CF1285D.Dr. Evil Underscores

普及/提高-

通过率：0%

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题目描述

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

输入格式

The first line contains integer $n$ ( $1\le n \le 10^5$ ).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i \le 2^{30}-1$ ).

输出格式

Print one integer — the minimum possible value of $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ .

输入输出样例

输入#1
```
3
1 2 3
```
输出#1
```
2
```
输入#2
```
2
1 5
```
输出#2
```
4
```

说明/提示

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

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

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