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 $$$\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$$$.
Input Format:
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 Format:
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 $$$X = 5$$$.