Dr. Evil Underscores

Today, as a friendship gift, Bakry gave Badawy n integers a_1, a_2, ..., a_n and challenged him to choose an integer X such that the value \underset{1 ≤ i ≤ n}{max} (a_i ⊕ X) is minimum possible, where ⊕ 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 ≤ i ≤ n}{max} (a_i ⊕ X).

Input

The first line contains integer n (1≤ n ≤ 10^5).

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

Output

Print one integer — the minimum possible value of \underset{1 ≤ i ≤ n}{max} (a_i ⊕ 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.

inputFormat

Input

The first line contains integer n (1≤ n ≤ 10^5).

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

outputFormat

Output

Print one integer — the minimum possible value of \underset{1 ≤ i ≤ n}{max} (a_i ⊕ 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.

样例

2
1 5

4