CF1285D 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) $ .

In the first sample, we can choose $ X = 3 $ . In the second sample, we can choose $ X = 5 $ .