width = nil
map = {}
for line in io.lines(arg[1]) do
    if not width then
        width = #line
    end
    for char in line:gmatch(".") do
        table.insert(map, char)
    end
end

function reachable_keys(map, pos_y, pos_x, keys, dist)
    local cell = map[width * pos_y + pos_x]
    if cell == "@" then
        cell = "."
    end
    if cell == "." then
        map[width * pos_y + pos_x] = "#"
        reachable_keys(map, pos_y + 1, pos_x, keys, dist + 1)
        reachable_keys(map, pos_y - 1, pos_x, keys, dist + 1)
        reachable_keys(map, pos_y, pos_x + 1, keys, dist + 1)
        reachable_keys(map, pos_y, pos_x - 1, keys, dist + 1)
    elseif string.byte(cell) >= 97 and string.byte(cell) <= 122 then
        table.insert(keys, {key=cell, y=pos_y, x=pos_x, dist=dist})
    end
    return keys
end

function find_paths(map, pos_y, pos_x)
    local keys = reachable_keys({table.unpack(map)}, pos_y, pos_x, {}, 0)
    local paths = {}
    for _, key in ipairs(keys) do
        --print(key.key, key.dist)
        local open_map = {table.unpack(map)}
        open_map[width * pos_y + pos_x] = "."
        open_map[width * key.y + key.x] = "@"
        for i, x in ipairs(open_map) do
            if x:lower() == key.key then
                open_map[i] = "."
                break
            end
        end
        local path = find_paths(open_map, key.y, key.x)
        if #path == 0 then
            table.insert(paths, {path={key.key}, dist=key.dist})
        else
            for _, p in ipairs(path) do
                table.insert(p.path, key.key)
                p.dist = p.dist + key.dist
                table.insert(paths, p)
            end
        end
    end
    return paths
end

pos_y = nil
pos_x = nil
for i, x in ipairs(map) do
    if x == "@" then
        pos_y = i // width
        pos_x = i % width
        break
    end
end

paths = find_paths(map, pos_y, pos_x)
smallest = nil
for _, path in ipairs(paths) do
    if not smallest or smallest.dist > path.dist then
        smallest = path
    end
end
print(table.concat(smallest.path, ","), smallest.dist)