CF1365E Maximum Subsequence Value

Ridhiman challenged Ashish to find the maximum valued subsequence of an array $ a $ of size $ n $ consisting of positive integers. The value of a non-empty subsequence of $ k $ elements of $ a $ is defined as $ \sum 2^i $ over all integers $ i \ge 0 $ such that at least $ \max(1, k - 2) $ elements of the subsequence have the $ i $ -th bit set in their binary representation (value $ x $ has the $ i $ -th bit set in its binary representation if $ \lfloor \frac{x}{2^i} \rfloor \mod 2 $ is equal to $ 1 $ ). Recall that $ b $ is a subsequence of $ a $ , if $ b $ can be obtained by deleting some(possibly zero) elements from $ a $ . Help Ashish find the maximum value he can get by choosing some subsequence of $ a $ .

The first line of the input consists of a single integer $ n $ $ (1 \le n \le 500) $ — the size of $ a $ . The next line consists of $ n $ space-separated integers — the elements of the array $ (1 \le a_i \le 10^{18}) $ .

Print a single integer — the maximum value Ashish can get by choosing some subsequence of $ a $ .

For the first test case, Ashish can pick the subsequence $ \{{2, 3}\} $ of size $ 2 $ . The binary representation of $ 2 $ is 10 and that of $ 3 $ is 11. Since $ \max(k - 2, 1) $ is equal to $ 1 $ , the value of the subsequence is $ 2^0 + 2^1 $ (both $ 2 $ and $ 3 $ have $ 1 $ -st bit set in their binary representation and $ 3 $ has $ 0 $ -th bit set in its binary representation). Note that he could also pick the subsequence $ \{{3\}} $ or $ \{{2, 1, 3\}} $ . For the second test case, Ashish can pick the subsequence $ \{{3, 4\}} $ with value $ 7 $ . For the third test case, Ashish can pick the subsequence $ \{{1\}} $ with value $ 1 $ . For the fourth test case, Ashish can pick the subsequence $ \{{7, 7\}} $ with value $ 7 $ .