public L1Maze(string[] input)
{
var fields = input.SelectMany((line, y) => line.Select((c, x) => (p: (x, y), c))).ToArray();
Corridors = new HashSet <(int, int)>(fields.Where(f => f.c != '#').Select(f => f.p));
Keys = fields.Where(f => char.IsLower(f.c)).ToDictionary(f => f.p, f => BitForKey(char.ToUpper(f.c)));
Doors = fields.Where(f => char.IsUpper(f.c)).ToDictionary(f => f.p, f => BitForKey(f.c));
StartPositions = fields.Where(f => f.c == '@').Select(f => f.p).ToArray();
StartPosition = StartPositions.First();
AllKeys = Keys.Values.Aggregate(0u, (a, k) => a | k);
}