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 \[3, 1\].