Problem Statement

You are given a sequence of $non-negative integers A=(a_1,\ldots,a_N)$.
Let us perform the following operation on A just once.

• Choose a non-negative integer x. Then, for every $i=1, \ldots, N,$ replace the value of a_i with the bitwise XOR of a_i and x.

Let M be the maximum value in A after the operation. Find the minimum possible value of M.
What is bitwise XOR?
The bitwise XOR of non-negative integers A and $B, A \oplus B$, is defined as follows.
- When $A \oplus B$ is written in binary, the $k-th lowest bit (k \geq 0)$ is 1 if exactly one of the k-th lowest bits of A and B is 1, and 0 otherwise.
For instance, $3 \oplus 5 = 6 ($in binary: $011 \oplus 101 = 110)$.

Input

The input is given from Standard Input in the following format:
N
$a_1 \ldots a_N$

Output

Print the answer.

Constraints

• $1 \leq N \leq 1.5 \times 10^5$
• $0 \leq a_i \lt 2^{30}$
• All values in the input are integers.

Sample Input 1

3
12 18 11

Sample Output 1

16

If we do the operation with x=2, the sequence becomes $(12 \oplus 2,18 \oplus 2, 11 \oplus 2) = (14,16,9)$, where the maximum value M is 16.
We cannot make M smaller than 16, so this value is the answer.

Sample Input 2

10
0 0 0 0 0 0 0 0 0 0

Sample Output 2

0

Sample Input 3

5
324097321 555675086 304655177 991244276 9980291

Sample Output 3

805306368

见题面 Input 部分

见题面 Output 部分