Birds on a Wire

An electrical wire of length $\ell$ centimetres hangs between two poles, and birds like to sit on it. Watching them from your balcony after work, you notice two habits. The birds never sit closer than $d$ centimetres to each other. The poles carry spikes that keep faeces from damaging the wood, so no bird sits closer than 6 centimetres to either pole.

You are given the length $\ell$, the distance $d$, and the positions of the birds already on the wire. Find how many more birds can sit on the wire. Assume the birds have zero width.

The first line contains three space separated integers: the length of the wire $\ell$, the distance $d$, and the number $n$ of birds already sitting on the wire.

Each of the next $n$ lines contains the position of one bird, in any order. A position is the distance measured from one pole, and the answer is the same whichever pole you measure from.

All numbers are integers with $1 \le \ell, d \le 1\,000\,000\,000$ and $0 \le n \le 20\,000$. The birds already on the wire are at least 6 centimetres from both poles and at least $d$ centimetres apart from each other.

If you object to fitting that many birds on a line hanging between two poles, you may imagine that the line is 0 centimetres above ground level, or that the birds are ants.

Print one line with one integer: the maximal number of additional birds that can sit on the wire.