Finding
a treasure hidden by pirates is easy if you have a map. Usually the map comes
with an algorithm that describes moving towards the treasure. E.g.: "Find
the white rock. Go 30 steps towards the forest, then 15 towards the lake, ...
, and 20 through the cave. The treasure is buried under the mark on the right
wall".
Usually one indication involves moving a certain number of steps in one of the
given directions (1 - north, 2 - north-east, 3 - east, 4 - south-east, 5 - south,
6 - south-west, 7 - west, 8 - north-west). One step always takes you from a
point with integer coordinates to another point with integer coordinates. So,
if at some moment you are in the point having the integer coordinates (X, Y),
moving 1 step in one of the 8 directions will take you in the following point
also having integer coordinates:
Direction
|
Where
to
|
1
|
(X,
Y+1)
|
2
|
(X+1,
Y+1)
|
3
|
(X+1,
Y)
|
4
|
(X+1,
Y-1)
|
5
|
(X,
Y-1)
|
6
|
(X-1,
Y-1)
|
7
|
(X-1,
Y)
|
8
|
(X-1,
Y+1)
|
Thus, the journey via the described route becomes simple. For example, in the
picture you go 3 steps north, 1 east, 1 north, 3 east, 2 south and 1 step west.
Task
Write a program that, following the pirates' indications, determines the point where the treasure is hidden. The axis Ox is oriented east and the axis Oy is oriented north. Initially, the treasure seeker is in the origin of the coordinate system (point with coordinates (0, 0)).
Input data
The first line of input
file comori.in contains
a natural number N, representing
the number of indications given. The
following N lines contain
the so-called indications, one indication per line. One indication is given
as two positive integers numbers separated by a space, d
p, where d
represents the number of the direction, and p
the number of steps.
Output data
Output file comori.out will contain a single line with two integers separated by a space, x y, representing the x-coordinate, and respectively the y-coordinate of the point where the treasure is hidden.
Constraints and clarifications
comori.in | comori.out | comori.in | comori.out |
6 1 3 3 1 1 1 3 3 5 2 7 1 |
3 2 |
1 8 10 |
-10 10 |
Time limit: 0.1 seconds/test
prof. Sergiu Corlat
Chişinău Moldavian-Turkish High-School
Contact: scorlat@gmail.com