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: $011 \\oplus 101 = 110$).

Constraints

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

Input

The input is given from Standard Input in the following format:

$N$ $a_1$ $\\ldots$ $a_N$

Output

Print the answer.

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