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 combinations as c
from itertools import chain

S=list("AKIHABARA") #0,4,6,8
l=[0,4,6,8]
o=set()

for k in chain(c(l,2),c(l,3),c(l,4)):
  b=[j if not i in k else "" for i,j in enumerate(S)]
  o.add("".join(b))
o.add("AKIHABARA")

s=input()
if s in o:
  print("YES")
else:
  print("NO")