Graph Traveler

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:

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.

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) → …

inputFormat

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.

outputFormat

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:

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.

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) → …

样例

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

1
1
2
1
3
2

</p>