr=bl;
	     cv+=mget(ar,br);
	   }else{
	     cl=cr=cv=-1;
	   }
	   return T(cl,cr,cv);
	 };
  
  auto g=[&](T a,Int b){b++;return a;};
  auto h=[&](Int a,Int b){b++;return a;};
  
  using LCT = LinkCutTree<T, Int>;
  LCT lct(f,g,h,T(-1,-1,0),0);  
  vector<LCT::Node* > vs(n);
  for(Int i=0;i<n;i++) vs[i]=lct.create(i,T(i,i,0));
  
  {
    using P = pair<Int, Int>;
    queue<P> q;
    q.emplace(0,-1);
    while(!q.empty()){
      int v,p;
      tie(v,p)=q.front();q.pop();
      if(~p) lct.link(vs[p],vs[v]);
      ps[v]=p;
      for(int u:G[v]){
	if(u==p) continue;
	q.emplace(u,v);
      }
    } 
  }
  
  Int q;
  cin>>q;
  while(q--){
    string op;
    cin>>op;
    if(op=="add"){
      Int x,d;
      cin>>x>>d;
      lct.expose(vs[x]);
      w[x]+=d;
      lct.update(vs[x]);
    }
    if(op=="send"){
      Int s,t;
      cin>>s>>t;
      lct.evert(vs[s]);
      lct.expose(vs[t]);
      cout<<get<2>(vs[t]->dat)<<endl;
    }
  }  
  
  return 0;
}

/*
  verified on 2018/06/14
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0367
*/



struct M{
  Int a,b,c,d;
  M():a(1),b(0),c(0),d(1){}
  M(Int a,Int b,Int c,Int d):a(a),b(b),c(c),d(d){}
  //M(const M &v):a(v.a),b(v.b),c(v.c),d(v.d){}
  bool operator!=(const M &x)const{
    return a!=x.a||b!=x.b||c!=x.c||d!=x.d;
  }
  bool operator==(const M &x)const{
    return !(*this!=x);
  }
};

signed YUKI_650(){
  const int MOD=1e9+7;
  using M2 = pair<M, M>;
  using LCT = LinkCutTree<M2, M2>;
  auto f=[MOD](M x,M y){
	   M r(0,0,0,0);
	   r.a=x.a*y.a+x.b*y.c;
	   r.b=x.a*y.b+x.b*y.d;
	   r.c=x.c*y.a+x.d*y.c;
	   r.d=x.c*y.b+x.d*y.d;	   
	   r.a%=MOD;r.b%=MOD;r.c%=MOD;r.d%=MOD;
	   return r;
	 };
  auto f2=[&](M2 x,M2 y){
	    return M2(f(x.first,y.first),f(y.second,x.second));
	  };
  auto g=[](M2 x,M2 y){x.first.a++;return y;};
  auto s=[](M2 x){swap(x.first,x.second);return x;};
  
  int n;
  cin>>n;
  vector<vector<int> > G(n);
  vector<int> X,Y;
  for(int i=1;i<n;i++){
    int a,b;
    cin>>a>>b;
    X.emplace_back(a);
    Y.emplace_back(b);
    G[a].emplace_back(b);
    G[b].emplace_back(a);
  }
  M ti=M();
  M ei(-1,-1,-1,-1);
  LCT lct(f2,g,g,s,M2(ti,ti),M2(ei,ei));

  
  vector<LCT::Node*> vs(n*2-1);
  for(int i=0;i<(int)vs.size();i++) vs[i]=lct.create(i,M2(ti,ti));
  
  vector<map<int, int> > rev(n);
  int idx=n;
  {
    using P = pair<int, int>;
    queue<P> q;
    q.emplace(0,-1);
    while(!q.empty()){
      int v,p;
      tie(v,p)=q.front();q.pop();
      if(~p){
	lct.link(vs[p],vs[idx]);
	lct.link(vs[idx],vs[v]);
	rev[p][v]=rev[v][p]=idx++;
      }
      for(int u:G[v])
	if(u!=p) q.emplace(u,v);
    }
  }
  
  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    char c;
    cin>>c;
    if(c=='x'){
      Int v,a,b,c,d;
      cin>>v>>a>>b>>c>>d;
      int z=rev[X[v]][Y[v]];
      lct.expose(vs[z]);
      vs[z]->val=M2(M(a,b,c,d),M(a,b,c,d));      
      lct.expose(vs[z]);
    }
    if(c=='g'){
      Int x,y;
      cin>>x>>y;
      lct.evert(vs[x]);
      lct.expose(vs[y]);
      M ans=vs[y]->dat.first;
      cout<<ans.a<<" "<<ans.b<<" "<<ans.c<<" "<<ans.d<<endl;
    }
  }
  
  return 0;
}
/*
  verified on 2018/06/14
  https://yukicoder.me/problems/no/650
*/


signed main(){
  //GRL_5_C();
  //GRL_5_D();
  GRL_5_E();
  //JOISC2013_DAY4_3();
  //AOJ_2450();
  //AOJ_0367();
  //YUKI_650();
  return 0;
}