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King Byteasar faces a serious matter. Two competing trade organisations, The Tailors Guild and The Sewers Guild asked, at the same time, for permissions to open their offices in each town of the kingdom.
There are towns in Byteotia.
Some of them are connected with bidirectional roads.
Each of the guilds postulate that every town should:
Two integers, and
(
,
),
are given in the first line of the standard input. These denote the number
of towns and roads in Byteotia, respectively.
The towns are numbered from
to
.
Then the roads are given as follows: the input line no.
describes
the
-th road; it holds the numbers
and
(
,
), denoting that the
-th road
connects the towns
and
.
Every pair of towns is (directly) connected by at most one road.
The roads do not cross - meeting only in towns - but may lead through tunnels
and overpasses.
Your program should print out one word in the first line of the standard output:
TAK (yes in Polish) - if the offices can be placed in towns according to these rules, or
NIE (no in Polish) - in the opposite case.
If the answers is TAK, then the following lines should give an
exemplary placement of the offices. Thus the line no.
should hold:
For the input data:
7 8 1 2 3 4 5 4 6 4 7 4 5 6 5 7 6 7
the correct result is:
TAK K S K S K K N
The towns in which an office of The Tailors Guild should open are marked with circles, whereas those in which an office of The Sewers Guild should open are marked with rhombi.
Task author: Marcin Pilipczuk.