Gildong is experimenting with an interesting machine Graph Traveler. In Graph Traveler, there is a directed graph consisting of n vertices numbered from 1 to n. The i-th vertex has m_i outgoing edges that are labeled as e_i[0], e_i[1], …, e_i[m_i-1], each representing the destination vertex of the edge. The graph can have multiple edges and self-loops. The i-th vertex also has an integer k_i written on itself.

A travel on this graph works as follows. 

  1. Gildong chooses a vertex to start from, and an integer to start with. Set the variable c to this integer. 
  2. After arriving at the vertex i, or when Gildong begins the travel at some vertex i, add k_i to c. 
  3. The next vertex is e_i[x] where x is an integer 0 ≤ x ≤ m_i-1 satisfying x ≡ c \pmod {m_i}. Go to the next vertex and go back to step 2. 



It's obvious that a travel never ends, since the 2nd and the 3rd step will be repeated endlessly.

For example, assume that Gildong starts at vertex 1 with c = 5, and m_1 = 2, e_1[0] = 1, e_1[1] = 2, k_1 = -3. Right after he starts at vertex 1, c becomes 2. Since the only integer x (0 ≤ x ≤ 1) where x ≡ c \pmod {m_i} is 0, Gildong goes to vertex e_1[0] = 1. After arriving at vertex 1 again, c becomes -1. The only integer x satisfying the conditions is 1, so he goes to vertex e_1[1] = 2, and so on.

Since Gildong is quite inquisitive, he's going to ask you q queries. He wants to know how many distinct vertices will be visited infinitely many times, if he starts the travel from a certain vertex with a certain value of c. Note that you should not count the vertices that will be visited only finite times.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 1000), the number of vertices in the graph.

The second line contains n integers. The i-th integer is k_i (-10^9 ≤ k_i ≤ 10^9), the integer written on the i-th vertex.

Next 2 ⋅ n lines describe the edges of each vertex. The (2 ⋅ i + 1)-st line contains an integer m_i (1 ≤ m_i ≤ 10), the number of outgoing edges of the i-th vertex. The (2 ⋅ i + 2)-nd line contains m_i integers e_i[0], e_i[1], …, e_i[m_i-1], each having an integer value between 1 and n, inclusive.

Next line contains an integer q (1 ≤ q ≤ 10^5), the number of queries Gildong wants to ask.

Next q lines contains two integers x and y (1 ≤ x ≤ n, -10^9 ≤ y ≤ 10^9) each, which mean that the start vertex is x and the starting value of c is y.

Output

For each query, print the number of distinct vertices that will be visited infinitely many times, if Gildong starts at vertex x with starting integer y.

Examples

Input


4
0 0 0 0
2
2 3
1
2
3
2 4 1
4
3 1 2 1
6
1 0
2 0
3 -1
4 -2
1 1
1 5


Output


1
1
2
1
3
2


Input


4
4 -5 -3 -1
2
2 3
1
2
3
2 4 1
4
3 1 2 1
6
1 0
2 0
3 -1
4 -2
1 1
1 5


Output


1
1
1
3
1
1

Note

The first example can be shown like the following image:

<image>

Three integers are marked on i-th vertex: i, k_i, and m_i respectively. The outgoing edges are labeled with an integer representing the edge number of i-th vertex.

The travel for each query works as follows. It is described as a sequence of phrases, each in the format "vertex (c after k_i added)".

  * 1(0) → 2(0) → 2(0) → … 
  * 2(0) → 2(0) → … 
  * 3(-1) → 1(-1) → 3(-1) → … 
  * 4(-2) → 2(-2) → 2(-2) → … 
  * 1(1) → 3(1) → 4(1) → 1(1) → … 
  * 1(5) → 3(5) → 1(5) → … 



The second example is same as the first example, except that the vertices have non-zero values. Therefore the answers to the queries also differ from the first example.

<image>

The queries for the second example works as follows:

  * 1(4) → 2(-1) → 2(-6) → … 
  * 2(-5) → 2(-10) → … 
  * 3(-4) → 1(0) → 2(-5) → 2(-10) → … 
  * 4(-3) → 1(1) → 3(-2) → 4(-3) → … 
  * 1(5) → 3(2) → 1(6) → 2(1) → 2(-4) → … 
  * 1(9) → 3(6) → 2(1) → 2(-4) → … 
#include <bits/stdc++.h>
using namespace std;
const int Maxn = 1005;
const int Maxm = 2520;
int n;
int a[Maxn];
vector<int> neigh[Maxn];
vector<pair<int, int> > seq;
int me[Maxn][Maxm];
vector<int> cycles;
int res[Maxn][Maxm];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    a[i] %= Maxm;
    if (a[i] < 0) a[i] += Maxm;
  }
  for (int i = 1; i <= n; i++) {
    int k;
    scanf("%d", &k);
    for (int j = 0; j < k; j++) {
      int e;
      scanf("%d", &e);
      neigh[i].push_back(e);
    }
  }
  for (int i = 1; i <= n; i++)
    for (int j = 0; j < Maxm; j++)
      if (!res[i][j]) {
        seq.clear();
        pair<int, int> v = pair<int, int>(i, j);
        while (!res[v.first][v.second] && !me[v.first][v.second]) {
          seq.push_back(v);
          me[v.first][v.second] = seq.size();
          v.second = (v.second + a[v.first]) % Maxm;
          v.first = neigh[v.first][v.second % int(neigh[v.first].size())];
        }
        if (res[v.first][v.second]) {
          for (int i = 0; i < seq.size(); i++) {
            pair<int, int> u = seq[i];
            res[u.first][u.second] = res[v.first][v.second];
          }
          continue;
        }
        set<int> tmp;
        for (int i = me[v.first][v.second] - 1; i < seq.size(); i++) {
          pair<int, int> u = seq[i];
          tmp.insert(u.first);
        }
        cycles.push_back(int(tmp.size()));
        for (int i = 0; i < seq.size(); i++) {
          pair<int, int> u = seq[i];
          res[u.first][u.second] = cycles.size();
        }
      }
  int q;
  scanf("%d", &q);
  while (q--) {
    int x, y;
    scanf("%d %d", &x, &y);
    y %= Maxm;
    if (y < 0) y += Maxm;
    printf("%d\n", cycles[res[x][y] - 1]);
  }
  return 0;
}
