Maximizing Bitwise AND Split Sum with One Swap

Given a non‐negative integer sequence \( A = a_1, a_2, \dots, a_n \) of length \( n \), define

\[ F(A)=\max_{1\le k<n}\Bigl((a_1\,\&\,a_2\,\&\,\cdots\,\&\,a_k)+(a_{k+1}\,\&\,a_{k+2}\,\&\,\cdots\,\&\,a_n)\Bigr) \]

where \( \& \) is the bitwise-and operator.

You are allowed to perform at most one swap operation. That is, you may choose two indices \( i \) and \( j \) with \( 1 \le i < j \le n \) and swap \( a_i \) with \( a_j \).

Your task is to compute the maximum possible value of \( F(A) \) after performing at most one swap.

inputFormat

The first line contains a single integer \( n \) (\( n\ge2 \)), the length of the sequence.

The second line contains \( n \) non-negative integers \( a_1, a_2, \dots, a_n \) separated by spaces.

outputFormat

Output a single integer, representing the maximum possible value of \( F(A) \) after performing at most one swap.

sample

3
1 2 3

3