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 $p_1, p_2, p_3, \dots p_k$.
  

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.

Constraints

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

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].

见题面 Input 部分

见题面 Output 部分