Looking for Waldo

문제

You may know the game Where is Waldo?. In this game you need to find a person named Waldo in a crowd of people. This problem is kind of similar. You need to find an axis-aligned rectangle of minimal area which contains the letters W, A, L, D and O and those letters are hidden in a crowd of other letters.

Figure L.1: Illustration of the second sample case.

입력

The input consists of:

• One line with two integers $hh$ and $ww$ $(1\le h,w\le {10}^5(1\backslash leq\; h,\; w\; \backslash leq\; 10^5$, $h\cdot w\le {10}^5)h\backslash cdot\{\}w\; \backslash leq\; 10^5)$, the height and width of the grid of letters.
• $hh$ lines, each with $ww$ upper case letters A-Z, the grid of letters.

출력

Output the area of the smallest axis-aligned rectangle which contains at least one of each of the letters W, A, L, D and O. If there is no rectangle containing those letters, output impossible.