You are given a string S.

Takahashi can insert the character A at any position in this string any number of times.

Can he change S into AKIHABARA?

Constraints

• $1 \leq |S| \leq 50$
• S consists of uppercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

If it is possible to change S into AKIHABARA, print YES; otherwise, print NO.

Examples

Input

KIHBR

Output

YES

Input

AKIBAHARA

Output

NO

Input

AAKIAHBAARA

Output

NO

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