Suppose that G is an undirected graph, and the value of stab is defined as follows:

Among the expression, G_{-i,-j } is the remainder after removing node i, node j and all edges that are directly relevant to the previous two nodes.cntCompent(X) is the number of connected components of X independently.

Thus, given a certain undirected graph G, you are supposed to calculating the value of stab .

Input consists of multiple cases.

The input will contain the description of several graphs. For each graph, the description consist of an integer N for the number of nodes, an integer M for the number of edges, and M pairs of integers for edges (3<=N,M<=5000).

Please note that the endpoints of edge is marked in the range of [0,N-1], and input cases ends with EOF.

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