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
from itertools import product


candidates = set()
non_as = ["KIH", "B", "R", ""]
for seps in product(["A", ""], repeat=4):
    candidates.add("".join(sep + non_a for sep, non_a in zip(seps, non_as)))

print("YES") if input() in candidates else print("NO")
