EllysSquareWords

Elly has a String S containing uppercase letters from the English alphabet. The girl can either do nothing, or she can take exactly one action: she can change all occurrences of one letter into another letter (e.g., change all 'T's into 'C's). The "score" of the resulting word is defined as the sum of the squared number of occurrences of each letter.

For example, let's S = "TOPCODERROCKS". It has one 'T', three 'O's, one 'P', two 'C's, one 'D', one 'E', two 'R's, one 'K', and one 'S'. Thus, if the girl doesn't change any letter the score of the word would be 1*1 + 3*3 + 1*1 + 2*2 + 1*1 + 1*1 + 2*2 + 1*1 + 1*1 = 23. However, if the girl chooses to change the 'R's into 'S's she would get "TOPCODESSOCKS" with score 27. Even better, if she changes the 'C's into 'O's she would get "TOPOODERROOKS" with score 35.

Now the girl wonders what is the maximal score that can be achieved for various words. Help her by writing a program, that given the String S returns the maximal score after at most one change of letters.