B"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. 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 equiv 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. 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 cdot n lines describe the edges of each vertex. The (2 cdot 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 cdot i + 2) -nd"...