E. Planar Perimetertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputUjan 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!InputThe first line of input contains a single integer f (1 \leq f \leq 10^5), the number of patches in the carpet. The next line contains f integers a_1, \ldots, a_f (3 \leq a_i \leq 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.OutputOutput the description of the carpet as a graph. First, output a single integer n (3 \leq n \leq 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 \leq v_{i,j} \leq 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 \leq j \leq 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 solution always exists; if there are multiple solutions, output any of them.ExamplesInput
2
3 3
Output
4
2 1 4 
1 2 3 
Input
3
5 3 5
Output
6
1 2 3 4 5
4 5 6
1 3 4 6 5
NoteIn the first sample, the two triangular faces are connected by a single edge, which results in the minimum perimeter 4.The figure shows one possible configuration for the second sample. The minimum perimeter in this case is 3.   
2
3 3

4 2 1 4  1 2 3  
['constructive algorithms', 'graphs', '*3200']