Professor Szu

The Byteotian University is located in the city of Byteion. Besides the main building, the university owns $n$ cottages for its academic staff. The cottages are connected by one-way alleys; there may be more than one alley between two cottages, and an alley may even loop from a building back to itself. Some alleys connect cottages to the main building as well. Every alley starts and ends at a cottage or at the main building. It is guaranteed that at least one cottage has a route to the main building.

Professor Szu wants to travel to the university by a different route every day. A route is a sequence of alleys where each alley starts at the point where the previous one ended; the main building and any cottage may be visited many times. Two routes are considered different if they differ in at least one alley. The order matters, and two distinct alleys joining the same pair of points are considered different.

For each cottage, count the number of different routes to the main building, and find the cottage (or cottages) with the greatest number of them. If the number of routes from some cottage to the main building exceeds 36,500, we assume the professor can stay there forever.

Your program should read the connections from standard input, then write to standard output the cottages in which the professor could stay the longest together with that longest possible number of routes (or the fact that it is forever).

The first line contains two integers $n$ and $m$ separated by a single space ($1 \le n, m \le 10^6$): the number of cottages and the number of alleys. Cottages are numbered from 1 to $n$, and the main building is numbered $n+1$. Each of the next $m$ lines contains two integers $a_i$ and $b_i$ separated by a single space ($1 \le a_i, b_i \le n+1$), describing a one-way alley from $a_i$ to $b_i$.

The first line should contain the largest number of different routes from any cottage to the main building, or the single word zawsze ("always" in Polish) if that number exceeds 36,500. The second line should contain the number of cottages that achieve this maximum (or that allow staying forever). The third line should list the numbers of those cottages in increasing order, separated by single spaces. All cottages in which the professor can stay forever are treated as equal.