Competitions
БГУ Личное Первенство
ABA
The string of letters is given. How many subsequences "ABA" does it contain? The letters "ABA" don't have to be consecutive. But the order of letters should be the same.
Input data
One line that contains only capital Latin letters. The length of the string is no more than 10^6.
Output data
Print the number of subsequences "ABA" in the string.
Examples
Input example #1
YARBRBAQ
Output example #1
2
Input example #2
ABAYBATATBBAZA
Output example #2
29