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;
typedef long long ll;
#define rep(i,n) for (ll i=0;i<(n);++i)
const ll MOD=1e9+7;
//const ll MOD=998244353;

class HeavyLightDecomposition{
    private:
    void dfs_sz(int v){
        if (G[v].size()&&G[v][0]==par[v]) swap(G[v][0],G[v].back());
        for (int &u:G[v]){
            if (u==par[v]) continue;
            par[u]=v; dep[u]=dep[v]+1;
            dfs_sz(u);
            sub[v]+=sub[u];
            if (sub[u]>sub[G[v][0]]) swap(u,G[v][0]);
        }
    }
    void dfs_hld(int v,int c,int &times){
        vid[v]=times++; type[v]=c;
        for (int u:G[v]){
            if (u==par[v]) continue;
            head[u]=(u==G[v][0]?head[v]:u);
            dfs_hld(u,c,times);
        }
    }
    public:
    vector<vector<int>> G;
    vector<int> vid,head,sub,par,dep,type;
    HeavyLightDecomposition(int n):
        G(n),vid(n,-1),head(n),sub(n,1),par(n,-1),dep(n,0),type(n){}
    void add_edge(int u,int v){
        G[u].emplace_back(v);
        G[v].emplace_back(u);
    }
    void build(vector<int> rs={0}){
        int c=0,times=0;
        for (int r:rs){
            dfs_sz(r);
            head[r]=r;
            dfs_hld(r,c++,times);
        }
    }
    int lca(int u,int v){
        for (;;v=par[head[v]]){
            if (vid[u]>vid[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)];
    }
    template<typename F>
    void update_path(int u,int v,const F &f,bool edge=false){
        for (;;v=par[head[v]]){
            if (vid[u]>vid[v]) swap(u,v);
            if (head[u]==head[v]) break;
            f(vid[head[v]],vid[v]+1);
        }
        f(vid[u]+edge,vid[v]+1);
    }
    template<typename F>
    void update_sub(int u,const F &f,bool edge=false){
        f(vid[u]+edge,vid[u]+sub[u]);
    }
    template<typename T,typename Q,typename F>
    T query(int u,int v,const T &id,const Q &q,const F &f,bool edge=false){
        T l=id,r=id;
        for (;;v=par[head[v]]){
            if (vid[u]>vid[v]) swap(u,v),swap(l,r);
            if (head[u]==head[v]) break;
            l=f(l,q(vid[head[v]],vid[v]+1));
        }
        return f(r,f(l,q(vid[u]+edge,vid[v]+1)));
    }
};

template<typename Monoid,typename OperatorMonoid>
struct LazySegmentTree{
    typedef function<Monoid(Monoid,Monoid)> F;
    typedef function<Monoid(Monoid,OperatorMonoid)> G;
    typedef function<OperatorMonoid(OperatorMonoid,OperatorMonoid)> H;
    int n,hi;
    F f;
    G g;
    H h;
    Monoid id0;
    OperatorMonoid id1;
    vector<Monoid> dat;
    vector<OperatorMonoid> laz;
    LazySegmentTree(int n_,F f,G g,H h,Monoid id0,OperatorMonoid id1):
                    f(f),g(g),h(h),id0(id0),id1(id1){init(n_);}
    void init(int n_){
        n=1,hi=0;
        while(n<n_) n<<=1,++hi;
        dat.assign(n<<1,id0);
        laz.assign(n<<1,id1);
    }
    void build(const vector<Monoid> &v){
        for (int i=0;i<v.size();++i) dat[i+n]=v[i];
        for (int i=n-1;i;--i) dat[i]=f(dat[i<<1|0],dat[i<<1|1]);
    }
    inline Monoid reflect(int k){
        return laz[k]==id1?dat[k]:g(dat[k],laz[k]);
    }
    inline void propagate(int k){
        if (laz[k]==id1) return;
        laz[k<<1|0]=h(laz[k<<1|0],laz[k]);
        laz[k<<1|1]=h(laz[k<<1|1],laz[k]);
        dat[k]=reflect(k);
        laz[k]=id1;
    }
    inline void thrust(int k){
        for (int i=hi;i;--i) propagate(k>>i);
    }
    inline void recalc(int k){
        while(k>>=1) dat[k]=f(reflect(k<<1|0),reflect(k<<1|1));
    }
    void update(int a,int b,OperatorMonoid x){
        thrust(a+=n),thrust(b+=n-1);
        for (int l=a,r=b+1;l<r;l>>=1,r>>=1){
            if (l&1) laz[l]=h(laz[l],x),++l;
            if (r&1) --r,laz[r]=h(laz[r],x);
        }
        recalc(a),recalc(b);
    }
    void set_val(int k,Monoid x){
        thrust(k+=n);
        dat[k]=x,laz[k]=id1;
        recalc(k);
    }
    Monoid query(int a,int b){
        if (a>=b) return id0;
        thrust(a+=n),thrust(b+=n-1);
        Monoid vl=id0,vr=id0;
        for (int l=a,r=b+1;l<r;l>>=1,r>>=1){
            if (l&1) vl=f(vl,reflect(l++));
            if (r&1) vr=f(reflect(--r),vr);
        }
        return f(vl,vr);
    }
    Monoid operator[](int i){
        return query(i,i+1);
    }
};

typedef pair<ll,ll> Pll;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n; cin >> n;
    HeavyLightDecomposition HLD(n);
    rep(i,n){
        int k; cin >> k;
        rep(j,k){
            int c; cin >> c;
            HLD.add_edge(i,c);
        }
    }
    HLD.build();
    auto f=[](Pll a,Pll b){return Pll{a.first+b.first,a.second+b.second};};
    auto g=[](Pll a,ll x){return Pll{a.first+x*a.second,a.second};};
    auto h=[](ll a,ll b){return a+b;};
    LazySegmentTree<Pll,ll> seg(n,f,g,h,{0,0},0);
    vector<Pll> v(n,Pll{0,1});
    seg.build(v);
    int q; cin >> q;
    rep(i,q){
        int c,v; ll w; cin>> c >> v;
        if (!c){
            cin >> w;
            HLD.update_path(0,v,[&](int l,int r){seg.update(l,r,w);},true);
        } else {
            ll ans=HLD.query(0,v,0LL,[&](int l,int r){return seg.query(l,r).first;},[](ll a,ll b){return a+b;});
            cout << ans << endl;
        }
    }
}