Flatland is a country with a number of cities, some of which have space stations. Cities are numbered consecutively and each has a road of length connecting it to the next city. It is not a circular route, so the first city doesn't connect with the last city. Determine the maximum distance from any city to its nearest space station.

**Example**

There are cities and city has a space station. They occur consecutively along a route. City is unit away and city is units away. City is units from its nearest space station as one is located there. The maximum distance is .

**Function Description**

Complete the *flatlandSpaceStations* function in the editor below.

flatlandSpaceStations has the following parameter(s):

*int n:*the number of cities*int c[m]:*the indices of cities with a space station

**Returns**

- *int:* the maximum distance any city is from a space station

**Input Format**

The first line consists of two space-separated integers, and .

The second line contains space-separated integers, the indices of each city that has a space-station. These values are *unordered* and distinct.

**Constraints**

- There will be at least city with a space station.
- No city has more than one space station.

**Output Format**

**Sample Input 0**

STDIN Function ----- -------- 5 2 n = 5, c[] size m = 2 0 4 c = [0, 4]

**Sample Output 0**

```
2
```

**Explanation 0**

This sample corresponds to following graphic:

The distance to the nearest space station for each city is listed below:

- has distance , as it contains a space station.
- has distance to the space station in .
- has distance to the space stations in and .
- has distance to the space station in .
- has distance , as it contains a space station.

We then take .

**Sample Input 1**

```
6 6
0 1 2 4 3 5
```

**Sample Output 1**

```
0
```

**Explanation 1**

In this sample, so every city has space station and we print as our answer.