Capital

There are $N$ cities connected by $M$ roads. Cities are numbered from 1 through $N$, and roads are numbered from 1 through $M$. For each pair of cities, there is a sequence of roads that connects them. Road $i$ has length $L_i$ kilometres and connects cities $A_i$ and $B_i$ in both directions. Every road has a positive length, so $L_i > 0$. The lengths of the roads are unknown.

For each road, all people on road $i$ travel from $A_i$ to $B_i$ in a single direction. Based on this, the following hypothesis is made:

• There is a capital city $S$.
• People move from the capital to other cities.
• People take the shortest path. So the shortest distance from $S$ to $A_i$ is less than or equal to the shortest distance from $S$ to $B_i$.

Find every capital city $S$ that satisfies these conditions when each road length can be any positive real number. You may assume that at least one city satisfies the conditions.

The first line contains two integers $N$ ($2 \le N \le 500$) and $M$ ($N-1 \le M \le \frac{N(N-1)}{2}$).

Each of the next $M$ lines contains $A_i$ and $B_i$ ($1 \le A_i, B_i \le N$). There are no self-loops or multiple edges. That is, $A_i \ne B_i$, and $\{A_i, B_i\} = \{A_j, B_j\}$ implies $i = j$.

On the first line, print the number of possible capital cities $K$.

On the second line, print the $K$ possible capital cities in increasing order, separated by spaces.