Score : $200$ points

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.

RNBQKBNR

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.

KRRBBNNQ

No

K is not between the two R's.

BRKRBQNN

No