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 int64 = long long;

template< typename T >
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  operator int() const { return to; }
};

template< typename T >
using Edges = vector< edge< T > >;
template< typename T >
using WeightedGraph = vector< Edges< T > >;
using UnWeightedGraph = vector< vector< int > >;
template< typename T >
using Matrix = vector< vector< T > >;

template< typename G >
struct CentroidPathDecomposition {
  struct Centroid {
    int ParIndex, ParDepth, Deep;
    vector< int > node;

    Centroid(int idx, int dep, int deep) : ParIndex(idx), ParDepth(dep), Deep(deep) {}

    inline size_t size() {
      return (node.size());
    }

    inline int &operator[](int k) {
      return (node[k]);
    }

    inline pair< int, int > Up() {
      return (make_pair(ParIndex, ParDepth));
    }
  };

  const G &graph;
  vector< int > SubTreeSize, NextPath;
  vector< int > TreeIndex, TreeDepth;
  vector< Centroid > Centroids;

  void BuildSubTreeSize() {
    stack< pair< int, int > > s;
    s.emplace(0, -1);
    while(!s.empty()) {
      auto p = s.top();
      s.pop();
      if(~SubTreeSize[p.first]) {
        NextPath[p.first] = -1;
        for(auto &to : graph[p.first]) {
          if(p.second == to) continue;
          SubTreeSize[p.first] += SubTreeSize[to];
          if(NextPath[p.first] == -1 || SubTreeSize[NextPath[p.first]] < SubTreeSize[to]) {
            NextPath[p.first] = to;
          }
        }
      } else {
        s.push(p);
        SubTreeSize[p.first] = 1;
        for(auto &to : graph[p.first]) {
          if(p.second != to) s.emplace(to, p.first);
        }
      }
    }
  }

  void BuildPath() {
    stack< pair< int, int > > s;
    Centroids.emplace_back(-1, -1, 0);
    s.emplace(0, -1);
    TreeIndex[0] = 0;
    while(!s.empty()) {
      auto p = s.top();
      s.pop();
      TreeDepth[p.first] = (int) Centroids[TreeIndex[p.first]].size();
      for(auto &to : graph[p.first]) {
        if(p.second == to) continue;
        if(to == NextPath[p.first]) { // Centroid-Path
          TreeIndex[to] = TreeIndex[p.first];
        } else {                  // Not Centroid-Path
          TreeIndex[to] = (int) Centroids.size();
          Centroids.emplace_back(TreeIndex[p.first], TreeDepth[p.first], Centroids[TreeIndex[p.first]].Deep + 1);
        }
        s.emplace(to, p.first);
      }
      Centroids[TreeIndex[p.first]].node.emplace_back(p.first);
    }
  }


  virtual void Build() {
    BuildSubTreeSize();
    BuildPath();
  }

  inline size_t size() {
    return (Centroids.size());
  }

  inline pair< int, int > Information(int idx) {
    return (make_pair(TreeIndex[idx], TreeDepth[idx]));
  }

  inline Centroid &operator[](int k) {
    return (Centroids[k]);
  }

  inline int LCA(int a, int b) {
    int TreeIdxA, TreeDepthA, TreeIdxB, TreeDepthB;
    tie(TreeIdxA, TreeDepthA) = Information(a);
    tie(TreeIdxB, TreeDepthB) = Information(b);
    while(TreeIdxA != TreeIdxB) {
      if(Centroids[TreeIdxA].Deep > Centroids[TreeIdxB].Deep) {
        tie(TreeIdxA, TreeDepthA) = Centroids[TreeIdxA].Up();
      } else {
        tie(TreeIdxB, TreeDepthB) = Centroids[TreeIdxB].Up();
      }
    }
    if(TreeDepthA > TreeDepthB) swap(TreeDepthA, TreeDepthB);
    return (Centroids[TreeIdxA][TreeDepthA]);
  }

  inline virtual void query(int a, int b, const function< void(int, int, int) > &f) {
    int TreeIdxA, TreeDepthA, TreeIdxB, TreeDepthB;
    tie(TreeIdxA, TreeDepthA) = Information(a);
    tie(TreeIdxB, TreeDepthB) = Information(b);
    while(TreeIdxA != TreeIdxB) {
      if(Centroids[TreeIdxA].Deep > Centroids[TreeIdxB].Deep) {
        f(TreeIdxA, 0, TreeDepthA + 1);
        tie(TreeIdxA, TreeDepthA) = Centroids[TreeIdxA].Up();
      } else {
        f(TreeIdxB, 0, TreeDepthB + 1);
        tie(TreeIdxB, TreeDepthB) = Centroids[TreeIdxB].Up();
      }
    }
    if(TreeDepthA > TreeDepthB) swap(TreeDepthA, TreeDepthB);
    f(TreeIdxA, TreeDepthA + 1, TreeDepthB + 1);
  }

  CentroidPathDecomposition(const G &g) : graph(g) {
    int SZ = g.size();
    SubTreeSize.assign(SZ, -1);
    NextPath.resize(SZ);
    TreeIndex.resize(SZ);
    TreeDepth.resize(SZ);
  }
};

template< typename Monoid, typename OperatorMonoid = Monoid >
struct LazySegmentTree {
  using F = function< Monoid(Monoid, Monoid) >;
  using G = function< Monoid(Monoid, OperatorMonoid) >;
  using H = function< OperatorMonoid(OperatorMonoid, OperatorMonoid) >;
  using P = function< OperatorMonoid(OperatorMonoid, int) >;

  int sz;
  vector< Monoid > data;
  vector< OperatorMonoid > lazy;
  const F f;
  const G g;
  const H h;
  const P p;
  const Monoid M1;
  const OperatorMonoid OM0;


  LazySegmentTree(int n, const F f, const G g, const H h, const P p,
                  const Monoid &M1, const OperatorMonoid OM0)
      : f(f), g(g), h(h), p(p), M1(M1), OM0(OM0) {
    sz = 1;
    while(sz < n) sz <<= 1;
    data.assign(2 * sz, M1);
    lazy.assign(2 * sz, OM0);
  }

  void set(int k, const Monoid &x) {
    data[k + sz] = x;
  }

  void build() {
    for(int k = sz - 1; k > 0; k--) {
      data[k] = f(data[2 * k + 0], data[2 * k + 1]);
    }
  }

  void propagate(int k, int len) {
    if(lazy[k] != OM0) {
      if(k < sz) {
        lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
        lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
      }
      data[k] = g(data[k], p(lazy[k], len));
      lazy[k] = OM0;
    }
  }

  Monoid update(int a, int b, const OperatorMonoid &x, int k, int l, int r) {
    propagate(k, r - l);
    if(r <= a || b <= l) {
      return data[k];
    } else if(a <= l && r <= b) {
      lazy[k] = h(lazy[k], x);
      propagate(k, r - l);
      return data[k];
    } else {
      return data[k] = f(update(a, b, x, 2 * k + 0, l, (l + r) >> 1),
                         update(a, b, x, 2 * k + 1, (l + r) >> 1, r));
    }
  }

  Monoid update(int a, int b, const OperatorMonoid &x) {
    return update(a, b, x, 1, 0, sz);
  }


  Monoid query(int a, int b, int k, int l, int r) {
    propagate(k, r - l);
    if(r <= a || b <= l) {
      return M1;
    } else if(a <= l && r <= b) {
      return data[k];
    } else {
      return f(query(a, b, 2 * k + 0, l, (l + r) >> 1),
               query(a, b, 2 * k + 1, (l + r) >> 1, r));
    }
  }

  Monoid query(int a, int b) {
    return query(a, b, 1, 0, sz);
  }

  Monoid operator[](const int &k) {
    return query(k, k + 1);
  }
};

using int64 = long long;

int main() {
  int N, Q;
  scanf("%d", &N);
  UnWeightedGraph g(N);
  for(int i = 0; i < N; i++) {
    int k;
    scanf("%d", &k);
    for(int j = 0; j < k; j++) {
      int x;
      scanf("%d", &x);
      g[i].emplace_back(x);
    }
  }
  CentroidPathDecomposition< UnWeightedGraph > tree(g);
  tree.Build();
  scanf("%d", &Q);
  auto f = [&](int64 x, int64 y) { return x + y; };
  auto p = [&](int64 x, int64 y) { return x * y; };
  vector< LazySegmentTree< int64 > > segs;
  for(int i = 0; i < tree.size(); i++) {
    segs.emplace_back(LazySegmentTree< int64 >(tree[i].size(), f, f, f, p, 0, 0));
  }
  while(Q--) {
    int T;
    scanf("%d", &T);
    if(T == 0) {
      int V, W;
      scanf("%d %d", &V, &W);
      tree.query(0, V, [&](int t, int x, int y) {
        segs[t].update(x, y, W);
      });
    } else {
      int U;
      scanf("%d", &U);
      int64 ret = 0;
      tree.query(0, U, [&](int t, int x, int y) {
        ret += segs[t].query(x, y);
      });
      printf("%lld\n", ret);
    }
  }

}