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Contest: Task: Related: TaskB TaskD

Score : $300$ points

Problem Statement

Given is a number sequence $A$ of length $N$.
Let us divide this sequence into one or more non-empty contiguous intervals.
Then, for each of these intervals, let us compute the bitwise $\mathrm{OR}$ of the numbers in it.
Find the minimum possible value of the bitwise $\mathrm{XOR}$ of the values obtained in this way.

What is bitwise $\mathrm{OR}$?

The bitwise $\mathrm{OR}$ of integers $A$ and $B$, $A\ \mathrm{OR}\ B$, is defined as follows:

  • When $A\ \mathrm{OR}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if at least one of $A$ and $B$ is $1$, and $0$ otherwise.
For example, we have $3\ \mathrm{OR}\ 5 = 7$ (in base two: $011\ \mathrm{OR}\ 101 = 111$).
Generally, the bitwise $\mathrm{OR}$ of $k$ integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1\ \mathrm{OR}\ p_2)\ \mathrm{OR}\ p_3)\ \mathrm{OR}\ \dots\ \mathrm{OR}\ p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots p_k$.

What is bitwise $\mathrm{XOR}$?

The bitwise $\mathrm{XOR}$ of integers $A$ and $B$, $A\ \mathrm{XOR}\ B$, is defined as follows:

  • When $A\ \mathrm{XOR}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise.
For example, we have $3\ \mathrm{XOR}\ 5 = 6$ (in base two: $011\ \mathrm{XOR}\ 101 = 110$).
Generally, the bitwise $\mathrm{XOR}$ of $k$ integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1\ \mathrm{XOR}\ p_2)\ \mathrm{XOR}\ p_3)\ \mathrm{XOR}\ \dots\ \mathrm{XOR}\ p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots p_k$.

Constraints

  • $1 \le N \le 20$
  • $0 \le A_i \lt 2^{30}$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $A_3$ $\dots$ $A_N$

Output

Print the answer.

Sample Input 1

3
1 5 7

Sample Output 1

2

If we divide $[1, 5, 7]$ into $[1, 5]$ and $[7]$, their bitwise $\mathrm{OR}$s are $5$ and $7$, whose $\mathrm{XOR}$ is $2$.
It is impossible to get a smaller result, so we print $2$.

Sample Input 2

3
10 10 10

Sample Output 2

0

We should divide this sequence into $[10]$ and $[10, 10]$.

Sample Input 3

4
1 3 3 1

Sample Output 3

0

We should divide this sequence into $[1, 3]$ and $[3, 1]$.