Friendship Editing

문제

Farmer John's $NN$ cows are labeled $11$ to $NN$ ($2\le N\le 162\backslash le\; N\backslash le\; 16$). The friendship relationships between the cows can be modeled as an undirected graph with $MM$ ($0\le M\le N(N-1)\mathrm{/}20\backslash le\; M\backslash le\; N(N-1)/2$) edges. Two cows are friends if and only if there is an edge between them in the graph.

In one operation, you can add or remove a single edge from the graph. Count the minimum number of operations required to ensure that the following property holds: If cows $aa$ and $bb$ are friends, then for every other cow $cc$, at least one of $aa$ and $bb$ is friends with $cc$.

입력

The first line contains $NN$ and $MM$.

The next $MM$ lines each contain a pair of friends $aa$ and $bb$ (). No pair of friends appears more than once.

출력

The number of edges you need to add or remove.