import Foundation

struct Coord : Hashable, CustomStringConvertible {
    let (x, y): (Int, Int)
    var description: String { return "(\(x), \(y))" }
    func dist(to: Coord) -> Int { return abs(x - to.x) + abs(y - to.y) }
}

struct Maze {
    let (w, h): (Int, Int)
    let walls: Set<Coord>
    let (start, end): (Coord, Coord)
    let cheatMax: Int

    func valid(_ cell: Coord) -> Bool {
        return cell.x >= 0 && cell.x < w && cell.y >= 0 && cell.y < h &&
            !walls.contains(cell)
    }

    func neighbors(of cell: Coord) -> [Coord] {
        return [(-1, 0), (1, 0), (0, -1), (0, 1)]
            .map { Coord(x: cell.x + $0, y: cell.y + $1) }.filter(valid)
    }

    func cheats(from entry: Coord) -> [Coord: Int] {
        return Dictionary(uniqueKeysWithValues: (2...cheatMax)
            .flatMap { dist -> [(Int, Int)] in
                (0..<dist).flatMap { d -> [(Int, Int)] in
                    [(d, dist-d), (dist-d, -d), (-d, d-dist), (d-dist, d)]
                }
            }
            .map { dx, dy -> Coord in Coord(x: entry.x + dx, y: entry.y + dy) }
            .filter(valid)
            .map { end -> (Coord, Int) in (end, entry.dist(to: end)) }
        )
    }

    func cheats() -> [Int] {
        var cost: [Coord: Int] = [start: 0]
        var jumps: [(Coord, Coord, Int)] = []
        var cell = start
        var prev = start
        var currentCost = 0
        while cell != end {
            // list potential cheats from current cell
            let newCheats = cheats(from: cell)
                .filter { dest, _ in !cost.keys.contains(dest) }
                .map { dest, dist in (cell, dest, dist) }
            jumps.append(contentsOf: newCheats)
            // add cost to table
            let next = neighbors(of: cell).filter { $0 != prev }[0]
            currentCost += 1
            cost[next] = currentCost 
            prev = cell
            cell = next
        }
        return jumps.map { from, to, dist in cost[to]! - cost[from]! - dist }
    }
}

func readInput(_ filePath: String, _ cheatMax: Int) throws -> Maze {
    let content = try String(contentsOfFile: filePath, encoding: .ascii)
    let lines = content.split(separator: "\n")
    let (w, h) = (lines[0].count, lines.count)
    var walls: Set<Coord> = []
    var (start, end) = (Coord(x: 0, y: 0), Coord(x: w-1, y: h-1))
    lines.enumerated().forEach { i, line in
        line.enumerated().forEach { j, cell in
            let coord = Coord(x: j, y: i)
            if cell == "#" {
                walls.insert(coord)
            } else if cell == "S" {
                start = coord
            } else if cell == "E" {
                end = coord
            }
        }
    }
    return Maze(
        w: w, h: h, walls: walls, start: start, end: end, cheatMax: cheatMax
    )
}

let maze = try readInput(CommandLine.arguments[1], Int(CommandLine.arguments[2])!)
print(maze.cheats().filter { $0 >= 100 }.count)