In an undirected graph, a clique is a subset of vertices that are fully connected, i.e. there is an edge between all pairs of vertices in the subset. A maximal clique is one in which the subset of vertices is not part of a larger clique. So, for instance, a fully connected graph has many cliques, but only one maximal clique.

Given an NxN adjacency matrix (A) for an undirected graph with N vertices, return the number (num) of maximal cliques.

Example

Consider the graph shown below,

which has the following adjacency matrix:

A = [ 0 1 0 0 0
      1 0 1 1 0
      0 1 0 1 0
      0 1 1 0 1
      0 0 0 1 0 ]

The number of maximal cliques is 3. The maximal cliques are {1,2}, {2,3,4}, and {4,5}.

NOTE: You may assume the data type of the adjacency matrix is double.