questhelperredux/QuestHelper/graph_core.lua

local GetTime = QuestHelper_GetTime

QuestHelper_File["graph_core.lua"] = "4.0.1.$svnversion$"
QuestHelper_Loadtime["graph_core.lua"] = GetTime()

-- Alright so what's the interface here
-- There's the obvious "find a path from A to B"
-- function QH_Graph_Pathfind(st, nd, make_path)
-- Right now, we're pretending that the world consists of infinite planes with links between them. That's where the whole "between-zone" thing occurs. So one way or another, we need to add links. We'll use name as an identifier so we can get rid of flight paths links later, and the coords will include a plane ID number.
-- function QH_Graph_Plane_Makelink(name, coord1, coord2, cost)
-- And then we need a way to get rid of links, so:

-- how does flying work zorba
-- how can we fly
-- howwwwww

-- Make a map from "phase" to "flyphase". Store all the links we're being told to make. When placing links, if the flyphase is flyable, we use the flyphase instead of the phase for placing. We don't place if it's an internal boundary (there's a few ways we can detect this, but let's just use the hacky one where we just look at the ID.) From there it's all pretty standard.

-- performance hack :(
local QH_Timeslice_Yield = QH_Timeslice_Yield
local tinsert, tremove = table.insert, table.remove
local pairs, ipairs = pairs, ipairs
local sqrt = math.sqrt
local GetTime = GetTime

local function heap_left(x) return (2*x) end
local function heap_right(x) return (2*x + 1) end

local function heap_sane(heap)
  local dmp = ""
  local finishbefore = 2
  for i = 1, #heap do
    if i == finishbefore then
      print(dmp)
      dmp = ""
      finishbefore = finishbefore * 2
    end
    dmp = dmp .. string.format("%f ", heap[i].c)
  end
  print(dmp)
  print("")
  for i = 1, #heap do
    --[[ assert(not heap[heap_left(i)] or heap[i].c <= heap[heap_left(i)].c) ]]
    --[[ assert(not heap[heap_right(i)] or heap[i].c <= heap[heap_right(i)].c) ]]
  end
end

local function heap_insert(heap, item)
  --[[ assert(item) ]]
  tinsert(heap, item)
  local pt = #heap
  while pt > 1 do
    local ptd2 = math.floor(pt / 2)
    if heap[ptd2].c <= heap[pt].c then
      break
    end
    local tmp = heap[pt]
    heap[pt] = heap[ptd2]
    heap[ptd2] = tmp
    pt = ptd2
  end
  --heap_sane(heap)
end

local function heap_extract(heap)
  local rv = heap[1]
  if #heap == 1 then tremove(heap) return rv end
  heap[1] = tremove(heap)
  local idx = 1
  while idx < #heap do
    local minix = idx
    --local hl, hr = heap_left(idx), heap_right(idx)
    local hl, hr = 2*idx, 2*idx+1 -- these had better be equivalent to the line above one
    if heap[hl] and heap[hl].c < heap[minix].c then minix = hl end
    if heap[hr] and heap[hr].c < heap[minix].c then minix = hr end
    if minix ~= idx then
      local tx = heap[minix]
      heap[minix] = heap[idx]
      heap[idx] = tx
      idx = minix
    else
      break
    end
  end
  --heap_sane(heap)
  return rv
end

-- incremented on each graph iteration, so we don't have to clear everything. "GRaph ID" :D
local grid = 0

-- Plane format: each plane contains an array of nodes that exist in that plane.
-- Each node contains both its parent ID and its coordinates within that plane. It may contain a node it links to, along with cost.
local plane = {}

local plane_to_flyplane = {}
local continent_to_flyplane = {}
local flyplanes_enabled = {}
local plane_multiplier = {}
local plane_cull = {}

-- canonical plane :D
local function canoplane(plane)
  if flyplanes_enabled[plane_to_flyplane[plane]] then return plane_to_flyplane[plane] else return plane end
end

local function xydist_raw(plane, stx, sty, ndx, ndy)
  local dx, dy = stx - ndx, sty - ndy
  return sqrt(dx * dx + dy * dy) / (plane_multiplier[plane] or 7)
end
local function xydist(st, nd)
  --QuestHelper: Assert(canoplane(st.p) == canoplane(nd.p))
  local dx, dy = st.x - nd.x, st.y - nd.y
  return sqrt(dx * dx + dy * dy) / (plane_multiplier[canoplane(nd.p)] or 7) -- we're getting a result in seconds, not in yards
end





function QH_Graph_Pathfind(st, nd, reverse, make_path)
  return QH_Graph_Pathmultifind(st, {nd}, reverse, make_path)[1]
end

local active = false
local prepared = false

  
  local extrctime = 0
  local wextrctime = 0
  local actualtime = 0
  local planetime = 0
  local linktime = 0
  
function QH_Graph_Pathmultifind(st, nda, reverse, make_path)
  --QuestHelper:TextOut("Starting PMF")
  QuestHelper: Assert(not active)
  QuestHelper: Assert(prepared)
  QuestHelper: Assert(st.x and st.y and st.p)
  active = true -- The fun thing about coroutines is that this is actually safe.
  local out = QuestHelper:CreateTable("graphcore output")  -- THIS HAD BETTER BE RELEASABLE OR IT WILL BE BAD
  
  local undone = QuestHelper:CreateTable("graphcore undone")
  local remaining = 0
  
  local link = QuestHelper:CreateTable("graphcore link")
  
  --local stats = QuestHelper:CreateTable("graphcore --stats")
  
  --stats.dests_complex = 0
  --stats.dests_total = 0

-- Ugly database hack
  if st.p == 26 then st.p = 48 end -- Alterac Mountains merged to Hillsbrad Foothills
  if st.p == 38 then st.p = 168 end -- Ditto Stranglethorn
-- end hack
  
  for k, v in ipairs(nda) do
    QuestHelper: Assert(v.x and v.y and v.p)
-- Ugly database hack pt. 2
    if v.p == 26 then v.p = 48 end -- Alterac Mountains merged to Hillsbrad Foothills
    if v.p == 38 then v.p = 168 end -- Ditto Stranglethorn
-- end hack    
    local cpvp = canoplane(v.p)
    if plane[cpvp] then
      --print("Destination plane insertion")
      local dest = QuestHelper:CreateTable("graphcore destination")
      dest.x, dest.y, dest.p, dest.goal = v.x, v.y, cpvp, k
      link[k] = dest
      tinsert(plane[cpvp], link[k])
      undone[k] = true
      remaining = remaining + 1
      --stats.dests_complex = --stats.dests_complex + 1
    end
    --stats.dests_total = --stats.dests_total + 1
  end
  
  local link_id = reverse and "rlinks" or "links"
  
  --stats.node_initialized_first = 0
  --stats.node_done = 0
  --stats.node_done_already = 0
  --stats.node_modified_before_use = 0
  --stats.node_link_reprocessed = 0
  --stats.node_link_first = 0
  --stats.node_link_alreadydone = 0
  --stats.node_inner_reprocessed = 0
  --stats.node_inner_first = 0
  --stats.node_inner_alreadydone = 0
  
  local dijheap = QuestHelper:CreateTable("graphcore heap container")
  local stnode = QuestHelper:CreateTable("graphcore stnode")
  do
    stnode.x, stnode.y, stnode.p, stnode.c, stnode.scan_id, stnode.scan_cost = st.x, st.y, canoplane(st.p), st.c, grid, 0
    QuestHelper: Assert(plane[canoplane(st.p)], "Plane " .. canoplane(st.p) .. " does not exist.")
    tinsert(plane[stnode.p], stnode)
    
    local hep = QuestHelper:CreateTable("graphcore heap")
    hep.c, hep.n = 0, stnode  -- more than the subtraction, less than the minimum
    heap_insert(dijheap, hep)
  end
  
  --stats.heap_max = #dijheap
  
  --QuestHelper:TextOut("Starting routing")
  
  local extrc = 0
  local actual = 0
  local planescan = 0
  local linkscan = 0
  
  local planeyes = 0
  local planeno = 0
  
  local linkyes = 0
  local linkno = 0
  
  while remaining > 0 and #dijheap > 0 do
    QH_Timeslice_Yield()
    local ett = GetTime()
    extrc = extrc + 1
    --stats.heap_max = math.max(--stats.heap_max, #dijheap)
    local cdj = heap_extract(dijheap)
    
    local snode = cdj.n
    --print(string.format("Extracted cost %f/%s pointing at %d/%f/%f", cdj.c, tostring(cdj.n.scan_cost), cdj.n.p, cdj.n.x, cdj.n.y))
    if snode.scan_cost == cdj.c then  -- if we've modified it since then, don't bother
      local actt = GetTime()
      actual = actual + 1
      -- Are we at an end node?
      if snode.goal then
        -- we wouldn't be here if we hadn't found a better solution
        --QuestHelper: Assert(undone[snode.goal])
        out[snode.goal] = cdj.c
        undone[snode.goal] = nil
        remaining = remaining - 1
      end
      
      -- Link to everything else on the plane
      if not cdj.pi then  -- Did we come from this plane? If so, there's no reason to scan it again  (flag means "plane internal")
        local planet = GetTime()
        planescan = planescan + 1
        for _, v in ipairs(plane[snode.p]) do
          if v.scan_id ~= grid or v.scan_cost > snode.scan_cost then
            planeyes = planeyes + 1
            local dst = xydist(snode, v)
            local modcost = snode.scan_cost + dst
            --print(string.format("Doing %d/%f vs %s/%s at %d/%f/%f", grid, modcost, tostring(v.scan_id), tostring(v.scan_cost), v.p, v.x, v.y))
            if v.scan_id ~= grid or v.scan_cost > modcost then
              v.scan_id = grid
              v.scan_cost = modcost
              v.scan_from = snode
              v.scan_processed = false
              v.scan_outnode = nil
              v.scan_outnode_from = nil
              
              do
                local ncdj = QuestHelper:CreateTable("graphcore heap")
                ncdj.c, ncdj.n, ncdj.pi = modcost, v, true
                heap_insert(dijheap, ncdj)
                --print(string.format("Inserting %f at %d/%f/%f, plane", snude.c, v.p, v.x, v.y))
              end
            end
          else
            planeno = planeno + 1
          end
        end
        planetime = planetime + GetTime() - planet
      end
      
      -- Link to everything we link to
      if not cdj.li and snode[link_id] then
        local linkt = GetTime()
        linkscan = linkscan + 1
        for _, lnk in pairs(snode[link_id]) do
          local mc2 = snode.scan_cost + lnk.cost
          local linkto = lnk.link
          if linkto.scan_id ~= grid or linkto.scan_cost > mc2 then
            linkyes = linkyes + 1
            linkto.scan_id = grid
            linkto.scan_cost = mc2
            linkto.scan_from = snode
            linkto.scan_outnode = lnk.outnode_to
            linkto.scan_outnode_from = lnk.outnode_from
            
            local hep = QuestHelper:CreateTable("graphcore heap")
            hep.c, hep.n, hep.li = mc2, linkto, true
            heap_insert(dijheap, hep)
            --print(string.format("Inserting %f at %d/%f/%f, link", hep.c, linkto.p, linkto.x, linkto.y))
          else
            linkno = linkno + 1
          end
        end
        linktime = linktime + GetTime() - linkt
      end
      actualtime = actualtime + GetTime() - actt
      extrctime = extrctime + GetTime() - ett
    else
      wextrctime = wextrctime + GetTime() - ett
    end
    QuestHelper:ReleaseTable(cdj)
  end
  
  --QuestHelper:TextOut(string.format("%d extracted, %d processed, %d planescan, %d linkscan, %d/%d plane, %d/%d link", extrc, actual, planescan, linkscan, planeyes, planeno, linkyes, linkno))
  --QuestHelper:TextOut(string.format("times: %f/%f extracted, %f processed, %f planescan, %f linkscan", extrctime, wextrctime, actualtime, planetime, linktime))
  
  for _, v in ipairs(dijheap) do
    QuestHelper:ReleaseTable(v)
  end
  QuestHelper:ReleaseTable(dijheap)
  dijheap = nil
  
  --QuestHelper:TextOut(string.format("Earlyout with %d/%d remaining", #dijheap, remaining))
  if remaining > 0 then
    for k, v in ipairs(nda) do
      if not out[k] then
        QuestHelper: Assert(false, string.format("Couldn't find path to %d/%f/%f from %d/%f/%f", nda[k].p, nda[k].x, nda[k].y, st.p, st.x, st.y))
      end
    end
  end
  QuestHelper: Assert(remaining == 0)
  
  grid = grid + 1
  QuestHelper: Assert(grid < 1000000000) -- if this ever triggers I will be amazed
  
  if make_path then
    --print("mpath")
    for k, v in pairs(out) do
      QH_Timeslice_Yield()
      --print(out[k])
      local rp = QuestHelper:CreateTable("graphcore return")
      rp.d = v
      
      out[k] = rp
      --print(out[k])
      
      if link[k] then
        QuestHelper: Assert(link[k].scan_from)
        local tpath = reverse and rp or QuestHelper:CreateTable("graphcore path reversal")
        local cpx = link[k].scan_from
        local mdlast = nil
        while cpx do
          QuestHelper: Assert(cpx)
          
          if cpx.scan_outnode then
            tinsert(tpath, cpx.scan_outnode)
          end
          if cpx.scan_outnode_from then
            tinsert(tpath, cpx.scan_outnode_from)
          end
          
          cpx = cpx.scan_from
        end
        QuestHelper: Assert(not mdlast)
        
        if not reverse then
          for i = #tpath, 1, -1 do
            tinsert(rp, tpath[i])
          end
          
          QuestHelper: Assert(tpath ~= rp)
          QuestHelper:ReleaseTable(tpath)
        end
      end
    end
  end
  
  QuestHelper:ReleaseTable(table.remove(plane[stnode.p])) -- always added last, so we remove it first
  for k, v in ipairs(nda) do
    if plane[canoplane(v.p)] and plane[canoplane(v.p)][#plane[canoplane(v.p)]].goal then   -- might not be the exact one, but we'll remove 'em all once we get there anyway :D
      QuestHelper:ReleaseTable(table.remove(plane[canoplane(v.p)]))
    end
  end
  
  QuestHelper:ReleaseTable(link)
  QuestHelper:ReleaseTable(undone)
  
  --QuestHelper:TextOut("Finishing")
  
  --for k, v in pairs(stats) do
    --print(k, v)
  --end
  
  active = false
  return out  -- THIS HAD BETTER BE RELEASABLE OR IT WILL BE BAD
end

function QH_Graph_Init()
  for c, d in pairs(QuestHelper_IndexLookup) do
    if type(c) == "number" then
      QuestHelper: Assert(d[0])
      continent_to_flyplane[c] = d[0]
      for z, p in pairs(d) do
        if type(z) == "number" then
          --QuestHelper:TextOut(string.format("%d/%d: %d", c, z, p))
          plane_to_flyplane[p] = d[0]
        end
      end
    end
  end
end

local linkages = {}

local function findnode(coord)
  local p = canoplane(coord.p)
  if not plane[p] then plane[p] = {} end
  for _, v in ipairs(plane[p]) do
    if v.x == coord.x and v.y == coord.y and v.name == coord.name then
      return v
    end
  end
  
  local nd = {x = coord.x, y = coord.y, p = p, name = coord.name}
  tinsert(plane[p], nd)
  return nd
end

function QH_Graph_Plane_Makelink(name, coord1, coord2, cost, cost_reverse)
  QuestHelper: Assert(not active)
  prepared = false
  
  --QuestHelper: TextOut(string.format("Link '%s' made from %d/%f/%f to %d/%f/%f of cost %f, asymflag %s", name, coord1.p, coord1.x, coord1.y, coord2.p, coord2.x, coord2.y, cost, tostring(not not asymmetrical)))
  QuestHelper: Assert(name)
  QuestHelper: Assert(coord1)
  QuestHelper: Assert(coord2)
  QuestHelper: Assert(cost)
  
  QuestHelper: Assert(cost >= 0)
  QuestHelper: Assert(not cost_reverse or cost_reverse >= 0)
  
  --cost = math.max(cost, 0.01)
  --if cost_reverse then cost_reverse = math.max(cost_reverse, 0.01) end
  
  local tlink = {name, coord1, coord2, cost, cost_reverse}
  if not linkages[name] then linkages[name] = {} end
  tinsert(linkages[name], tlink)
  --print(name, coord1.map_desc[1], coord2.map_desc[1], coord)
end

function QH_Graph_Plane_Destroylinks(name)
  QuestHelper: Assert(not active)
  prepared = false
  
  linkages[name] = nil
  
  -- we'll actually clean things out once the refresh function is called
end

function QH_Graph_Flyplaneset(fpset, speed, cull)
  QuestHelper: Assert(not active)
  prepared = false
  
  local index = QuestHelper_IndexLookup[fpset][0]
  if not flyplanes_enabled[index] or plane_multiplier[index] ~= speed or plane_cull[index] ~= cull then
    flyplanes_enabled[index] = true
    plane_multiplier[index] = speed
    plane_cull[index] = cull
  end
  
  -- we'll actually clean things out once the refresh function is called
end

function QH_Graph_Plane_Refresh()
  --QuestHelper:TextOut("Graph plane refresh now")
  QuestHelper: Assert(not active)
  
  plane = {}  -- reset it all
  
  -- we take all our links, process them, and jam them together
  -- mmmm
  -- jam
  
  for name, v in pairs(linkages) do
    --print("Starting linkage", name)
    local titx = {}
    local nodeitems = {}
    local nodedests = {}
    
    local function makenodedest(outnode, package)
      if not nodedests[outnode] then
        nodedests[outnode] = {x = package.x, y = package.y, p = package.p, c = package.c, map_desc = package.map_desc, condense_class = package.condense_class} -- note: this is where the actual node objects that eventually get passed into the routing controller's path replot engine come from. So if you intend for anything to exist in that module, it's gotta be inserted here.
      end
    end
  
    for _, i in ipairs(v) do
      local name, coord1, coord2, cost, cost_reverse = unpack(i)
      
      QuestHelper: Assert(name)
      QuestHelper: Assert(coord1)
      QuestHelper: Assert(coord2)
      QuestHelper: Assert(cost)
    
      i.n1, i.n2 = findnode(coord1), findnode(coord2)
      
      table.insert(titx, i)
      
      if not nodeitems[i.n1] then nodeitems[i.n1] = QuestHelper:CreateTable("graph plane refresh") end
      if not nodeitems[i.n2] then nodeitems[i.n2] = QuestHelper:CreateTable("graph plane refresh") end
      
      table.insert(nodeitems[i.n1], i)
      table.insert(nodeitems[i.n2], i)
      
      makenodedest(i.n1, coord1)
      makenodedest(i.n2, coord2)
    end
    
    --QuestHelper:TextOut(string.format("%d titx", #titx))
    
    -- all nodes are created, links are posted
    
    local nodedone = {}
    local mark
    mark = function(tnode, acum)
      if acum[tnode] then return end
      acum[tnode] = true
      nodedone[tnode] = true
      
      for _, d in ipairs(nodeitems[tnode]) do
        mark(d.n1, acum)
        mark(d.n2, acum)
      end
    end
    
    local infinity = 1e10
    
    for _, connect in ipairs(titx) do
      QH_Timeslice_Yield()
      
      QuestHelper: Assert(nodedone[connect.n1] == nodedone[connect.n2])
      
      if not nodedone[connect.n1] then
        local nods = QuestHelper:CreateTable("graph plane nods")
        local nods_reverse = QuestHelper:CreateTable("graph plane nods_reverse")
        mark(connect.n1, nods)
        
        local lookupindex = 1
        for k, v in pairs(nods) do
          nods[k] = lookupindex
          nods_reverse[lookupindex] = k
          lookupindex = lookupindex + 1
        end
        
        --QuestHelper:TextOut(string.format("Processing cluster of %d", lookupindex))
        
        local tab = QuestHelper:CreateTable("graph plane floyd core")
        for r = 1, lookupindex do
          local inner = QuestHelper:CreateTable("graph plane floyd inner")
          table.insert(tab, inner)
          for tr = 1, lookupindex do
            table.insert(inner, infinity)
          end
        end
        
        for k, _ in pairs(nods) do
          for _, titem in pairs(nodeitems[k]) do
            local a, b = nods[titem.n1], nods[titem.n2]
            tab[a][b] = math.min(tab[a][b], titem[4])
            if titem[5] then
              tab[b][a] = math.min(tab[b][a], titem[5])
            end
          end
        end
        
        for pivot in ipairs(tab) do
          for s in ipairs(tab) do
            for e in ipairs(tab) do
              tab[s][e] = math.min(tab[s][e], tab[s][pivot] + tab[pivot][e])
            end
          end
        end
        
        -- add node link destinations here (we only need one sample per item)
        for s, t in ipairs(tab) do
          local n1 = nods_reverse[s]
          for e, c in ipairs(t) do
            local n2 = nods_reverse[e]
            
            local doit = true
            
            if c == infinity then doit = false end
            if doit then
              local n1p = canoplane(nodedests[n1].p)
              local n2p = canoplane(nodedests[n2].p)
              
              if n1p == n2p then
                if name == "static_transition" then doit = false end -- ha ha, yep, that's how we find out, tooootally reliable
                if plane_cull[n1p] then doit = false end  -- DENIED
                
                if doit then
                  local xyd = xydist_raw(n1p, nodedests[n1].x, nodedests[n1].y, nodedests[n2].x, nodedests[n2].y)
                  
                  if c >= xyd then doit = false end -- it's faster to just fly directly. this won't fuck with the total-connectedness at all, because if it is faster to just fly directly from cluster A to cluster B, we'll just pick up cluster B when we get there
                end
              end
            end
            
            
            if doit then
              if not n1.links then n1.links = {} end
              if not n2.rlinks then n2.rlinks = {} end
              
              --if name == "flightpath" then print("linking from", nodedests[n1].map_desc[1], "to", nodedests[n2].map_desc[1]) end
              tinsert(n1.links, {cost = c, link = n2, outnode_to = nodedests[n2], outnode_from = nodedests[n1]})
              tinsert(n2.rlinks, {cost = c, link = n1, outnode_to = nodedests[n1], outnode_from = nodedests[n2]})
            end
          end
        end
        
        QuestHelper:ReleaseTable(nods)
        QuestHelper:ReleaseTable(nods_reverse)
        for _, v in ipairs(tab) do QuestHelper:ReleaseTable(v) end
        QuestHelper:ReleaseTable(tab)
      end
    end
    
    for _, v in pairs(titx) do v.n1, v.n2 = nil, nil end
    for _, v in pairs(nodeitems) do QuestHelper:ReleaseTable(v) end
  end
  
  prepared = true
  --QuestHelper:TextOut("Graph plane refresh done")
end



--[[
local function QH_Graph_Plane_ReallyMakeLink(item)
  local name, coord1, coord2, cost, cost_reverse = unpack(item)
  
  QuestHelper: Assert(not active)
  
  --QuestHelper: TextOut(string.format("Link '%s' made from %d/%f/%f to %d/%f/%f of cost %f, asymflag %s", name, coord1.p, coord1.x, coord1.y, coord2.p, coord2.x, coord2.y, cost, tostring(not not asymmetrical)))
  QuestHelper: Assert(name)
  QuestHelper: Assert(coord1)
  QuestHelper: Assert(coord2)
  QuestHelper: Assert(cost)
  
  local n1p = canoplane(coord1.p)
  local n2p = canoplane(coord2.p)
  
  if n1p == n2p then
    if name == "static_transition" then return end -- ha ha, yep, that's how we find out, tooootally reliable
    
    local xyd = xydist_raw(n1p, coord1.x, coord1.y, coord2.x, coord2.y)
    if plane_cull[n1p] then return end  -- DENIED
    if cost >= xyd and (not cost_reverse or cost_reverse >= xyd) then
      return  -- DENIED
    end
  end
  
  local node1 = findnode(coord1)
  local node2 = findnode(coord2)
  
  local n1d = {x = coord1.x, y = coord1.y, p = coord1.p, c = coord1.c, map_desc = coord1.map_desc, condense_class = coord1.condense_class}
  local n2d = {x = coord2.x, y = coord2.y, p = coord2.p, c = coord2.c, map_desc = coord2.map_desc, condense_class = coord2.condense_class}
  
  if not node1.links then node1.links = {} end
  if not node2.rlinks then node2.rlinks = {} end
  
  tinsert(node1.links, {cost = cost, link = node2, outnode_to = n2d, outnode_from = n1d})
  tinsert(node2.rlinks, {cost = cost, link = node1, outnode_to = n1d, outnode_from = n2d})
  
  if cost_reverse then
    if not node1.rlinks then node1.rlinks = {} end
    if not node2.links then node2.links = {} end
    
    tinsert(node1.rlinks, {cost = cost_reverse, link = node2, outnode_to = n2d, outnode_from = n1d})
    tinsert(node2.links, {cost = cost_reverse, link = node1, outnode_to = n1d, outnode_from = n2d})
  end
end
]]