Given a sequence of $n$ non-negative integers $[a_1, \dots, a_n]$, find a subsequence $[a_{i_1}, a_{i_2}, \dots, a_{i_k}]$ ($1 \le i_1 < i_2 < \dots < i_k \le n$) such that $\sum_{j=1}^{k-1}(a_{i_j} \operatorname{and} a_{i_{j+1}})$ is maximized. You only need to output this maximum value.

Here, $\operatorname{and}$ denotes the bitwise AND operation.

A subsequence is defined as a sequence obtained by deleting zero or more elements from the original sequence while maintaining the relative order of the remaining elements.

Input

The first line contains a positive integer $n$. The next line contains $n$ integers $a_1 \sim a_n$.

Output

Output a single integer representing the maximum value of $\sum_{j=1}^{k-1}(a_{i_j} \operatorname{and} a_{i_{j+1}})$.

Examples

Input 1

5
1 2 3 1 3

Output 1

5

Note 1

One optimal solution is to choose the subsequence $[a_2, a_3, a_5]$.

Input 2

2
1000000000000 987654321234

Output 2

965637836800

Examples 3, 4

See the provided files.

Constraints

All data satisfy: $1 \le n \le 10^{6}$, $0 \le a_i \le 10^{12}$.

• Subtask 1 (20 points): $n \le 20$.
• Subtask 2 (25 points): $n \le 5000$.
• Subtask 3 (20 points): $n \le 10^5, a_i < 512$.
• Subtask 4 (15 points): $n \le 2 \times 10^5$, each $a_i$ is generated independently and uniformly at random in $[0, 10^{12}]$.
• Subtask 5 (20 points): No additional constraints.