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
l = []
a = 'AKIHABARA'

def rec(s, i):
    if i == len(a):
        l.append(s)
        return
    if a[i] == 'A':
        rec(s, i+1)
    rec(s + a[i], i+1)

rec('', 0)
print("YES" if input() in l else "NO")