102971: [Atcoder]ABC297 B - chess960

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

问题描述

高桥正在玩一个叫做Chess960的游戏。 他决定写一个代码来判断一个随机的初始状态是否满足Chess960的条件。

给你一个长度为8的字符串$S$。$S$中恰好有一个K和Q，以及恰好两个R、B和N。判断$S$是否满足以下所有条件。

• 假设$S$从左数第$x$个和第$y$个字符是B$；那么$x$和$y$的奇偶性不同。

• K在两个R之间。更正式地说，假设$S$从左数第$x$个和第$y$个字符是R，第$z$个字符是K$；那么$x<z<y$。

条件

• $S$是一个长度为$8$的字符串，其中恰好有一个K和Q，以及恰好两个R、B和N。

输入

输入从标准输入按以下格式给出：

$S$

输出

如果$S$满足条件，打印Yes；否则打印No。

样例输入1

RNBQKBNR

样例输出1

Yes

第$3$个和第$6$个字符是B$，并且$3$和$6$的奇偶性不同。 此外，K在两个R之间。因此，条件得到满足。

样例输入2

KRRBBNNQ

样例输出2

No

K不在两个R之间。

样例输入3

BRKRBQNN

样例输出3

No