codeforces#P1365E. Maximum Subsequence Value
Maximum Subsequence Value
Description
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 $a$.
Input
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 $(1 \le a_i \le 10^{18})$.
Output
Print a single integer — the maximum value Ashish can get by choosing some subsequence of $a$.
Samples
3
2 1 3
3
3
3 1 4
7
1
1
1
4
7 7 1 1
7
Note
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 $7$.