Add One

You are given $n$ integers $a_1, a_2, \ldots, a_n$. You must perform the following operation exactly $n-1$ times.

• Choose two numbers $x$ and $y$ in the sequence, remove them, and add a number with the value $x \oplus y$.

This alone is boring, so at any moment you may choose one number and add one to it. You must perform this add-one operation exactly once.

Eventually only one number remains. Maximize it and print the maximum value.

The first line contains a single integer $n$ ($1 \le n \le 10^6$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i < 2^{60}$).

Print a single line containing the maximum value of the remaining number.

In the first example, the optimal strategy is:

• Choose 1 and 2: [1, 2, 1, 2] to [1, 2, 3]
• Choose 1 and 2: [1, 2, 3] to [3, 3]
• Add one to the number 3: [3, 3] to [3, 4]
• Choose 3 and 4: [3, 4] to [7]