interesting problem >.<

first we make the string in order like aabbbccc, to make that, we let ba->ab, ca->ac, cb->bc.

then we unique it, make aa->a, bb->b, cc->c

finally we can solve it like if

change("ca","ac");
change("cb","bc");
change("ba","ab");
change("aa","a");
change("bb","b");
change("cc","c");
change("abc","3");
change("ab","2");
change("bc","2");
change("ac","2");
change("a","1");
change("b","1");
change("c","1");