Illumination

You inherited a haunted house. Its floor plan is an $n \times n$ square grid with no interior walls, and $l$ lamps sit at fixed cells.

Each lamp lights either the row it stands in or the column it stands in, never both at once. The light reaches $r$ cells in both directions along the chosen line, so a lamp that no exterior wall blocks lights as many as $2r + 1$ cells, counting its own.

If one cell is lit by two lamps that both light a row, or by two lamps that both light a column, the bright spot drives the ghosts away for good and your property loses value. A cell lit by one lamp that lights a row together with one lamp that lights a column causes no trouble.

Decide whether every lamp can be given a row or a column without driving the ghosts away.

The first line contains three positive integers $n$, $r$ and $l$ ($1 \le n, r, l \le 1000$).

Each of the next $l$ lines contains two positive integers $r_i$ and $c_i$ ($1 \le r_i, c_i \le n$), meaning that a lamp stands in row $r_i$ and column $c_i$.

All lamp positions are distinct.

Print 1 on a single line if such an assignment exists, and 0 otherwise.