A12980 | Make Them Similar

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?

The first line contains one integer $n$ ( $2 \le n \le 100$ ).

The second line contains $n$ integers $a_1$ , $a_2$ , ..., $a_n$ ( $0 \le a_i \le 2^{30} - 1$ ).

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.