5122: CF1208 - F. Bits And Pieces
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Description
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].
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].
Input
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 $a$.
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 $a$.
Output
Output a single integer, the maximum value of the expression given in the statement.
Sample 1 Input
3
2 4 6
Sample 1 Output
6
The only possible triplet is $(1, 2, 3)$. Hence, the answer is $2 | (4 \& 6) = 6$.
Sample 2 Input
4
2 8 4 7
Sample 2 Output
12
There are $4$ possible triplets:
1. $(1, 2, 3)$, value of which is $2|(8\&4) = 2$.
2. $(1, 2, 4)$, value of which is $2|(8\&7) = 2$.
3. $(1, 3, 4)$, value of which is $2|(4\&7) = 6$.
4. $(2, 3, 4)$, value of which is $8|(4\&7) = 12$.
The maximum value hence is $12$.
1. $(1, 2, 3)$, value of which is $2|(8\&4) = 2$.
2. $(1, 2, 4)$, value of which is $2|(8\&7) = 2$.
3. $(1, 3, 4)$, value of which is $2|(4\&7) = 6$.
4. $(2, 3, 4)$, value of which is $8|(4\&7) = 12$.
The maximum value hence is $12$.
Sample 3 Input
3
2 0 0
Sample 3 Output
2