Description

Farmer John's $N$ cows are labeled $1$ to $N$ ($2\le N\le 16$). The friendship relationships between the cows can be modeled as an undirected graph with $M$ ($0\le M\le N(N-1)/2$) 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 $a$ and $b$ are friends, then for every other cow $c$, at least one of $a$ and $b$ is friends with $c$.

Input Format

The first line contains $N$ and $M$.

The next $M$ lines each contain a pair of friends $a$ and $b$ ($1\le a<b\le N$). No pair of friends appears more than once.

Output Format

The number of edges you need to add or remove.

3 1
1 2

1

3 2
1 2
2 3

0

4 4
1 2
1 3
1 4
2 3

1

Hint

For Sample 1:

The network violates the property. We can add one of edges $(2,3)$ or $(1,3)$, or remove edge $(1,2)$ to fix this.

For Sample 2:

No changes are necessary.

SCORING:

• Inputs 4-13: One input for each $N\in [6, 15]$ in increasing order.
• Inputs 14-18: $N=16$