Game with palindroms (Hard)

Giraffe Boris and centaur Eugene are playing with the string in the following game. Of course, they are doing moves one by one. Since Boris was a little older than Eugene, he started first. If a player can form from the string, using all it’s characters, palindrome, he wins, otherwise, he removes any character he liked from the string.

Who will win if both use the optimal strategy?

Input

The only line of input contains string, consisting of lowercase English letters, it’s length doesn’t exceed 10^6.

Output

If Boris wins - print Boris. If you Eugene wins - print Eugene.

Examples