MST

You are given a complete undirected graph with n vertices. A number ai is assigned to each vertex, and the weight of an edge between vertices i and j is equal to ai xor aj.

Calculate the weight of the minimum spanning tree in this graph.

Input

The first line contains n (1 ≤ n ≤ 200000) — the number of vertices in the graph.

The second line contains n integers a1, a2, ..., an (0 ≤ ai < 230) — the numbers assigned to the vertices.

Output

Print one number — the weight of the minimum spanning tree in the graph.

Examples

Input

5 1 2 3 4 5

Output

8

Input

4 1 2 3 4

Output

8

inputFormat

Input

The first line contains n (1 ≤ n ≤ 200000) — the number of vertices in the graph.

The second line contains n integers a1, a2, ..., an (0 ≤ ai < 230) — the numbers assigned to the vertices.

outputFormat

Output

Print one number — the weight of the minimum spanning tree in the graph.

Examples

Input

5 1 2 3 4 5

Output

8

Input

4 1 2 3 4

Output

8

样例

5
1 2 3 4 5

8

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