Given an undirected graph. Density of a graph is \(\frac{|E|}{|V|}\). Your task is to choose non-empty set of vertices V such that subgraph induced on V has maximal density and print this density. But if maximal density is strictly greater than 1, just print ">1".

Input format

The first line of input contains two integers n and m - number of edges and vertices in the graph, respectively (\(1 \le n \le 10^{5}\), \(0 \le m \le 2 \cdot 10^{5}\)).

Then m lines with edge descriptions follows. Each line contains two integers u, v - vertices incident to this edge (\(1 \le u, v \le n\), \(u \ne v\)).

Output format

If maximal density of a subgraph is not bigger than 1, then print it as irreducible fraction. Otherwise, print ">1" (without quotes).

Scoring

\(n \le 17\), \(m \le 50\) - 15 points.

\(n \le 17\), \(m \le 2 \cdot 10^{5}\) - 10 points.

\(n \le 70\), \(m \le 200\) - 20 points.

\(n \le 70\), \(m \le 2 \cdot 10^{5}\) - 5 points.

\(n \le 10^{5}\), \(m \le 2 \cdot 10^{5}\) - 50 points.