Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Map

time limit per test

2 secondsmemory limit per test

128 megabytesinput

standard inputoutput

standard outputThere is an area map that is a rectangular matrix *n* × *m*, each cell of the matrix contains the average height of a corresponding area part. Peter works for a company that has to build several cities within this area, each of the cities will occupy a rectangle *a* × *b* cells on the map. To start construction works in a particular place Peter needs to remove excess ground from the construction site where a new city will be built. To do so he chooses a cell of the minimum height within this site, and removes excess ground from other cells of the site down to this minimum level. Let's consider that to lower the ground level from *h*_{2} to *h*_{1} (*h*_{1} ≤ *h*_{2}) they need to remove *h*_{2} - *h*_{1} ground units.

Let's call a site's position optimal, if the amount of the ground removed from this site is minimal compared to other possible positions. Peter constructs cities according to the following algorithm: from all the optimum site's positions he chooses the uppermost one. If this position is not unique, he chooses the leftmost one. Then he builds a city on this site. Peter repeats this process untill he can build at least one more city. For sure, he cannot carry out construction works on the occupied cells. Would you, please, help Peter place cities according to the algorithm?

Input

The first line contains four space-separated integers: map sizes *n*, *m* and city sizes *a*, *b* (1 ≤ *a* ≤ *n* ≤ 1000, 1 ≤ *b* ≤ *m* ≤ 1000). Then there follow *n* lines, each contains *m* non-negative space-separated numbers, describing the height matrix. Each number doesn't exceed 10^{9}.

Output

In the first line output *k* — the amount of constructed cities. In each of the following *k* lines output 3 space-separated numbers — the row number and the column number of the upper-left corner of a subsequent construction site, and the amount of the ground to remove from it. Output the sites in the order of their building up.

Examples

Input

2 2 1 2

1 2

3 5

Output

2

1 1 1

2 1 2

Input

4 4 2 2

1 5 3 4

2 7 6 1

1 1 2 2

2 2 1 2

Output

3

3 1 2

3 3 3

1 2 9

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/21/2019 16:53:43 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|