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;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;
template<class S,class T> ostream& operator << (ostream& out,const pair<S,T>& o){ out << "(" << o.first << "," << o.second << ")"; return out; }
template<class T> ostream& operator << (ostream& out,const vector<T> V){ for(int i = 0; i < V.size(); i++){ out << V[i]; if(i!=V.size()-1) out << " ";} return out; }
template<class T> ostream& operator << (ostream& out,const vector<vector<T> > Mat){ for(int i = 0; i < Mat.size(); i++) { if(i != 0) out << endl; out << Mat[i];} return out; }
template<class S,class T> ostream& operator << (ostream& out,const map<S,T> mp){ out << "{ "; for(auto it = mp.begin(); it != mp.end(); it++){ out << it->first << ":" << it->second; if(mp.size()-1 != distance(mp.begin(),it)) out << ", "; } out << " }"; return out; }


// HL-Decomposition
struct HLD{
    typedef ll TYPE;
    typedef pair<TYPE,TYPE> PTT;
    TYPE V; // 頂点数
    TYPE root;
    vector<vector<TYPE>> G;
    vector<TYPE> parent,Hchild,number,id,group,depth;
    vector<PTT> paths; // [u,v]間の経路を分解(最大でもlogN)
    vector<PTT> Ledges; // pathsを結ぶライドエッジ
    
    HLD() {root = V = -1; }
    HLD(TYPE V):
    V(V),root(0),G(V),parent(V,-1),Hchild(V,-1),number(V,-1),id(V,-1),group(V,-1),depth(V,0){}
    void init(TYPE V){
        V = V; root = 0;
        G.clear(); parent.clear(); Hchild.clear(); number.clear();
        id.clear(); group.clear(); depth.clear();
        G.resize(V); parent.assign(V,-1); Hchild.assign(V,-1);
        number.assign(V,-1); id.assign(V,-1); group.assign(V,-1); depth.assign(V,0);
    }
    
    void add_edge(TYPE u,TYPE v){ G[u].push_back(v); G[v].push_back(u);}
    void build(TYPE _root = 0){
        root = _root;
        int num = 0;
        dfs1(); init_number(num); dfs2();
    }
    TYPE dfs1(TYPE pos = -1,TYPE pre = -1){
        if(pos == -1) pos = root;
        TYPE maxw = -1, weight = 1;
        for(TYPE next:G[pos]){
            if(next == pre) continue;
            TYPE child_weight = dfs1(next,pos);
            weight += child_weight;
            if(maxw < child_weight){ Hchild[pos] = next; maxw = child_weight; }
        }
        return weight;
    }
    void dfs2(TYPE pos = -1,TYPE pre = -1,TYPE dep = 0,TYPE g = -1){
        if(pos == -1) pos = g = root;
        parent[pos] = pre; depth[pos] = dep; group[pos] = g;
        for(TYPE next:G[pos]){
            if(next == pre) continue;
            dfs2(next,pos,dep+1,Hchild[pos]==next?g:next);
        }
    }
    void init_number(int& num,TYPE pos = -1,TYPE pre = -1){
        if(pos == -1) pos = root;
        number[pos] = num++;
        id[number[pos]] = pos;
        if(Hchild[pos] >= 0) init_number(num,Hchild[pos],pos);
        for(TYPE next:G[pos]){
            if(next != pre && next != Hchild[pos]) init_number(num,next,pos);
        }
    }
    
    void buildPaths(TYPE u,TYPE v){
        if(depth[group[u]] < depth[group[v]]) swap(u,v);
        TYPE num_u=number[u], num_v=number[v];
        if(same(u,v)){ paths.push_back({min(num_u,num_v),max(num_u,num_v)}); return;}
        TYPE group_u = group[u];
        buildPaths(parent[group_u],v);
        paths.push_back({number[group_u], number[u]});
        Ledges.push_back({number[parent[group_u]], number[group_u]});
    }
    
    TYPE lca(TYPE u,TYPE v){
        if(depth[group[u]] < depth[group[v]]) swap(u,v);
        if(same(u,v)) return depth[u] < depth[v]?u:v;
        return lca(parent[group[u]],v);
    }
    pair<vector<PTT>,vector<PTT>> getPath(TYPE u,TYPE v){
        paths.clear(); Ledges.clear();
        buildPaths(u,v);
        return make_pair(paths,Ledges);
    }
    bool same(TYPE a,TYPE b){return group[a] == group[b];}
};

// ================================= //
// use example

/*
 update : [s,t)にxを加算する
 query : [s,t) の総和を出力する
 */
const ll INIT = 0;
struct SegTree {
    int N;
    ll init_v;
    vector<ll> node, lazy;
    SegTree(int _N):init_v(INIT) {
        N = 1; while (N < _N) N *= 2;
        node.resize(2 * N - 1, init_v); lazy.resize(2 * N - 1, init_v);
    }
    
    void lazy_evaluate(int k) {
        node[k] += lazy[k]; // add のため加算
        if (k < N - 1) { lazy[2 * k + 1] += lazy[k] / 2; lazy[2 * k + 2] += lazy[k] / 2; }
        lazy[k] = 0;
    }
    
    /* [a,b) 引数の範囲に注意!! s~tまでを更新→update(s,t+1,~) */
    ll update(int a, int b, int x) { return update(a, b, 0, 0, N, x); }
    ll update(int a, int b, int k, int l, int r, int x) {
        if (r <= a || b <= l) { lazy_evaluate(k); return node[k]; }
        if (a <= l && r <= b) { lazy[k] += (r - l) * x; lazy_evaluate(k); return node[k]; }
        else {
            lazy_evaluate(k);
            ll vl = update(a, b, 2 * k + 1, l, (l + r) / 2, x);
            ll vr = update(a, b, 2 * k + 2, (l + r) / 2, r, x);
            return node[k] = vl + vr;
        }
    }
    
    /* [a,b) 引数の範囲に注意!! */
    ll query(int a, int b) { return query(a, b, 0, 0, N); }
    ll query(int a, int b, int k, int l, int r) {
        if (r <= a || b <= l) return init_v;
        if (a <= l && r <= b) { lazy_evaluate(k); return node[k]; }
        else {
            lazy_evaluate(k);
            ll vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
            ll vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
            return vl + vr;
        }
    }
};


// LCA : http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C&lang=jp
void GRL_5_C(){
    ll n; cin >> n;
    HLD hld(n);
    for(int i = 0; i < n;i++){
        ll k; cin >> k;
        for(int j = 0; j < k;j++){
            ll c; cin >> c;
            hld.add_edge(i, c);
        }
    }
    hld.build();
    ll q; cin >> q;
    while(q--){
        ll u,v; cin >> u >> v;
        cout << hld.lca(u,v) << endl;
    }
}


// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_E&lang=jp
void GRL_5_E(){
    ll n; cin >> n;
    HLD hld(n);
    for(int i = 0; i < n;i++){
        ll k; cin >> k;
        for(int j = 0; j < k;j++){
            ll c; cin >> c;
            hld.add_edge(i, c);
        }
    }
    hld.build();
    SegTree ST(n);
    
    // add(v,w): 節点 v の親と、節点 v の間にある辺の重みを w 増加させる
    auto query0=[&](ll u,ll w){
        auto path = hld.getPath(0, u).first;
        path[0].first++;
        for(auto p:path){
            ll l = p.first, r = p.second;
            ST.update(l,r+1,w);
        }
    };
    
    // getSum(u) : 根から節点 u までの間にある辺の重みの総和を報告する。
    auto query1 = [&](ll u){
        auto path = hld.getPath(0,u).first;
        path[0].first++;
        ll ret = 0;
        for(auto p:path){
            ll l = p.first, r = p.second;
            ret += ST.query(l,r+1);
        }
        return ret;
    };
    
    ll q; cin >> q;
    while(q--){
        ll com; cin >> com;
        if(com == 0){
            ll v,w; cin >> v >> w;
            query0(v,w);
        }else{
            ll u; cin >> u;
            cout << query1(u) << endl;
        }
    }
}
int main(void) {
    cin.tie(0); ios_base::sync_with_stdio(false);
    //GRL_5_C();
    GRL_5_E();
    return 0;
}