Score : $200$ points

问题陈述

高桥正在玩一个名为 Chess960 的游戏。他决定编写一段代码来判断一个随机初始状态是否满足 Chess960 的条件。

给定一个长度为八的字符串 $S$，其中 $S$ 包含恰好一个 K 和一个 Q，以及恰好两个 R、两个 B 和两个 N。请确定 $S$ 是否满足以下所有条件：

• 假设从左起第 $x$ 个和第 $y$ 个字符（$x < y$）均为 B，则 $x$ 和 $y$ 的奇偶性不同。

• K 在两个 R 之间。更形式化地表述，假设从左起第 $x$ 个和第 $y$ 个字符（$x < y$）为 R，而第 $z$ 个字符为 K；那么应有 $x < z < y$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is playing a game called Chess960. He has decided to write a code that determines if a random initial state satisfies the conditions of Chess960.

You are given a string $S$ of length eight. $S$ has exactly one K and Q, and exactly two R's, B's , and N's. Determine if $S$ satisfies all of the following conditions.

• Suppose that the $x$-th and $y$-th $(x < y)$ characters from the left of $S$ are B; then, $x$ and $y$ have different parities.

• K is between two R's. More formally, suppose that the $x$-th and $y$-th $(x < y)$ characters from the left of $S$ are R and the $z$-th is K; then $x< z < y$.

Constraints

• $S$ is a string of length $8$ that contains exactly one K and Q, and exactly two R's, B's , and N's.

Input

The input is given from Standard Input in the following format:

$S$

Output

Print Yes if $S$ satisfies the conditions; print No otherwise.

Sample Input 1

RNBQKBNR

Sample Output 1

Yes

The $3$-rd and $6$-th characters are B, and $3$ and $6$ have different parities. Also, K is between the two R's. Thus, the conditions are fulfilled.

Sample Input 2

KRRBBNNQ

Sample Output 2

No

K is not between the two R's.

Sample Input 3

BRKRBQNN

Sample Output 3

No

update @ 2024/3/10 12:19:58