Score : $200$ points

问题描述

考虑一个 $xy$-平面。$x$ 轴的正方向指向东方，$y$ 轴的正方向指向北方。 高桥初始位于点 $(x, y) = (0, 0)$ 并面向东方（沿 $x$ 轴正方向）。

给定一个长度为 $N$ 的字符串 $T = t_1t_2\ldots t_N$，由字符 S 和 R 组成。高桥将按照以下顺序对每个 $i = 1, 2, \ldots, N$ 执行以下移动操作。

• 若 $t_i =$ S，高桥将在当前朝向前进距离 $1$。
• 若 $t_i =$ R，高桥将在不改变位置的情况下顺时针旋转 $90$ 度。结果，高桥的方向会发生如下变化：
  • 如果他在转向前面向东（沿 $x$ 轴正方向），则转向后他将面向南（沿 $y$ 轴负方向）。
  • 如果他在转向前面向南（沿 $y$ 轴负方向），则转向后他将面向西（沿 $x$ 轴负方向）。
  • 如果他在转向前面向西（沿 $x$ 轴负方向），则转向后他将面向北（沿 $y$ 轴正方向）。
  • 如果他在转向前面向北（沿 $y$ 轴正方向），则转向后他将面向东（沿 $x$ 轴正方向）。

请输出执行完上述所有步骤后高桥所处的坐标。

以上为通义千问 qwen-max 翻译，仅供参考。

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

update @ 2024/3/10 10:28:45