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.

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

Input

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

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

Output

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

Note

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

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