Game with palindromes (Hard)#4367
Giraffe Boris and centaur Eugene once played a game with a string. They took turns, with Boris, being a bit older, going first. On a player's turn, if they can rearrange the string using all its characters to form a palindrome, they win; otherwise, they remove any character they like from the string.
Who will win if both follow the optimal strategy?
The input consists of a single string of lowercase Latin letters, with length not exceeding 10^6.
If Boris wins, output Boris. If Eugene wins, output Eugene.
Example 1