Description:
Let's call two numbers similar if their binary representations contain the same number of digits equal to $$$1$$$. For example:
- $$$2$$$ and $$$4$$$ are similar (binary representations are $$$10$$$ and $$$100$$$);
- $$$1337$$$ and $$$4213$$$ are similar (binary representations are $$$10100111001$$$ and $$$1000001110101$$$);
- $$$3$$$ and $$$2$$$ are not similar (binary representations are $$$11$$$ and $$$10$$$);
- $$$42$$$ and $$$13$$$ are similar (binary representations are $$$101010$$$ and $$$1101$$$).
You are given an array of $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$. You may choose a non-negative integer $$$x$$$, and then get another array of $$$n$$$ integers $$$b_1$$$, $$$b_2$$$, ..., $$$b_n$$$, where $$$b_i = a_i \oplus x$$$ ($$$\oplus$$$ denotes bitwise XOR).
Is it possible to obtain an array $$$b$$$ where all numbers are similar to each other?
Input Format:
The first line contains one integer $$$n$$$ ($$$2 \le n \le 100$$$).
The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$0 \le a_i \le 2^{30} - 1$$$).
Output Format:
If it is impossible to choose $$$x$$$ so that all elements in the resulting array are similar to each other, print one integer $$$-1$$$.
Otherwise, print any non-negative integer not exceeding $$$2^{30} - 1$$$ that can be used as $$$x$$$ so that all elements in the resulting array are similar.
Note:
None