XOR Sum 2

Time limit2sMemory limit512 MB

Summary

Pick any subsequence of up to 100,000 numbers under 10^18 so that the XOR of the chosen elements is maximum.

Level: Hard8 of 10
Topics: Bit manipulation, Greedy, Math
Solved: No attempts yet

Problem

You are given a sequence $A$ of $N$ numbers.

You want to choose a subsequence of $A$ . The XOR sum of a subsequence is the value obtained by XORing all of its elements together.

Given the sequence $A$ , write a program that finds the subsequence with the largest XOR sum.

Input

The first line contains the length of the sequence $N$ ( $1 \le N \le 100{,}000$ ). The second line contains the $N$ numbers of the sequence $A$ . Each number in $A$ is a positive integer less than or equal to $10^{18}$ .

Output

Print the XOR sum of the subsequence of $A$ whose XOR sum is the largest.

Examples1

Example 1
Input
```
3
1 2 4
```
Expected output
```
7
```