Codeforces Round 613 (Div. 2) |
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Finished |

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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 2010-2023 Mike Mirzayanov

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