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
import itertools
import sys
s=input()
for i in itertools.product(["A",""],repeat=4):
  if i[0]+"KIH"+i[1]+"B"+i[2]+"R"+i[3]==s:
    print("YES")
    sys.exit()
    
print("NO")
