You are playing a pinball-like game on a (h \times w) grid. The game begins with a small ball located at the center of a specific cell marked as (S). Each cell of the grid is either: A block-type wall ((#)) that prevents the ball from entering the cell, reflecting it instead. A thin oblique wall, either left-leaning ((\\)) or right-leaning ((/)), which reflects the ball according to its orientation. A free cell ((.)) where the ball can move freely. The goal is to make the ball escape the grid. At the start, you can nudge the ball in one of four directions: up ((U)), down ((D)), left ((L)), or right ((R)). The ball traverses a free cell in one second, it enters and exits a cell containing a thin oblique wall in one second, and it bounces off a block-type wall in no time (the block-type wall occupies all of its cell). Collisions between the ball and all walls, both block-type and oblique, are perfectly elastic, causing the ball to reflect upon contact. For example, the ball takes two seconds to enter a free cell, traverse it, bounce off an adjacent block-type wall, and traverse back the free cell until it exits. As the ball moves, you may destroy oblique walls at any time, permanently converting them into free cells. You may destroy multiple oblique walls throughout the game, at any given time. Determine whether it is possible for the ball to escape, and if so, find the minimum number of oblique walls that need to be destroyed, along with the precise time each chosen wall should be destroyed. The first line contains two integers (h) and (w) ((1\le h, w \le 1000)) — the size of the grid. The next (h) lines describe the grid at the beginning of the game. The (i)-th of these lines contains (w) characters, describing the cells on the (i)-th row. A dot ((.)) denotes a free cell, a hash sign ($$$\texttt{#