# A STRIP OF LAND

Time Limit: 20000MS

Memory Limit: 65536K

## Description

The residents of Dingilville are trying to locate a region to build an airport. The map of the land is at hand. The map is a rectangular grid of unit squares, each identified by a pair of coordinates (x,y), where x is the horizontal (west-east) and y is the vertical (south-north) coordinate. The height of every square is shown on the map. Your task is to find a rectangular region of squares with the largest area (i.e. a rectangular region consisting of the largest number of squares) such that 1.the height difference between the highest and the lowest squares of the region is less than or equal to a given limit C, and 2.the width (i.e. the number of squares along the west-east direction) of the region is at most 100. In case there is more than one such region you are required to report only one of them.

## Input

The first line contains three integers: U, V and C. Each of the following V lines contains the integers Hxy for x = 1,...,U. More specifically, Hxy occurs as the x'th number on the (V-y+2)'th input line. a.1 <= U <= 700, 1 <= V <= 700 where U and V designate the dimensions of the map. More specifically, U is the number of squares in the west-east direction, and V, in the south-north direction. b.0 <= C <= 10 c.-30,000 <= Hxy <= 30,000 where the integer Hxy is the height of the square at coordinates (x, y), 1 <= x <= U, 1 <= y <= V. d.The southwest corner square of the map has the coordinates (1,1) and the northeast corner has the coordinates (U,V).

## Output

Output the largest area.

## Sample Input

10 15 4
41 40 41 38 39 39 40 42 40 40
39 40 43 40 36 37 35 39 42 42
44 41 39 40 38 40 41 38 35 37
38 38 33 39 36 37 32 36 38 40
39 40 39 39 39 40 40 41 43 41
39 40 41 38 39 38 39 39 39 42
36 39 39 39 39 40 39 41 40 41
31 37 36 41 41 40 39 41 40 40
40 40 40 42 41 40 39 39 39 39
42 40 44 40 38 40 39 39 37 41
41 41 40 39 39 40 41 40 39 40
47 45 49 43 43 41 41 40 39 42
42 41 41 39 40 39 42 40 42 42
41 44 49 43 46 41 42 41 42 42
45 40 42 42 46 42 44 40 42 41

## Sample Output

35

N/A