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 UL=unsigned int;
using LL=long long;
using ULL=unsigned long long;
#define rep(i,n) for(UL i=0; i<(n); i++)

struct RSQ{
 struct Node{ ULL x,s; };
 UL N;
 vector<Node> V;
 void init(UL n){
  N=1; while(N<n) N<<=1;
  V.resize(N*2);
 }
 ULL sum(UL l,UL r,UL a=0,UL b=0,UL i=~0u){
  if(i==~0u){ a=0; i=1; b=N; }
  if(r<=a || b<=l) return 0;
  if(l<=a && b<=r) return V[i].s;
  ULL q1=sum(l,r,a,(a+b)>>1,i<<1);
  ULL q2=sum(l,r,(a+b)>>1,b,(i<<1)+1);
  return q1+q2+V[i].x*(min(r,b)-max(l,a));
 }
 void add(UL l,UL r,ULL x,UL a=0,UL b=0,UL i=~0u){
  if(i==~0u){ a=0; i=1; b=N; }
  if(r<=a || b<=l) return;
  if(l<=a && b<=r){ V[i].x+=x; V[i].s+=x*(b-a); return; }
  add(l,r,x,a,(a+b)>>1,i<<1);
  add(l,r,x,(a+b)>>1,b,(i<<1)+1);
  V[i].s = V[i<<1].s + V[(i<<1)+1].s + V[i].x*(b-a);
 }
};

UL N;
vector<UL> E[100000];
UL hlZ[100000];
UL hlL[100000];
UL hlH[100000];
UL hlP[100000];
UL hlR[100000];
UL hlRP = 0;

RSQ G;

void DFS(UL p){
 UL x=~0u;
 for(UL e:E[p]){
  if(hlP[p]==e) continue;
  hlP[e]=p;
  DFS(e);
  hlZ[p]+=hlZ[e];
  if(x==~0u) x=e; else if(hlZ[x]<hlZ[e]) x=e;
 }
 if(x!=~0u){ hlH[x]=p; hlL[p]=hlL[x]+1; }
}

void hlDFS(UL p){
 if(hlH[p]!=p){
  hlR[p]=hlR[hlP[p]]+1;
  hlH[p]=hlH[hlP[p]];
 }
 else{
  hlR[p]=hlRP;
  hlRP+=hlL[p]+1;
 }
 for(UL e:E[p]){
  if(hlP[p]==e) continue;
  hlDFS(e);
 }
}

int main(){
 scanf("%u",&N);
 rep(u,N){
  UL K; scanf("%u",&K);
  rep(k,K){
   UL v; scanf("%u",&v);
   E[u].push_back(v);
   E[v].push_back(u);
  }
 }
 rep(i,N){ hlH[i]=i; hlP[i]=~0u; hlZ[i]=1; hlL[i]=0; }
 DFS(0);
 hlDFS(0);
 G.init(N);
 UL Q; scanf("%u",&Q);
 rep(q,Q){
  UL c; scanf("%u",&c);
  if(c==0){
   UL p,x; scanf("%u%u",&p,&x);
   while(p!=~0u){
    G.add(hlR[hlH[p]],hlR[p]+1,x);
    p=hlP[hlH[p]];
   }
  }
  if(c==1){
   UL p; scanf("%u",&p);
   ULL ans=0;
   while(p!=~0u){
    ans += G.sum(hlR[hlH[p]],hlR[p]+1);
    p=hlP[hlH[p]];
   }
   ans -= G.sum(hlR[0],hlR[0]+1);
   printf("%llu\n",ans);
  }
 }

 return 0;
}