B"Koxia and Mahiru are enjoying the Winter Festival. The streets of the Winter Festival can be represented as a n x n undirected grid graph. Formally, the set of vertices is {(i,j) ; | ; 1 <= q i,j <= q n } and two vertices (i_1,j_1) and (i_2,j_2) are connected by an edge if and only if |i_1-i_2|+|j_1-j_2|=1 . Koxia and Mahiru are planning to visit The Winter Festival by traversing 2n routes. Although routes are not planned yet, the endpoints of the routes are already planned as follows: Your task is to find a routing scheme -- 2n paths where each path connects the specified endpoints. Let's define the congestion of an edge as the number of times it is used (both directions combined) in the routing scheme. In order to ensure that Koxia and Mahiru won't get too bored because of traversing repeated edges, please find a routing scheme that minimizes the maximum congestion among all edges. The first line contains an integer n ( 2 <= q n <= q 200 ) -- the size of the network. The second line contains n integers p_1, p_2, ... , p_n ( 1 <= q p_i <= q n ). The third line contains n integers q_1, q_2, ... , q_n ( 1 <= q q_i <= q n ). It is guaranteed that both p and q are permutations of length n . Output 2n lines, each line describing a route. The first n lines should describe the connections from top to bottom. The i -th line should describe the route starting at vertex (1, i) and ending at vertex (n, p_i) . The next n lines should describe the connections from left to right. The (i+n) -th line should describe the route starting at vertex (i, 1) and ending at vertex (q_i, n) . Each line describing a route should start with an integer k ( 2 <= k <= 10^5 ) -- the number of vertices the route passes, including the starting and ending vertices. Then output all the vertices on the route in order. "...