B'Ujan has finally cleaned up his house and now wants to decorate the interior. He decided to place a beautiful carpet that would really tie the guest room together. He is interested in carpets that are made up of polygonal patches such that each side of a patch is either a side of another (different) patch, or is an exterior side of the whole carpet. In other words, the carpet can be represented as a planar graph, where each patch corresponds to a face of the graph, each face is a simple polygon. The perimeter of the carpet is the number of the exterior sides. Ujan considers a carpet beautiful if it consists of f patches, where the i -th patch has exactly a_i sides, and the perimeter is the smallest possible. Find an example of such a carpet, so that Ujan can order it! The first line of input contains a single integer f ( 1 <= q f <= q 10^5 ), the number of patches in the carpet. The next line contains f integers a_1, ldots, a_f ( 3 <= q a_i <= q 3 cdot 10^5 ), the number of sides of the patches. The total number of the sides of the patches a_1 + ldots + a_f does not exceed 3 cdot10^5 . Output the description of the carpet as a graph. First, output a single integer n ( 3 <= q n <= q 3 cdot 10^5 ), the total number of vertices in your graph (the vertices must be numbered from 1 to n ). Then output f lines containing the description of the faces. The i -th line should describe the i -th face and contain a_i distinct integers v_{i,1}, ldots, v_{i,a_i} ( 1 <= q v_{i,j} <= q n ), which means that the vertices v_{i,j} and v_{i,(j bmod{a_i})+1} are connected by an edge for any 1 <= q j <= q a_i . The graph should be planar and satisfy the restrictions described in the problem statement. Its perimeter should be the smallest possible. There should be no double edges or self-loops in the graph. The graph should be connected. Note that a'...