Please, try EDU on Codeforces! New educational section with videos, subtitles, texts, and problems.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Dr. Evil Underscores

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

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

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

Examples

Input

3 1 2 3

Output

2

Input

2 1 5

Output

4

Note

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

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/07/2020 23:33:13 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|