Dr
Description
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 $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
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 $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
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 $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$.
Samples
3
1 2 3
2
2
1 5
4
Note
In the first sample, we can choose $X = 3$.
In the second sample, we can choose $X = 5$.