문제
PS 문제에는 항상 XOR만 사용된다는 점에 분노한 XNOR이 음이 아닌 정수 $N$개를 모아 반란을 일으키기로 했다!
XNOR은 체계적이기 때문에, 반란을 일으키기 전 반란의 강도를 계산해 보기로 했다. XNOR이 일으키는 반란이기 때문에, 반란의 강도는 주어진 수를 앞에서부터 차례로 XNOR한 결과가 된다. XNOR이 모은 정수들은 모두 부호 없는 $B$비트 정수로 표현할 수 있기 때문에, $B$비트 정수 간의 XNOR을 사용한다.
반란의 강도가 높을수록 성공할 확률이 높아지기 때문에, XNOR은 $N$개의 수 중 하나 이상의 수를 선택해서 반란의 강도를 최대화하기로 했다. 이때 선택된 수의 순서를 바꿀 수는 없다.
출력
첫 번째 줄에 XNOR이 만들어 낼 수 있는 최대 반란의 강도를 출력한다.
XNOR이 $[2, 3, 4, 5]$를 선택하면, $((2 \text{ XNOR } 3) \text{ XNOR } 4) \text{ XNOR } 5 = 7$이 된다.
3ドル$비트 정수이므로, 2ドル^3-1 = 7$보다 더 큰 수를 만들 수는 없다.
하나 이상의 수를 선택해야 하므로, 가능한 경우가 하나밖에 없다.
노트
두 수의 Bitwise XNOR 연산은 두 수를 이진수로 변환한 뒤, 각 비트를 비교하여 같으면 1ドル,ドル 다르면 0ドル$을 비트별로 계산하는 연산이다. 예로, 1100ドル_{(2)}\text{ XNOR } 0110_{(2)}=0101_{(2)}$가 된다.
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