400462: GYM100187 B A Lot of Joy

Two boys Gena and Petya wrote on two strips of paper the same string s that consisted of lowercase Latin letters. Then each boy took one strip, cut it into small pieces so that each piece contained exactly one letter and put all pieces into his pocket. After that Gena and Petya repeated the following procedure until their pockets became empty: they took one piece from their pockets and rejoiced if the letters on these pieces were equal.

Determine the expected number of times the boys rejoiced during this process.

The input contains the only string s which was initially written on Gena's and Petya's strips. The string has length between 1 and 200000, inclusively, and consists of lowercase Latin letters.

Output the only real number — the expected number of times Gena and Petya rejoiced during their business. The absolute or relative error of the answer should not exceed 10^- 9.

abc

1.000000000000000

zzz

3.000000000000000