The Worm Turns

Winston the Worm wakes up in a rectangular patch of earth divided into cells. Each cell contains either a piece of food or a rock. Winston starts by eating the food in some cell, then chooses one of the four directions -- north, south, east, or west -- and crawls in a straight line as long as the cell directly ahead of him still contains uneaten food, eating each cell he enters.

When the cell directly ahead is a rock, a cell whose food he has already eaten, or lies outside the patch, he turns $90^\circ$ (to his left or to his right) and again crawls as far as he can in a straight line, eating food; he can only move onto uneaten food. He never enters a cell twice. When he can no longer move in any direction, he stops.

By choosing his starting cell, his initial direction, and which way to turn at each obstacle, Winston can influence how much food he eats. Your task is to determine a starting cell and an initial direction that let Winston eat as many pieces of food as possible.

The input contains several test cases. Each test case begins with two positive integers $m$ and $n$, the number of rows and columns of the patch; rows and columns are numbered starting at $0$. Then follows a non-negative integer $r$, the number of rocks, and after it $2r$ integers giving the row and column of each rock. The product $m \times n$ never exceeds $625$. A line containing two zeros follows the last test case and is not processed.

For each test case, print its number (starting from $1$) followed by four values in the format

Case k: amount row column direction

where amount is the maximum number of pieces of food Winston can eat, (row, column) is a starting cell from which he can eat that many pieces, and direction is one of E, N, S, W, the direction in which he first moves. If several starting cells allow the maximum, output the one that is smallest in (row, column) order. If that cell allows the maximum with several initial directions, output the first of E, N, S, W that does. You may assume there is always at least one piece of food adjacent to Winston's starting position.