After seeing all the beautiful landscaping around Cossin,
Yraglac is inspired to work on his own gardening. Since food is
such a scarce commodity on Mars, he decides it would be nice to
plant an agricultural crop: Martian rice. The unique thing
about Martian rice is that it will only grow in flat areas
where water can pool, which makes it important to terrace the
garden carefully. Given a height profile of Yraglac’s garden,
can you help him determine how much of the land can grow rice
on?
Yraglac’s garden is divided into a regular grid of perfectly
square $1 \textrm{ m } \times 1
\textrm{ m}$ cells, and he provides you a map indicating
the exact height of the land within each cell. The entire
garden is surrounded by a wall that is higher than the highest
cell. In our model of the Mars world, rain water (real or
artificial) can flow from a cell to any of its four adjacent
cells (north, east, south, or west), provided the adjacent
cell’s height is lower than or equal to the cell’s height. A
cell is said to be able to collect or pool water if any water
landing in the cell cannot flow to another cell of lower
height, either directly or through any of its neighbouring
cells. Arrows in the diagram below illustrate possible
directions of water flow between cells, and circles indicate
the four cells that can collect water.
Input
The input begins with two integers, $x \; y$, which indicate the
dimensions of Yraglac’s garden, in metres ($1 \le x, y \le 500$). Then following
$y$ lines containing
$x$ integers, $h_{ij}$, each which indicate the
heights of each cell in Yraglac’s garden ($0 \le h_{ij} \le 999$).
Output
Output the number of square metres of land that Yraglac can
grow his rice crop on.
Sample Input 1 
Sample Output 1 
4 3
0 0 4 3
0 2 2 3
2 1 4 3

4

Sample Input 2 
Sample Output 2 
7 2
0 4 1 4 2 4 3
0 4 1 4 2 4 3

8

Sample Input 3 
Sample Output 3 
5 3
1 1 1 1 1
3 3 3 3 3
5 5 5 5 5

5

Sample Input 4 
Sample Output 4 
4 4
8 8 8 8
8 4 8 8
8 8 2 8
8 8 8 8

2
