Maximum Subsequence Value
题意翻译
### 题目描述
给出一个长度为 $n$ 的数列 $a$,你需要选出一个子序列,使其价值最大,输出最大的价值。
对于一个长度为 $k$ 的子序列,若在这个子序列中有不少于 $\max(1,k-2)$ 个数的二进制位 $i$ 上是 $1$,则其价值增加 $2^i$。
### 输入格式
第一行有一个正整数 $n$,表示数列长度。
之后一行 $n$ 个整数,表示数列 $a$。
保证 $1\le n\le500$,$1\le a_i\le10^{18}$。
### 输出格式
输出最大的价值。
题目描述
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 $ .
输入输出格式
输入格式
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}) $ .
输出格式
Print a single integer — the maximum value Ashish can get by choosing some subsequence of $ a $ .
输入输出样例
输入样例 #1
3
2 1 3
输出样例 #1
3
输入样例 #2
3
3 1 4
输出样例 #2
7
输入样例 #3
1
1
输出样例 #3
1
输入样例 #4
4
7 7 1 1
输出样例 #4
7
说明
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 $ .