It is Advent season. There are ~M~ street lights in a street ~N~ metres long (the meters of the street are denoted with numbers from ~1~ to ~N~). Each of the lights lights up the meter of the street it's located in and ~K~ meters to the left and to the right of that location. In other words, if the light is located at meter ~X~, it lights up all metres of the street from ~X - K~ to ~X + K~, inclusively. Of course, it is possible for a meter 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 position from ~1~ to ~N~) so that the entire street is lit up.
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]~.
You must output the required number from the task.
Sample Input 1
5 2 2 1 5
Sample Output 1
Clarification of the first test case:
It's not necessary to add lights to the street, since all ~N~ meters are already lit up.
Sample Input 2
26 3 3 3 19 26
Sample Output 2
Sample Input 3
13 2 10 1 2
Sample Output 3
Clarification of the third test case:
It is necessary to add one lamp, for example at location ~13~.