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 $13$.