Problem about Cliques

Given an undirected, unweighted graph, your task is to determine the number of subcliques within the graph. A subclique is defined as a subgraph that forms a complete graph. In a complete graph with V vertices, there are exactly 2^V subcliques. Conversely, in an empty graph with V vertices, there are exactly V+1 subcliques.

Input

The input begins with the integer V (1 ≤ V ≤ 60), representing the number of vertices in the graph.

Following this, the graph's adjacency matrix is provided over V rows. In this matrix, a 0 signifies no edge between vertices, while a 1 indicates an edge is present. The main diagonal of the matrix always contains zeros, and the matrix is symmetric.

Output

Output the total number of subcliques in the given graph.

Examples