A13264 | Dr. Evil Underscores

Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ .

The first line contains integer $n$ ( $1\le n \le 10^5$ ).

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

Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ .