Achluophobic Angus  light.X

Bessie's newest calf, Calfbert, has become achluophic: she is
afraid of the dark. Bessie has decided light up the entire field
so Calfbert will be able to sleep soundly. Farmer John has already
set up lamps in his field which light it completely, but, being an
environmentally friendly cow, Bessie wishes to use as few of these
lamps as possible.

Farmer John's field is a rectangular grid with R rows (1 <= R
<= 24) numbered 1..R and C columns (1 <= C <= 24) numbered 1..C
with L (1 <= L <= 256) lamps located in some of the squares of the
grid. Each lamp, when lit, illuminates a 3x3 region (9 squares
total) with the center being the actual location of the lamp. The
light from some lamps spills outside the field, with no effect that
we care about. No square contains more than one lamp.

Given the set of lamps FJ has installed, your job is to find the
minimal number of lamps that will still light every square of the
entire field.

PROBLEM NAME: light

INPUT FORMAT:

* Line 1: Three space-separated integers: R, C, and L

* Lines 2..L+1: Each line contains two space-separated integers, L_R &
        L_C, that represent row and column respectively of a lamp's
        location

SAMPLE INPUT:

5 8 7
2 2
4 2
2 4
3 4
4 4
2 7
4 7

OUTPUT FORMAT:

* Line 1: One integer that is the minimum number of lit lamps required
        to illuminate  each square in the field

SAMPLE OUTPUT:

6