The evil emperor Cactus has in his possession the Magic Keg and has flooded the Enchanted Forest! The Painter and the three little hedgehogs now have to return to the Beaver's den, where they will be safe from the water, as quickly as possible!

The map of the Enchanted Forest consists of \(R\) rows and \(C\) columns. Empty fields are represented by . characters, flooded fields by * and rocks by X. Additionally, the Beaver's den is represented by D and the Painter and the three little hedgehogs are shown as S.

Every minute the Painter and the three little hedgehogs can move to one of the \(4\) neighbouring fields (up, down, left or right). Every minute the flood expands as well, so that all empty fields that have at least one common side with a flooded field become flooded too. Neither the water nor the Painter and the hedgehogs can pass through rocks. Naturally, the Painter and the hedgehogs cannot pass through flooded fields, and the water cannot flood the Beaver's den.

Write a program that, given a map of the Enchanted Forest, outputs the shortest time needed for the Painter and the three little hedgehogs to safely reach the Beaver's den.

Note: The Painter and the hedgehogs cannot move into a field that is about to be flooded (in the same minute).

The first line contains two integers \(R\) and \(C\), both smaller than or equal to \(50\).

The following \(R\) lines each contain \(C\) characters (., *, X, D or S). The map contains exactly one D and exactly one S.

Output the shortest possible time needed for the Painter and the three little hedgehogs to safely reach the Beaver's den. If this is impossible, output the word KAKTUS on a line by itself.

riseoj 작성

출처 COCI 2006/2007 Contest 1