D. Dr. Evil Underscorestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputToday, 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).InputThe 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).OutputPrint one integer — the minimum possible value of \underset{1 \leq i \leq n}{\max} (a_i \oplus X).ExamplesInput
3
1 2 3
Output
2
Input
2
1 5
Output
4
NoteIn the first sample, we can choose X = 3.In the second sample, we can choose X = 5.
3
1 2 3

2 
['bitmasks', 'brute force', 'dfs and similar', 'divide and conquer', 'dp', 'greedy', 'strings', 'trees', '*1900']