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Contest: Task: Related: TaskA TaskC

Score : $200$ points

Problem Statement

Consider an $xy$-plane. The positive direction of the $x$-axis is in the direction of east, and the positive direction of the $y$-axis is in the direction of north.
Takahashi is initially at point $(x, y) = (0, 0)$ and facing east (in the positive direction of the $x$-axis).

You are given a string $T = t_1t_2\ldots t_N$ of length $N$ consisting of S and R. Takahashi will do the following move for each $i = 1, 2, \ldots, N$ in this order.

  • If $t_i =$ S, Takahashi advances in the current direction by distance $1$.
  • If $t_i =$ R, Takahashi turns $90$ 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 $x$-axis) before he turns, he will face south (in the negative direction of the $y$-axis) after he turns.
    • If he is facing south (in the negative direction of the $y$-axis) before he turns, he will face west (in the negative direction of the $x$-axis) after he turns.
    • If he is facing west (in the negative direction of the $x$-axis) before he turns, he will face north (in the positive direction of the $y$-axis) after he turns.
    • If he is facing north (in the positive direction of the $y$-axis) before he turns, he will face east (in the positive direction of the $x$-axis) after he turns.

Print the coordinates Takahashi is at after all the steps above have been done.

Constraints

  • $1 \leq N \leq 10^5$
  • $N$ is an integer.
  • $T$ is a string of length $N$ consisting of S and R.

Input

Input is given from Standard Input in the following format:

$N$
$T$

Output

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

$x$ $y$

Sample Input 1

4
SSRS

Sample Output 1

2 -1

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

  1. $t_1 =$ S, so he advances in the direction of east by distance $1$, arriving at $(1, 0)$.
  2. $t_2 =$ S, so he advances in the direction of east by distance $1$, arriving at $(2, 0)$.
  3. $t_3 =$ R, so he turns $90$ degrees clockwise, resulting in facing south.
  4. $t_4 =$ S, so he advances in the direction of south by distance $1$, arriving at $(2, -1)$.

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

Sample Input 2

20
SRSRSSRSSSRSRRRRRSRR

Sample Output 2

0 1