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 $a$.

里迪曼向阿西什发起挑战，要求他找出一个由 $n$ 个正整数组成的数组 $a$ 的最大值子序列。

一个非空子序列（含 $k$ 个元素）的值定义为：对所有满足条件的整数 $i \ge 0$，求和 $\sum 2^i$；其中“条件”是指：该子序列中至少有 $\max(1, k - 2)$ 个元素在二进制表示中第 $i$ 位为 $1$（即，若某数 $x$ 满足 $\left\lfloor \frac{x}{2^i} \right\rfloor \bmod 2 = 1$，则称其二进制表示中第 $i$ 位被置位）。

注意：若数组 $b$ 可通过从 $a$ 中删除若干（可能为零）元素得到，则称 $b$ 是 $a$ 的一个子序列。

请帮助阿西什找出：通过选择 $a$ 的某个子序列所能获得的最大值。

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 $(1 \le a_i \le 10^{18})$.

输入的第一行包含一个整数 $n$ $(1 \le n \le 500)$ —— 表示数组 $a$ 的大小。

第二行包含 $n$ 个以空格分隔的整数 —— 数组的元素 $(1 \le a_i \le 10^{18})$。

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

输出一个整数——Ashish 通过选择数组 $a$ 的某个子序列所能获得的最大值。

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 $7$.

对于第一个测试用例，Ashish 可以选择长度为 $2$ 的子序列 $\{2, 3\}$。$2$ 的二进制表示为 10，$3$ 的二进制表示为 11。由于 $\max(k - 2, 1)$ 等于 $1$，该子序列的值为 $2^0 + 2^1$（因为 $2$ 和 $3$ 的二进制表示中第 $1$ 位均为 $1$，且 $3$ 的二进制表示中第 $0$ 位为 $1$）。注意，他也可以选择子序列 $\{3\}$ 或 $\{2, 1, 3\}$。

对于第二个测试用例，Ashish 可以选择子序列 $\{3, 4\}$，其值为 $7$。

对于第三个测试用例，Ashish 可以选择子序列 $\{1\}$，其值为 $1$。

对于第四个测试用例，Ashish 可以选择子序列 $\{7, 7\}$，其值为 $7$。