write a go solution for Description:
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], ldots, 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 xequivcpmodm_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 xequivcpmodm_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 Format:
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], ldots, 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 Format:
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.

Note:
The first example can be shown like the following 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)to2(0)to2(0)toldots
- 2(0)to2(0)toldots
- 3(-1)to1(-1)to3(-1)toldots
- 4(-2)to2(-2)to2(-2)toldots
- 1(1)to3(1)to4(1)to1(1)toldots
- 1(5)to3(5)to1(5)toldots

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.

The queries for the second example works as follows:

- 1(4)to2(-1)to2(-6)toldots
- 2(-5)to2(-10)toldots
- 3(-4)to1(0)to2(-5)to2(-10)toldots
- 4(-3)to1(1)to3(-2)to4(-3)toldots
- 1(5)to3(2)to1(6)to2(1)to2(-4)toldots
- 1(9)to3(6)to2(1)to2(-4)toldots. Output only the code with no comments, explanation, or additional text.