Studies

The Computer Science program at Byteland University (BU) consists of $n$ levels. Each level corresponds to a semester, but the number of levels can be larger or smaller than the number of semesters in a classical CS program.

During the studies a student may submit various kinds of applications to the dean. A single application moves the student from the current level to another level and, at the same time, affects the student's budget. The effect can be a gain (a scholarship, a positive amount) or a loss (charges for extra classes, a negative amount).

Byteman is a lazy but very clever BU student. He does not care about graduating quickly; the only thing he cares about is maximizing his income. The dean behaves deterministically, meaning the outcome of a given application (the level it leads to and the associated cost) is always the same. Byteman may submit the same application as many times as he likes.

A level $v$ guarantees infinite income when the following holds: the student can start at level $v$, submit a sequence of applications, and finally return to the starting level $v$ while the total of the costs earned along the way is positive. Repeating such a closed process lets him grow his income without bound.

Given the description of all possible applications, write a program that finds every starting level that can lead to infinite income.

The first line contains two integers $n$ and $m$ separated by a single space ($2 \le n \le 300$, $1 \le m \le n(n-1)$): the number of levels and the number of applications to analyze.

Each of the following $m$ lines describes one application with three integers $a_i$, $b_i$, $c_i$ ($1 \le a_i, b_i \le n$, $a_i \ne b_i$, $-10^9 \le c_i \le 10^9$). It means that submitting the application at level $a_i$ moves the student to level $b_i$ after the dean's decision, with an associated cost $c_i$ (a positive value is a gain, a negative value is a loss).

No ordered pair $(a_i, b_i)$ appears more than once, but $(a_i, b_i)$ and $(b_i, a_i)$ may both appear.

On the first line print one integer $k$, the number of starting levels that can yield infinite income. On the second line print those level numbers, each in the range $1$ to $n$, in increasing order separated by single spaces. If $k$ is $0$, leave the second line empty.