During his physics research, the Ph.D. candidate Ulf
invented some new metals as the existing ones were not good
enough. He is now investigating the properties of the new
metals, and is interested in knowing how reactive they are, so
that he won’t blow his house up while mixing them with
water.
He wants to order the metals by reactivity into a socalled
reactivity series, where the metal with the highest reactivity
comes first, and lowest reactivity comes last. Normally, Ulf
(who is also proficient in computer science) would make an
optimal scheme of measurements such that he has to make as few
measurements as possible to determine such a series.
Unfortunately, having invented entirely new substances, he was
eager to begin experimenting, and randomly took pairs of
elements and compared their reactivity.
Ulf’s experiments consisted of taking two different metals,
and testing which one had the highest reactivity. You may
assume Ulf never makes mistakes in his experiments, and that
the reactivity is distinct for all elements (i.e. for any pair
of metals, one will always be the more reactive one). This
relation is such that if metal $A$ is more reactive than metal
$B$ which in turn is more
reactive than metal $C$,
it follows that $A$ is
more reactive than $C$ as
well.
Before continuing his experiments, he is wondering whether
the measurements he already has are enough to determine a
unique reactivity series of all his metals.
Input
The first line will consist of two integers $1 \le N \le 1\, 000$, the number of
metals Ulf had discovered and $0
\le K \le \frac{N(N1)}{2}$, the number of experiments
Ulf performed. This is followed by $K$ lines, each consisting of two
space separated integers $0 \le A
\not= B \le N1$, stating that the $A$:th metal has a higher reactivity
than the $B$:th metal. The
metals are numbered from 0 to $N1$.
Output
Output consists of $N$
integers from 0 to $N1$,
creating a reactivity series. The number of the metal with
highest reactivity is the first one, with every following metal
being of lower reactivity than the previous one. If it is
impossible to construct a unique series containing
all the metals, output the message "back to the lab" instead.
Sample Input 1 
Sample Output 1 
2 1
0 1

0 1

Sample Input 2 
Sample Output 2 
4 4
0 1
0 2
2 3
1 3

back to the lab
