It is Advent season. There are ~M~ street lights in a street ~N~ metres long (the metres of the street are denoted with numbers from ~1~ to ~N~). Each of the lights lights up the metre of the street it's located in and ~K~ metres to the left and to the right of that location. In other words, if the light is located at metre ~X~, it lights up all metres of the street from ~X-K~ to ~X+K~, inclusively. Of course, it is possible for a metre of the street to be lit up by multiple street lights. All lights have distinct locations.

The problem is that there is a possibility that the lights don't light up all ~N~ metres of the street. It is your task to determine the minimal amount of additional lights needed to be put up (at a position from ~1~ to ~N~) so that the entire street is lit up.

Input Specification

The first line of input contains the number ~N~ ~(1 \le N \le 1000)~.
The second line of input contains the number ~M~ ~(1 \le M \le N)~.
The third line contains the number ~K~ ~(0 \le K \le N)~.
Each of the following ~M~ lines contains a number. The numbers are sorted in ascending order and represent the positions of each of the ~M~ street lights.
The positions will be distinct and from the interval ~[1, N]~.

Output Specification

You must output the required number from the task.

Sample Input 1

5
2
2
1
5

Sample Output 1

0

Explanation for Sample Output 1

It's not necessary to add lights to the street, since all ~N~ metres are already lit up.

Sample Input 2

26
3
3
3
19
26

Sample Output 2

2

Sample Input 3

13
2
10
1
2

Sample Output 3

1

Explanation for Sample Output 3

It is necessary to add one lamp, for example at location ~13~.