Score : $500$ points

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 $M$.

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.

3
12 18 11

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.

10
0 0 0 0 0 0 0 0 0 0

0

5
324097321 555675086 304655177 991244276 9980291

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