Score : $400$ points

问题描述

有三位编号分别为 $1$、$2$ 和 $3$ 的高桥，以及三顶颜色分别为红色、绿色和蓝色的帽子。每位高桥都戴了一顶帽子。高桥 $i$ 当前所戴帽子的颜色由字符 $S_i$ 表示。其中，R 对应红色，G 对应绿色，B 对应蓝色。现在，他们将 精确地 进行 $10^{18}$ 次以下操作。

操作

• 从三位高桥中选择两位。这两位交换他们所戴的帽子。

在经过 $10^{18}$ 次重复操作后，是否可能使高桥 $i$ 戴上对应于字符 $T_i$ 颜色的帽子？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are three Takahashis numbered $1$, $2$ and $3$, and three hats colored red, green, and blue. Each Takahashi is wearing one hat. The color of the hat that Takahashi $i$ is currently wearing is represented by a character $S_i$. Here, R corresponds to red, G to green, and B to blue. Now, they will do the following operation exactly $10^{18}$ times.

Operation

• Choose two out of the three Takahashis. The two exchange the hats they are wearing.

Is it possible to make Takahashi $i$ wearing the hat of color corresponding to character $T_i$ after the $10^{18}$ repetitions?

Constraints

• $S_1, S_2, S_3$ are a permutation of R, G, B.
• $T_1, T_2, T_3$ are a permutation of R, G, B.

Input

Input is given from Standard Input in the following format:

$S_1$ $S_2$ $S_3$

$T_1$ $T_2$ $T_3$

Output

If it is possible to make Takahashi $i$ wearing the hat of color corresponding to character $T_i$ after the $10^{18}$ repetitions, print Yes; otherwise, print No.

Sample Input 1

R G B
R G B

Sample Output 1

Yes

For example, the objective can be achieved by repeating $10^{18}$ times the operation of swapping the hats of Takahashi $1$ and Takahashi $2$.

update @ 2024/3/10 10:29:08