Problem2236--Go Straight and Turn Right

2236: Go Straight and Turn Right

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Time Limit : 1.000 sec  Memory Limit : 128 MB

SubmitSolved: 10Submit Num: 26Statistics

Description

Time Limit: 2 sec / Memory Limit: 1024 MB

Score : 200200 points

Problem Statement

Consider an xyxy-plane. The positive direction of the xx-axis is in the direction of east, and the positive direction of the yy-axis is in the direction of north.
Takahashi is initially at point (x, y) = (0, 0)(x,y)=(0,0) and facing east (in the positive direction of the xx-axis).
You are given a string T = t_1t_2\ldots t_NT=t1t2…tN of length NN consisting of S and R. Takahashi will do the following move for each i = 1, 2, \ldots, Ni=1,2,…,N in this order.
  • If t_i =ti= S, Takahashi advances in the current direction by distance 11.
  • If t_i =ti= R, Takahashi turns 9090 degrees clockwise without changing his position. As a result, Takahashi's direction changes as follows.
    • If he is facing east (in the positive direction of the xx-axis) before he turns, he will face south (in the negative direction of the yy-axis) after he turns.
    • If he is facing south (in the negative direction of the yy-axis) before he turns, he will face west (in the negative direction of the xx-axis) after he turns.
    • If he is facing west (in the negative direction of the xx-axis) before he turns, he will face north (in the positive direction of the yy-axis) after he turns.
    • If he is facing north (in the positive direction of the yy-axis) before he turns, he will face east (in the positive direction of the xx-axis) after he turns.
Print the coordinates Takahashi is at after all the steps above have been done.

Constraints

  • 1 \leq N \leq 10^51≤N≤105
  • NN is an integer.
  • TT is a string of length NN consisting of S and R.

Input

Input is given from Standard Input in the following format: 
NNTT

Output

Print the coordinates (x, y)(x,y) Takahashi is at after all the steps described in the Problem Statement have been completed, in the following format, with a space in between: 
xxyy

Output



Sample Input Copy 

4
SSRS

Sample Output Copy 

2 -1

HINT

Takahashi is initially at (0, 0)(0,0) facing east. Then, he moves as follows.

  1. t_1 =t1= S, so he advances in the direction of east by distance 11, arriving at (1, 0)(1,0).
  2. t_2 =t2= S, so he advances in the direction of east by distance 11, arriving at (2, 0)(2,0).
  3. t_3 =t3= R, so he turns 9090 degrees clockwise, resulting in facing south.
  4. t_4 =t4= S, so he advances in the direction of south by distance 11, arriving at (2, -1)(2,−1).

Thus, Takahashi's final position, (x, y) = (2, -1)(x,y)=(2,−1), should be printed.

Source/Category

AtCoder 
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