Dr. Evil Underscores

Description:

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 $$$\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$$$.

Sample Input:

3
1 2 3

Sample Output:

2

Sample Input:

2
1 5

Sample Output:

4

Note:

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

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