Task: A Journey to Mars
Byteazar has decided on going to Mars to tour the space stations there being in existence.
All marsian space stations lie on a circumference of a circle. Byteazar lands in one of them
and then moves around by means of a special vehicle which is powered by an appropriate fuel.
A litre of this fuel allows him to travel one meter. However, the provisions of the fuel are meagre,
different quantities of it are available in each space station. Byteazar may refuel in the
space station he is currently in, though he cannot get more fuel than it is available
in that very place (the capacity of his fuel tank is unlimited). This quantity of fuel should
allow him to reach the next space station. Byteazar has to decide where to land, so that he
can visit all of the space stations. In the end he has to return to the space station in which
he has landed. During his journey Byteazar has to travel on the circumference of the circle,
constantly in one of the two possible directions.
Task
Write a programme which:
- reads from the standard input the number of space stations, distances between them and
the amount of fuel available in each of them,
- for each of the space stations checks, whether Byteazar can land there i.e.
whether by starting in that very station and travelling in a freely chosen direction
he is able to visit all of the space stations and return to his spaceship,
- writes the outcome to the standard output.
Input
The first line of the standard input contains a single integer
N
(3 <= N <= 1 000 000). It denotes the
number of space stations on Mars.
The space stations are numbered from 1 to
N. In the next N lines
there is a description of all of the stations and the distances between them. The
i + 1st line contains two integers pi
and di
(pi<= 0, di > 0).
The first one denotes the amount of fuel (in litres) available in the
ith space station. The other denotes thr distance (in metres)
between the ith and i + 1st
space station
(obviously dN denotes the distance between the
Nth and the 1st space station).
The total amount of available fuel, as well as the sum of all distances between the space stations
does not exceed 2 000 000 000.
Output
The programme should write N lines to the standard output.
The ith line
should contain the word TAK (YES is Polish), if Byteazar can land in the
ith space station or NIE (NO in Polish) when it is not possible.
Example
For the input data:5
3 1
1 2
5 2
0 1
5 4
the correct outcome is:
TAK
NIE
TAK
NIE
TAK