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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#include <tuple>
#define mkp make_pair
#define mkt make_tuple
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;
template<class T> void chmin(T &a,const T &b){if(a>b) a=b;}
template<class T> void chmax(T &a,const T &b){if(a<b) a=b;}

struct Edge{
    int to,id;
    ll dist;
    Edge(int to,ll dist=1,int id=0):to(to),dist(dist),id(id){}
};

// this class's update method is empty.
struct HeavyLightDecomposition{
    vector<vector<Edge>> g;
    vector<int> in,out,head,par,dep,sz;
    int times;
    int root;

    HeavyLightDecomposition(int V,vector<vector<Edge>> &G,int root=0):
        g(G),in(V),out(V),head(V),par(V),dep(V),sz(V),root(root){
            times=0;
            sz_dfs(root,-1);
            hld_dfs(root,-1);
    }
    
    void sz_dfs(int now,int p){
        par[now]=p;
        sz[now]=1;
        if(p==-1) dep[now]=0;
        else dep[now]=dep[p]+1;

        for(auto &e:g[now]){
            if(e.to==p) continue;
            sz_dfs(e.to,now);
            sz[now]+=sz[e.to];
            if(sz[e.to]>sz[g[now][0].to]) swap(e,g[now][0]);
        }
    }

    void hld_dfs(int now,int p){
        in[now]=times++;
        for(auto e:g[now]){
            if(e.to==p) continue;
            head[e.to]=(e.to == g[now][0].to ? head[now] : e.to);
            hld_dfs(e.to,now);
        }
        out[now]=times;
    }


    int lca(int u,int v){
        for(;;v=par[head[v]]){
            if(in[u]>in[v]) swap(u,v);
            if(head[u]==head[v]) return u;
        }
    }
    int distance(int u,int v){
        return dep[u]+dep[v]-2*dep[lca(u,v)];
    }

    /*ex)
        hld.update(u,x,[&](int a,int b,ll x){
            seg.add(a,b,x);
        });
    */
    template<class T,class G>
    void update(int u,int v,const T &x,const G &g){//辺の時は0を使わない(INFのまま)
        //g(in[v]+1,out[v],x);//部分木(辺)
        //g(in[v],out[v],x);//部分木（頂点）
        //g(in[v],in[v]+1,x);//一点
        for(;;v=par[head[v]]){
            if(in[u]>in[v]) swap(u,v);
            if(head[u]==head[v]) break;
            g(in[head[v]],in[v]+1,x);
        }
        if(u==v) return;
        g(in[u]+1,in[v]+1,x);
    }

    /*ex)
        ll ans=0;
        hld.query(u,v,[&](int a,int b){
            ans+=seg.getSum(a,b);
        },true);
    */
    template<class F>
    void query(int u,int v,const F &f,bool isedge){
        for(;;v=par[head[v]]){
            if(in[u]>in[v]) swap(u,v);
            if(head[u]==head[v]) break;
            f(in[head[v]],in[v]+1);
        }
        if(isedge&&u==v) return;
        f(in[u]+isedge,in[v]+1);
    }
};

class LazySegmentTree{
private:
  int n;
  vector<ll> node,lazy;

public:
  LazySegmentTree(vector<ll> v){
      n=1;
      while(n<v.size()) n*=2;
      node.resize(2*n-1,0);
      lazy.resize(2*n-1,0);
      
      for(int i=0;i<v.size();i++) node[i+n-1]=v[i];
      for(int i=n-2;i>=0;i--) node[i]=node[2*i+1]+node[2*i+2];
  }

  void eval(int k,int l,int r){
      if(lazy[k]!=0){
          node[k]+=lazy[k];
          if(r-l>1){
              lazy[2*k+1]+=lazy[k]/2;
              lazy[2*k+2]+=lazy[k]/2;
          }
          lazy[k]=0;
      }
  }

  void add(int a,int b,ll x,int k=0,int l=0,int r=-1){
      if(r<0) r=n;
      eval(k,l,r);
      if(b<=l||r<=a) return;
      if(a<=l&&r<=b){
          lazy[k]+=(r-l)*x;
          eval(k,l,r);
      }else{
          add(a,b,x,2*k+1,l,(r+l)/2);
          add(a,b,x,2*k+2,(r+l)/2,r);
          node[k]=node[2*k+1]+node[2*k+2];
      }
  }

  ll getSum(int a,int b,int k=0,int l=0,int r=-1){
      if(r<0) r=n;
      eval(k,l,r);
      if(b<=l||r<=a) return 0;
      if(a<=l&&r<=b) return node[k];

      ll vl,vr;
      vl=getSum(a,b,2*k+1,l,(l+r)/2);
      vr=getSum(a,b,2*k+2,(l+r)/2,r);
      return vl+vr;
  }
};

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  int N;
  cin>>N;
  vector<vector<Edge>> g(N);
  rep(i,N){
      int K;cin>>K;
      rep(j,K){
          int a;cin>>a;
          g[i].push_back(a);
      }
  }

  HeavyLightDecomposition hld(N,g);
  LazySegmentTree seg(vector<ll> (N,0));
  
  int Q;
  cin>>Q;
  rep(q,Q){
      int t;cin>>t;
      if(t==0){
          int v,w;
          cin>>v>>w;
          hld.update(0,v,w,[&](int a,int b,ll x){
              seg.add(a,b,x);
          });
      }else{
          int u;cin>>u;
          ll ans=0;
          hld.query(0,u,[&](int a,int b){
              ans+=seg.getSum(a,b);
          },true);
          cout<<ans<<endl;
      }
  }

  return 0;
}