IOI '99 - Antalya-Belek, Turkey

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 Specification

The first line contains three integers: the number of squares in the east-west direction, ~U~ ~(1 \le U \le 700)~, the number of squares in the north-south direction, ~V~ ~(1 \le V \le 700)~, and ~C~ ~(0 \le C \le 10)~.
Each of the following ~V~ lines contains the integers ~H_{xy}~ ~(-30\,000 \le H_{xy} \le 30\,000)~ for ~x = 1, \dots, U~. More specifically, ~H_{xy}~ occurs as the ~x^{th}~ number on the ~(V-y+2)^{th}~ input line.

Output Specification

The output should consist of a single line containing four space-separated integers describing the region found: ~X_{\min}~, ~Y_{\min}, X_{\max}~, ~Y_{\max}~, where ~(X_{\min}, Y_{\min})~ are the coordinates of the southwest corner square, and ~(X_{\max}, Y_{\max})~ are the coordinates of the northeast corner square of the region.

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

4 5 8 11