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;

struct HLDecomposition {
  Int n,pos;
  vector<vector<Int> > G;
  vector<Int> vid, head, sub, hvy, par, dep, inv, type;
  
  HLDecomposition(){}
  HLDecomposition(Int sz):
    n(sz),pos(0),G(n),
    vid(n,-1),head(n),sub(n,1),hvy(n,-1),
    par(n),dep(n),inv(n),type(n){}
  
  void add_edge(Int u, Int v) {
    G[u].push_back(v);
    G[v].push_back(u);
  }

  void build(vector<Int> rs={0}) {
    Int c=0;
    for(Int r:rs){
      dfs(r);
      bfs(r, c++);
    }
  }
  
  void dfs(Int rt) {
    using T = pair<Int, Int>;
    stack<T> st;
    par[rt]=-1;
    dep[rt]=0;
    st.emplace(rt,0);
    while(!st.empty()){
      Int v=st.top().first;
      Int &i=st.top().second;
      if(i<(Int)G[v].size()){
	Int u=G[v][i++];
	if(u==par[v]) continue;
	par[u]=v;
	dep[u]=dep[v]+1;
	st.emplace(u,0);
      }else{
	st.pop();
	Int res=0;
	for(Int u:G[v]){
	  if(u==par[v]) continue;
	  sub[v]+=sub[u];
	  if(res<sub[u]) res=sub[u],hvy[v]=u;
	}
      }
    }
  }

  void bfs(Int r,Int c) {
    Int &k=pos;
    queue<Int> q({r});
    while(!q.empty()){
      Int h=q.front();q.pop();
      for(Int i=h;i!=-1;i=hvy[i]) {
	type[i]=c;
	vid[i]=k++;
	inv[vid[i]]=i;
	head[i]=h;
	for(Int j:G[i])
	  if(j!=par[i]&&j!=hvy[i]) q.push(j);
      }
    }
  }
  
  // for_each(vertex)
  // [l,r] <- attention!!
  void for_each(Int u, Int v, const function<void(Int, Int)>& f) {
    while(1){
      if(vid[u]>vid[v]) swap(u,v);
      f(max(vid[head[v]],vid[u]),vid[v]);
      if(head[u]!=head[v]) v=par[head[v]];
      else break;
    }
  }
  
  // for_each(edge)
  // [l,r] <- attention!!
  void for_each_edge(Int u, Int v, const function<void(Int, Int)>& f) {
    while(1){
      if(vid[u]>vid[v]) swap(u,v);
      if(head[u]!=head[v]){
	f(vid[head[v]],vid[v]);
        v=par[head[v]];
      } else{
	if(u!=v) f(vid[u]+1,vid[v]);
	break;
      }
    }
  }

  Int lca(Int u,Int v){
    while(1){
      if(vid[u]>vid[v]) swap(u,v);
      if(head[u]==head[v]) return u;
      v=par[head[v]];
    }
  }

  Int distance(Int u,Int v){
    return dep[u]+dep[v]-2*dep[lca(u,v)];
  }
};



template <typename T,typename E>
struct SegmentTree{
  typedef function<T(T,T)> F;
  typedef function<T(T,E)> G;
  typedef function<E(E,E)> H;
  typedef function<E(E,Int)> P;
  Int n;
  F f;
  G g;
  H h;
  T d1;
  E d0;
  P p;
  vector<T> dat;
  vector<E> laz;
  SegmentTree(Int n_,F f,G g,H h,T d1,E d0,
	      vector<T> v=vector<T>(),P p=[](E a,Int b){return a;}):
    f(f),g(g),h(h),d1(d1),d0(d0),p(p){
    init(n_);
    if(n_==(Int)v.size()) build(n_,v);
  }
  void init(Int n_){
    n=1;
    while(n<n_) n*=2;
    dat.clear();
    dat.resize(2*n-1,d1);
    laz.clear();
    laz.resize(2*n-1,d0);
  }
  void build(Int n_, vector<T> v){
    for(Int i=0;i<n_;i++) dat[i+n-1]=v[i];
    for(Int i=n-2;i>=0;i--)
      dat[i]=f(dat[i*2+1],dat[i*2+2]);
  }
  inline void eval(Int len,Int k){
    if(laz[k]==d0) return;
    if(k*2+1<n*2-1){
      laz[k*2+1]=h(laz[k*2+1],laz[k]);
      laz[k*2+2]=h(laz[k*2+2],laz[k]);
    }
    dat[k]=g(dat[k],p(laz[k],len));
    laz[k]=d0;
  }
  T update(Int a,Int b,E x,Int k,Int l,Int r){
    eval(r-l,k);
    if(r<=a||b<=l) return dat[k];
    if(a<=l&&r<=b){
      laz[k]=h(laz[k],x);
      return g(dat[k],p(laz[k],r-l));
    }
    return dat[k]=f(update(a,b,x,k*2+1,l,(l+r)/2),
		    update(a,b,x,k*2+2,(l+r)/2,r));
  }
  T update(Int a,Int b,E x){
    return update(a,b,x,0,0,n);
  }
  T query(Int a,Int b,Int k,Int l,Int r){
    eval(r-l,k);
    if(r<=a||b<=l) return d1;
    if(a<=l&&r<=b) return dat[k];
    T vl=query(a,b,k*2+1,l,(l+r)/2);
    T vr=query(a,b,k*2+2,(l+r)/2,r);
    return f(vl,vr);
  }
  T query(Int a,Int b){
    return query(a,b,0,0,n);
  }
  void update(Int k,T x){
    query(k,k+1);//evaluate
    k+=n-1;
    dat[k]=x;
    while(k){
      k=(k-1)/2;
      dat[k]=f(dat[k*2+1],dat[k*2+2]);
    }
  }
};

//INSERT ABOVE HERE
signed main(){
  Int n;
  cin>>n;
  HLDecomposition hld(n);
  for(Int i=0;i<n;i++){
    Int k;
    cin>>k;
    for(Int j=0;j<k;j++){
      Int c;
      cin>>c;
      hld.add_edge(i,c);
    }
  }
  hld.build();
  auto G=hld.G;
  auto vid=hld.vid;
  auto inv=hld.inv;

  SegmentTree<Int, Int>::F f=[](Int a,Int b){return a+b;};
  SegmentTree<Int, Int>::G g=[](Int a,Int b){return a+b;};
  SegmentTree<Int, Int>::H h=[](Int a,Int b){return a+b;};
  SegmentTree<Int, Int>::P p=[](Int a,Int b){return a*b;};
  vector<Int> v(n,0);
  SegmentTree<Int, Int> seg(n,f,g,h,0,0,v,p);
  
  Int q;
  cin>>q;
  for(Int i=0;i<q;i++){
    Int t;
    cin>>t;
    if(t==0){
      Int v,w;
      cin>>v>>w;
      hld.for_each_edge(0,v,[&](Int l,Int r){
	  seg.update(l,r+1,w);
	});
    }
    if(t==1){
      Int u;
      cin>>u;
      Int ans=0;
      hld.for_each_edge(0,u,[&](Int l,Int r){
	  ans+=seg.query(l,r+1);
	});
      cout<<ans<<endl;
    }
  }
  
  return 0;
}