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;

const int N = 1e5+10;
typedef long long ll;

vector<int> G[N];
int top[N],son[N],p[N],cnt[N];
int idx[N];
int tot = 0;

ll bit[N];
ll bit1[N];
int sz;

void add(int i,int x)
{
    ll tmp = i;
    while(i<=sz)
    {
        bit[i] += x;
        bit1[i] += (tmp - 1)*x;
        i += i&-i;
    }
}

ll getSum(int i)
{
    ll sum = 0,tmp = i;
    while(i>0)
    {
        sum += bit[i]*tmp;
        sum -= bit1[i];
        i -= i&-i;
    }
    return sum;
}

void dfs(int v)
{
    cnt[v] = 1;
    son[v] = -1;
    for(int i=0;i<G[v].size();i++)
    {
        int u = G[v][i];
        dfs(u);
        cnt[v] += cnt[u];
        p[u] = v;
        if(son[v]==-1 || cnt[son[v]] < cnt[u])  son[v] = u;
    }
}

void dfs1(int v,int t)
{
    if(v==-1) return;
    top[v] = t;
    idx[v] = ++tot;
    dfs1(son[v],t);
    for(int i=0;i<G[v].size();i++)
    {
        int u = G[v][i];
        if(u == son[v]) continue;
        dfs1(u,u);
    }
}

void addWeight(int v,int w)
{
    do{
        int t = top[v];
        int l = idx[t], r = idx[v];
        if(!t)
        {
            int s = idx[son[0]];
            add(s,w);
            add(r+1,-w);
        }else{
            add(l,w);
            add(r+1,-w);
        }
        v = p[t];
    }while(v != 0);
}

ll getWeight(int v)
{
    ll ans = 0;
    do{
        int t = top[v];
        int l = idx[t], r = idx[v];
        ans += getSum(r) - getSum(l-1);
        v = p[t];
    }while(v != 0);
    return ans;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin>>n;
    sz = n;

    for(int i=0;i<n;i++)
    {
        int k;
        cin>>k;
        while(k--)
        {
            int child;
            cin>>child;
            G[i].push_back(child);
        }

    }

    dfs(0);
    dfs1(0,0);
    int q;
    cin>>q;
    while(q--)
    {
        int op;
        cin>>op;
        if(op){
            int v;
            cin>>v;
            cout<<getWeight(v)<<endl;
        }else
        {
            int v,w;
            cin>>v>>w;
            addWeight(v,w);
        }
    }
    return 0;
}