Given an undirected, unweighted graph, your task is to determine the number of subcliques in the graph. A subclique is a subgraph that forms a complete graph. In a complete graph with vertices, there are exactly 2^V subcliques. In an empty graph with vertices, there are exactly V + 1 subcliques.
The input begins with the integer (1 \leq V \leq 60)—the number of vertices in the graph.
Then follow rows with the adjacency matrix of the graph. A indicates there is no edge, and a indicates an edge is present. The main diagonal always contains zeros. The matrix is symmetric.
Print the number of subcliques in the given graph.
Example 1