CF1208F.Bits And Pieces

普及/提高-

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题目描述

You are given an array $a$ of $n$ integers.

You need to find the maximum value of $a_{i} | ( a_{j} \& a_{k} )$ over all triplets $(i,j,k)$ such that $i < j < k$ .

Here $\&$ denotes the bitwise AND operation, and $|$ denotes the bitwise OR operation.

输入格式

The first line of input contains the integer $n$ ( $3 \le n \le 10^{6}$ ), the size of the array $a$ .

Next line contains $n$ space separated integers $a_1$ , $a_2$ , ..., $a_n$ ( $0 \le a_{i} \le 2 \cdot 10^{6}$ ), representing the elements of the array $a$ .

输出格式

Output a single integer, the maximum value of the expression given in the statement.

输入输出样例

输入#1
```
3
2 4 6
```
输出#1
```
6
```
输入#2
```
4
2 8 4 7
```
输出#2
```
12
```

说明/提示

In the first example, the only possible triplet is $(1, 2, 3)$ . Hence, the answer is $2 | (4 \& 6) = 6$ .

In the second example, there are $4$ possible triplets:

$(1, 2, 3)$ , value of which is $2|(8\&4) = 2$ .
$(1, 2, 4)$ , value of which is $2|(8\&7) = 2$ .
$(1, 3, 4)$ , value of which is $2|(4\&7) = 6$ .
$(2, 3, 4)$ , value of which is $8|(4\&7) = 12$ .

The maximum value hence is $12$ .

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