Dr. Evil Underscores

有一个长度为 $n\ (1\leq n\leq 10^5)$ 的整数序列 $a_1,\cdots,a_n\ \ (0\leq a_i\leq 2^{30}-1)$，你需要找到一个非负整数 $X$ 使得 $\max(a_i\oplus X)$ 最小，其中 $\oplus$ 为按位异或运算。 输入这个序列，输出 $\max(a_i\oplus X)$ 的最小值。

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) $ .

3
1 2 3

2

2
1 5

4

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