Loopy / grid.c: new grid type, 'Hats'.

The big mathematical news this month is that a polygon has been
discovered that will tile the plane but only aperiodically. Penrose
tiles achieve this with two tile types; it's been an open question for
decades whether you could do it with only one tile. Now someone has
announced the discovery of such a thing, so _obviously_ this
mathematically exciting tiling ought to be one of the Loopy grid
options!

The polygon, named a 'hat' by its discoverers, consists of the union
of eight cells of the 'Kites' periodic tiling that Loopy already
implements. So all the vertex coordinates of the whole tiling are
vertices of the Kites grid, which makes handling the coordinates in an
exact manner a lot easier than Penrose tilings.

What's _harder_ than Penrose tilings is that, although this tiling can
be generated by a vaguely similar system of recursive expansion, the
expansion is geometrically distorting, which means you can't easily
figure out which tiles can be discarded early to save CPU. Instead
I've come up with a completely different system for generating a patch
of tiling, by using a hierarchical coordinate system to track a
location within many levels of the expansion process without ever
simulating the process as a whole. I'm really quite pleased with that
technique, and am tempted to try switching the Penrose generator over
to it too - except that we'd have to keep the old generator around to
stop old game ids being invalidated, and also, I think it would be
slightly trickier without an underlying fixed grid and without
overlaps in the tile expansion system.

However, before coming up with that, I got most of the way through
implementing the more obvious system of actually doing the expansions.
The result worked, but was very slow (because I changed approach
rather than try to implement tree-pruning under distortion). But the
code was reusable for two other useful purposes: it generated the
lookup tables needed for the production code, and it also generated a
lot of useful diagrams. So I've committed it anyway as a supporting
program, in a new 'aux' source subdirectory, and in aux/doc is a
writeup of the coordinate system's concepts, with all those diagrams.
(That's the kind of thing I'd normally put in a huge comment at the
top of the file, but doing all those diagrams in ASCII art would be
beyond miserable.)

From a gameplay perspective: the hat polygon has 13 edges, but one of
them has a vertex of the Kites tiling in the middle, and sometimes two
other tile boundaries meet at that vertex. I've chosen to represent
every hat as having degree 14 for Loopy purposes, because if you only
included that extra vertex when it was needed, then people would be
forever having to check whether this was a 13-hat or a 14-hat and it
would be nightmarish to play.

Even so, there's a lot of clicking involved to turn all those fiddly
individual edges on or off. This grid is noticeably nicer to play in
'autofollow' mode, by setting LOOPY_AUTOFOLLOW in the environment to
either 'fixed' or 'adaptive'. I'm tempted to make 'fixed' the default,
except that I think it would confuse players of ordinary square Loopy!

1 files changed, 2183 insertions, 0 deletions

diff --git a/hat-tables.h b/hat-tables.h
new file mode 100644
index 0000000..5b3b0ed
--- /dev/null
+++ b/hat-tables.h
@@ -0,0 +1,2183 @@
+/*
+ * Header file autogenerated by aux/hatgen.c
+ *
+ * To regenerate, run 'hatgen --tables > hat-tables.h'
+ */
+
+static const unsigned hats_in_metatile[] = { 4, 1, 2, 2, };
+
+static const TileType children_H[] = {
+    TT_H, TT_H, TT_H, TT_T, TT_P, TT_P, TT_P, TT_F, TT_F, TT_F, TT_F, TT_F, TT_F,
+};
+static const TileType children_T[] = {
+    TT_H, TT_P, TT_P, TT_P, TT_F, TT_F, TT_F,
+};
+static const TileType children_P[] = {
+    TT_H, TT_H, TT_P, TT_P, TT_P, TT_F, TT_F, TT_F, TT_F, TT_F, TT_F,
+};
+static const TileType children_F[] = {
+    TT_H, TT_H, TT_P, TT_P, TT_F, TT_F, TT_F, TT_F, TT_F, TT_F, TT_F,
+};
+static const TileType *const children[] = {
+    children_H,
+    children_T,
+    children_P,
+    children_F,
+};
+static const size_t nchildren[] = {
+    13,
+    7,
+    11,
+    11,
+};
+
+static const MetatilePossibleParent permitted_parents_H[] = {
+    { TT_H, 0 },
+    { TT_H, 1 },
+    { TT_H, 2 },
+    { TT_T, 0 },
+    { TT_P, 0 },
+    { TT_P, 1 },
+    { TT_F, 0 },
+    { TT_F, 1 },
+};
+static const MetatilePossibleParent permitted_parents_T[] = {
+    { TT_H, 3 },
+};
+static const MetatilePossibleParent permitted_parents_P[] = {
+    { TT_H, 4 },
+    { TT_H, 5 },
+    { TT_H, 6 },
+    { TT_T, 1 },
+    { TT_T, 2 },
+    { TT_T, 3 },
+    { TT_P, 2 },
+    { TT_P, 3 },
+    { TT_P, 4 },
+    { TT_F, 2 },
+    { TT_F, 3 },
+};
+static const MetatilePossibleParent permitted_parents_F[] = {
+    { TT_H, 7 },
+    { TT_H, 8 },
+    { TT_H, 9 },
+    { TT_H, 10 },
+    { TT_H, 11 },
+    { TT_H, 12 },
+    { TT_T, 4 },
+    { TT_T, 5 },
+    { TT_T, 6 },
+    { TT_P, 5 },
+    { TT_P, 6 },
+    { TT_P, 7 },
+    { TT_P, 8 },
+    { TT_P, 9 },
+    { TT_P, 10 },
+    { TT_F, 4 },
+    { TT_F, 5 },
+    { TT_F, 6 },
+    { TT_F, 7 },
+    { TT_F, 8 },
+    { TT_F, 9 },
+    { TT_F, 10 },
+};
+static const MetatilePossibleParent *const permitted_parents[] = {
+    permitted_parents_H,
+    permitted_parents_T,
+    permitted_parents_P,
+    permitted_parents_F,
+};
+static const size_t n_permitted_parents[] = {
+    8,
+    1,
+    11,
+    22,
+};
+
+static const KitemapEntry kitemap_H[] = {
+    /* hat #0 in metatile #0 (type H) */
+    {1,0,0}, {7,3,0}, {3,0,4}, {4,0,4},
+    {4,3,0}, {0,0,0}, {5,0,0}, {2,0,0},
+    {3,0,4}, {3,0,0}, {1,0,0}, {5,0,0},
+    {2,0,0}, {1,2,1}, {4,0,0}, {6,2,1},
+    {3,0,3}, {5,0,0}, {6,2,1}, {3,0,0},
+    {4,0,0}, {6,0,0}, {2,0,0}, {1,0,0},
+    {5,0,0}, {7,0,0}, {4,3,0}, {3,3,0},
+    {6,0,0}, {2,0,3}, {7,1,0}, {0,0,3},
+    /* hat #1 in metatile #0 (type H) */
+    {1,1,0}, {2,0,5}, {7,1,8}, {0,0,5},
+    {3,0,2}, {0,1,0}, {5,1,0}, {2,1,0},
+    {7,1,8}, {3,1,0}, {1,1,0}, {5,1,0},
+    {2,1,0}, {4,1,8}, {4,1,0}, {0,3,0},
+    {2,3,0}, {5,1,0}, {0,3,0}, {3,1,0},
+    {4,1,0}, {6,1,0}, {2,1,0}, {1,1,0},
+    {5,1,0}, {7,1,0}, {3,0,2}, {4,0,2},
+    {6,1,0}, {3,3,0}, {0,0,3}, {7,0,0},
+    /* hat #2 in metatile #0 (type H) */
+    {1,2,0}, {1,0,7}, {7,1,4}, {6,0,7},
+    {3,0,8}, {0,2,0}, {5,2,0}, {2,2,0},
+    {7,1,4}, {3,2,0}, {1,2,0}, {5,2,0},
+    {2,2,0}, {4,1,4}, {4,2,0}, {6,3,0},
+    {1,3,0}, {5,2,0}, {6,3,0}, {3,2,0},
+    {4,2,0}, {6,2,0}, {2,2,0}, {1,2,0},
+    {5,2,0}, {7,2,0}, {3,0,8}, {4,0,8},
+    {6,2,0}, {0,3,0}, {3,1,8}, {4,1,8},
+    /* hat #3 in metatile #0 (type H) */
+    {7,2,0}, {1,3,0}, {3,1,0}, {4,1,0},
+    {0,3,0}, {4,2,0}, {2,3,0}, {5,3,0},
+    {3,3,0}, {4,1,0}, {5,3,0}, {1,3,0},
+    {7,1,0}, {2,3,0}, {6,0,0}, {4,3,0},
+    {5,3,0}, {1,0,0}, {3,3,0}, {6,0,0},
+    {6,3,0}, {4,3,0}, {1,3,0}, {2,3,0},
+    {7,3,0}, {5,3,0}, {3,2,0}, {4,2,0},
+    {0,0,0}, {6,3,0}, {3,1,4}, {4,1,4},
+    /* hat #0 in metatile #1 (type H) */
+    {1,0,1}, {7,3,1}, {3,0,9}, {4,0,9},
+    {4,3,1}, {0,0,1}, {5,0,1}, {2,0,1},
+    {3,0,9}, {3,0,1}, {1,0,1}, {5,0,1},
+    {2,0,1}, {1,0,10}, {4,0,1}, {6,0,10},
+    {0,0,6}, {5,0,1}, {6,0,10}, {3,0,1},
+    {4,0,1}, {6,0,1}, {2,0,1}, {1,0,1},
+    {5,0,1}, {7,0,1}, {4,3,1}, {3,3,1},
+    {6,0,1}, {1,0,6}, {7,1,1}, {6,0,6},
+    /* hat #1 in metatile #1 (type H) */
+    {1,1,1}, {1,1,2}, {7,0,3}, {6,1,2},
+    {0,1,6}, {0,1,1}, {5,1,1}, {2,1,1},
+    {7,0,3}, {3,1,1}, {1,1,1}, {5,1,1},
+    {2,1,1}, {4,0,3}, {4,1,1}, {0,3,1},
+    {2,3,1}, {5,1,1}, {0,3,1}, {3,1,1},
+    {4,1,1}, {6,1,1}, {2,1,1}, {1,1,1},
+    {5,1,1}, {7,1,1}, {0,1,6}, {7,0,6},
+    {6,1,1}, {3,3,1}, {6,0,6}, {7,0,1},
+    /* hat #2 in metatile #1 (type H) */
+    {1,2,1}, {2,0,4}, {7,1,9}, {0,0,4},
+    {3,0,0}, {0,2,1}, {5,2,1}, {2,2,1},
+    {7,1,9}, {3,2,1}, {1,2,1}, {5,2,1},
+    {2,2,1}, {4,1,9}, {4,2,1}, {6,3,1},
+    {1,3,1}, {5,2,1}, {6,3,1}, {3,2,1},
+    {4,2,1}, {6,2,1}, {2,2,1}, {1,2,1},
+    {5,2,1}, {7,2,1}, {3,0,0}, {4,0,0},
+    {6,2,1}, {0,3,1}, {3,0,3}, {4,0,3},
+    /* hat #3 in metatile #1 (type H) */
+    {7,2,1}, {1,3,1}, {3,1,1}, {4,1,1},
+    {0,3,1}, {4,2,1}, {2,3,1}, {5,3,1},
+    {3,3,1}, {4,1,1}, {5,3,1}, {1,3,1},
+    {7,1,1}, {2,3,1}, {6,0,1}, {4,3,1},
+    {5,3,1}, {1,0,1}, {3,3,1}, {6,0,1},
+    {6,3,1}, {4,3,1}, {1,3,1}, {2,3,1},
+    {7,3,1}, {5,3,1}, {3,2,1}, {4,2,1},
+    {0,0,1}, {6,3,1}, {3,1,9}, {4,1,9},
+    /* hat #0 in metatile #2 (type H) */
+    {1,0,2}, {7,3,2}, {3,0,5}, {4,0,5},
+    {4,3,2}, {0,0,2}, {5,0,2}, {2,0,2},
+    {3,0,5}, {3,0,2}, {1,0,2}, {5,0,2},
+    {2,0,2}, {1,1,0}, {4,0,2}, {6,1,0},
+    {0,0,3}, {5,0,2}, {6,1,0}, {3,0,2},
+    {4,0,2}, {6,0,2}, {2,0,2}, {1,0,2},
+    {5,0,2}, {7,0,2}, {4,3,2}, {3,3,2},
+    {6,0,2}, {1,0,3}, {7,1,2}, {6,0,3},
+    /* hat #1 in metatile #2 (type H) */
+    {1,1,2}, {1,1,6}, {7,1,12}, {6,1,6},
+    {0,1,1}, {0,1,2}, {5,1,2}, {2,1,2},
+    {7,1,12}, {3,1,2}, {1,1,2}, {5,1,2},
+    {2,1,2}, {4,1,12}, {4,1,2}, {0,3,2},
+    {2,3,2}, {5,1,2}, {0,3,2}, {3,1,2},
+    {4,1,2}, {6,1,2}, {2,1,2}, {1,1,2},
+    {5,1,2}, {7,1,2}, {0,1,1}, {7,0,3},
+    {6,1,2}, {3,3,2}, {6,0,3}, {7,0,2},
+    /* hat #2 in metatile #2 (type H) */
+    {1,2,2}, {1,0,11}, {7,1,5}, {6,0,11},
+    {3,0,12}, {0,2,2}, {5,2,2}, {2,2,2},
+    {7,1,5}, {3,2,2}, {1,2,2}, {5,2,2},
+    {2,2,2}, {4,1,5}, {4,2,2}, {6,3,2},
+    {1,3,2}, {5,2,2}, {6,3,2}, {3,2,2},
+    {4,2,2}, {6,2,2}, {2,2,2}, {1,2,2},
+    {5,2,2}, {7,2,2}, {3,0,12}, {4,0,12},
+    {6,2,2}, {0,3,2}, {3,1,12}, {4,1,12},
+    /* hat #3 in metatile #2 (type H) */
+    {7,2,2}, {1,3,2}, {3,1,2}, {4,1,2},
+    {0,3,2}, {4,2,2}, {2,3,2}, {5,3,2},
+    {3,3,2}, {4,1,2}, {5,3,2}, {1,3,2},
+    {7,1,2}, {2,3,2}, {6,0,2}, {4,3,2},
+    {5,3,2}, {1,0,2}, {3,3,2}, {6,0,2},
+    {6,3,2}, {4,3,2}, {1,3,2}, {2,3,2},
+    {7,3,2}, {5,3,2}, {3,2,2}, {4,2,2},
+    {0,0,2}, {6,3,2}, {3,1,5}, {4,1,5},
+    /* hat #0 in metatile #3 (type T) */
+    {1,0,3}, {4,0,2}, {7,0,0}, {7,1,0},
+    {7,0,2}, {0,0,3}, {5,0,3}, {2,0,3},
+    {7,0,0}, {3,0,3}, {1,0,3}, {5,0,3},
+    {2,0,3}, {4,0,0}, {4,0,3}, {7,2,1},
+    {3,1,1}, {5,0,3}, {7,2,1}, {3,0,3},
+    {4,0,3}, {6,0,3}, {2,0,3}, {1,0,3},
+    {5,0,3}, {7,0,3}, {7,0,2}, {7,1,2},
+    {6,0,3}, {2,1,1}, {6,1,2}, {0,1,1},
+    /* hat #1 in metatile #3 (type T) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #2 in metatile #3 (type T) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #3 (type T) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #4 (type P) */
+    {1,0,4}, {-1,-1,-1}, {0,2,1}, {7,1,9},
+    {-1,-1,-1}, {0,0,4}, {5,0,4}, {2,0,4},
+    {0,2,1}, {3,0,4}, {1,0,4}, {5,0,4},
+    {2,0,4}, {2,0,0}, {4,0,4}, {0,0,0},
+    {3,1,4}, {5,0,4}, {0,0,0}, {3,0,4},
+    {4,0,4}, {6,0,4}, {2,0,4}, {1,0,4},
+    {5,0,4}, {7,0,4}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,4}, {2,1,4}, {-1,-1,-1}, {0,1,4},
+    /* hat #1 in metatile #4 (type P) */
+    {1,1,4}, {-1,-1,-1}, {7,0,4}, {-1,-1,-1},
+    {0,1,7}, {0,1,4}, {5,1,4}, {2,1,4},
+    {7,0,4}, {3,1,4}, {1,1,4}, {5,1,4},
+    {2,1,4}, {4,0,4}, {4,1,4}, {7,3,0},
+    {3,2,0}, {5,1,4}, {7,3,0}, {3,1,4},
+    {4,1,4}, {6,1,4}, {2,1,4}, {1,1,4},
+    {5,1,4}, {7,1,4}, {0,1,7}, {7,0,7},
+    {6,1,4}, {2,2,0}, {6,0,7}, {0,2,0},
+    /* hat #2 in metatile #4 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #4 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #5 (type P) */
+    {1,0,5}, {-1,-1,-1}, {0,1,0}, {7,1,8},
+    {-1,-1,-1}, {0,0,5}, {5,0,5}, {2,0,5},
+    {0,1,0}, {3,0,5}, {1,0,5}, {5,0,5},
+    {2,0,5}, {2,0,2}, {4,0,5}, {0,0,2},
+    {3,1,5}, {5,0,5}, {0,0,2}, {3,0,5},
+    {4,0,5}, {6,0,5}, {2,0,5}, {1,0,5},
+    {5,0,5}, {7,0,5}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,5}, {2,1,5}, {-1,-1,-1}, {0,1,5},
+    /* hat #1 in metatile #5 (type P) */
+    {1,1,5}, {-1,-1,-1}, {7,0,5}, {-1,-1,-1},
+    {0,1,11}, {0,1,5}, {5,1,5}, {2,1,5},
+    {7,0,5}, {3,1,5}, {1,1,5}, {5,1,5},
+    {2,1,5}, {4,0,5}, {4,1,5}, {7,3,2},
+    {3,2,2}, {5,1,5}, {7,3,2}, {3,1,5},
+    {4,1,5}, {6,1,5}, {2,1,5}, {1,1,5},
+    {5,1,5}, {7,1,5}, {0,1,11}, {7,0,11},
+    {6,1,5}, {2,2,2}, {6,0,11}, {0,2,2},
+    /* hat #2 in metatile #5 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #5 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #6 (type P) */
+    {1,0,6}, {4,0,1}, {0,1,10}, {7,0,10},
+    {7,0,1}, {0,0,6}, {5,0,6}, {2,0,6},
+    {0,1,10}, {3,0,6}, {1,0,6}, {5,0,6},
+    {2,0,6}, {-1,-1,-1}, {4,0,6}, {-1,-1,-1},
+    {3,1,6}, {5,0,6}, {-1,-1,-1}, {3,0,6},
+    {4,0,6}, {6,0,6}, {2,0,6}, {1,0,6},
+    {5,0,6}, {7,0,6}, {7,0,1}, {7,1,1},
+    {6,0,6}, {2,1,6}, {6,1,1}, {0,1,6},
+    /* hat #1 in metatile #6 (type P) */
+    {1,1,6}, {1,1,1}, {7,0,6}, {6,1,1},
+    {0,1,2}, {0,1,6}, {5,1,6}, {2,1,6},
+    {7,0,6}, {3,1,6}, {1,1,6}, {5,1,6},
+    {2,1,6}, {4,0,6}, {4,1,6}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,6}, {-1,-1,-1}, {3,1,6},
+    {4,1,6}, {6,1,6}, {2,1,6}, {1,1,6},
+    {5,1,6}, {7,1,6}, {0,1,2}, {7,1,12},
+    {6,1,6}, {-1,-1,-1}, {6,1,12}, {-1,-1,-1},
+    /* hat #2 in metatile #6 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #6 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #7 (type F) */
+    {1,0,7}, {2,0,8}, {-1,-1,-1}, {0,0,8},
+    {0,2,0}, {0,0,7}, {5,0,7}, {2,0,7},
+    {-1,-1,-1}, {3,0,7}, {1,0,7}, {5,0,7},
+    {2,0,7}, {-1,-1,-1}, {4,0,7}, {-1,-1,-1},
+    {3,1,7}, {5,0,7}, {-1,-1,-1}, {3,0,7},
+    {4,0,7}, {6,0,7}, {2,0,7}, {1,0,7},
+    {5,0,7}, {7,0,7}, {0,2,0}, {7,1,4},
+    {6,0,7}, {2,1,7}, {6,1,4}, {0,1,7},
+    /* hat #1 in metatile #7 (type F) */
+    {1,1,7}, {1,1,4}, {7,0,7}, {6,1,4},
+    {-1,-1,-1}, {0,1,7}, {5,1,7}, {2,1,7},
+    {7,0,7}, {3,1,7}, {1,1,7}, {5,1,7},
+    {2,1,7}, {4,0,7}, {4,1,7}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,7}, {-1,-1,-1}, {3,1,7},
+    {4,1,7}, {6,1,7}, {2,1,7}, {1,1,7},
+    {5,1,7}, {7,1,7}, {-1,-1,-1}, {-1,-1,-1},
+    {6,1,7}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #2 in metatile #7 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #7 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #8 (type F) */
+    {1,0,8}, {-1,-1,-1}, {0,0,7}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,8}, {5,0,8}, {2,0,8},
+    {0,0,7}, {3,0,8}, {1,0,8}, {5,0,8},
+    {2,0,8}, {1,2,0}, {4,0,8}, {6,2,0},
+    {3,1,8}, {5,0,8}, {6,2,0}, {3,0,8},
+    {4,0,8}, {6,0,8}, {2,0,8}, {1,0,8},
+    {5,0,8}, {7,0,8}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,8}, {2,1,8}, {-1,-1,-1}, {0,1,8},
+    /* hat #1 in metatile #8 (type F) */
+    {1,1,8}, {-1,-1,-1}, {7,0,8}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,8}, {5,1,8}, {2,1,8},
+    {7,0,8}, {3,1,8}, {1,1,8}, {5,1,8},
+    {2,1,8}, {4,0,8}, {4,1,8}, {7,2,0},
+    {3,1,0}, {5,1,8}, {7,2,0}, {3,1,8},
+    {4,1,8}, {6,1,8}, {2,1,8}, {1,1,8},
+    {5,1,8}, {7,1,8}, {-1,-1,-1}, {-1,-1,-1},
+    {6,1,8}, {2,1,0}, {0,0,5}, {0,1,0},
+    /* hat #2 in metatile #8 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #8 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #9 (type F) */
+    {1,0,9}, {-1,-1,-1}, {0,0,10}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,9}, {5,0,9}, {2,0,9},
+    {0,0,10}, {3,0,9}, {1,0,9}, {5,0,9},
+    {2,0,9}, {2,0,1}, {4,0,9}, {0,0,1},
+    {3,1,9}, {5,0,9}, {0,0,1}, {3,0,9},
+    {4,0,9}, {6,0,9}, {2,0,9}, {1,0,9},
+    {5,0,9}, {7,0,9}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,9}, {2,1,9}, {-1,-1,-1}, {0,1,9},
+    /* hat #1 in metatile #9 (type F) */
+    {1,1,9}, {-1,-1,-1}, {7,0,9}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,9}, {5,1,9}, {2,1,9},
+    {7,0,9}, {3,1,9}, {1,1,9}, {5,1,9},
+    {2,1,9}, {4,0,9}, {4,1,9}, {7,3,1},
+    {3,2,1}, {5,1,9}, {7,3,1}, {3,1,9},
+    {4,1,9}, {6,1,9}, {2,1,9}, {1,1,9},
+    {5,1,9}, {7,1,9}, {-1,-1,-1}, {-1,-1,-1},
+    {6,1,9}, {2,2,1}, {0,0,4}, {0,2,1},
+    /* hat #2 in metatile #9 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #9 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #10 (type F) */
+    {1,0,10}, {2,0,9}, {-1,-1,-1}, {0,0,9},
+    {3,0,1}, {0,0,10}, {5,0,10}, {2,0,10},
+    {-1,-1,-1}, {3,0,10}, {1,0,10}, {5,0,10},
+    {2,0,10}, {-1,-1,-1}, {4,0,10}, {-1,-1,-1},
+    {3,1,10}, {5,0,10}, {-1,-1,-1}, {3,0,10},
+    {4,0,10}, {6,0,10}, {2,0,10}, {1,0,10},
+    {5,0,10}, {7,0,10}, {3,0,1}, {4,0,1},
+    {6,0,10}, {2,1,10}, {0,0,6}, {0,1,10},
+    /* hat #1 in metatile #10 (type F) */
+    {1,1,10}, {2,0,6}, {7,0,10}, {0,0,6},
+    {-1,-1,-1}, {0,1,10}, {5,1,10}, {2,1,10},
+    {7,0,10}, {3,1,10}, {1,1,10}, {5,1,10},
+    {2,1,10}, {4,0,10}, {4,1,10}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,10}, {-1,-1,-1}, {3,1,10},
+    {4,1,10}, {6,1,10}, {2,1,10}, {1,1,10},
+    {5,1,10}, {7,1,10}, {-1,-1,-1}, {-1,-1,-1},
+    {6,1,10}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #2 in metatile #10 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #10 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #11 (type F) */
+    {1,0,11}, {2,0,12}, {-1,-1,-1}, {0,0,12},
+    {0,2,2}, {0,0,11}, {5,0,11}, {2,0,11},
+    {-1,-1,-1}, {3,0,11}, {1,0,11}, {5,0,11},
+    {2,0,11}, {-1,-1,-1}, {4,0,11}, {-1,-1,-1},
+    {3,1,11}, {5,0,11}, {-1,-1,-1}, {3,0,11},
+    {4,0,11}, {6,0,11}, {2,0,11}, {1,0,11},
+    {5,0,11}, {7,0,11}, {0,2,2}, {7,1,5},
+    {6,0,11}, {2,1,11}, {6,1,5}, {0,1,11},
+    /* hat #1 in metatile #11 (type F) */
+    {1,1,11}, {1,1,5}, {7,0,11}, {6,1,5},
+    {-1,-1,-1}, {0,1,11}, {5,1,11}, {2,1,11},
+    {7,0,11}, {3,1,11}, {1,1,11}, {5,1,11},
+    {2,1,11}, {4,0,11}, {4,1,11}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,11}, {-1,-1,-1}, {3,1,11},
+    {4,1,11}, {6,1,11}, {2,1,11}, {1,1,11},
+    {5,1,11}, {7,1,11}, {-1,-1,-1}, {-1,-1,-1},
+    {6,1,11}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #2 in metatile #11 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #11 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #12 (type F) */
+    {1,0,12}, {-1,-1,-1}, {0,0,11}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,12}, {5,0,12}, {2,0,12},
+    {0,0,11}, {3,0,12}, {1,0,12}, {5,0,12},
+    {2,0,12}, {1,2,2}, {4,0,12}, {6,2,2},
+    {3,1,12}, {5,0,12}, {6,2,2}, {3,0,12},
+    {4,0,12}, {6,0,12}, {2,0,12}, {1,0,12},
+    {5,0,12}, {7,0,12}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,12}, {2,1,12}, {-1,-1,-1}, {0,1,12},
+    /* hat #1 in metatile #12 (type F) */
+    {1,1,12}, {-1,-1,-1}, {7,0,12}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,12}, {5,1,12}, {2,1,12},
+    {7,0,12}, {3,1,12}, {1,1,12}, {5,1,12},
+    {2,1,12}, {4,0,12}, {4,1,12}, {7,2,2},
+    {3,1,2}, {5,1,12}, {7,2,2}, {3,1,12},
+    {4,1,12}, {6,1,12}, {2,1,12}, {1,1,12},
+    {5,1,12}, {7,1,12}, {-1,-1,-1}, {7,1,6},
+    {6,1,12}, {2,1,2}, {6,1,6}, {0,1,2},
+    /* hat #2 in metatile #12 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #12 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+};
+static const KitemapEntry kitemap_T[] = {
+    /* hat #0 in metatile #0 (type H) */
+    {1,0,0}, {7,3,0}, {3,0,3}, {4,0,3},
+    {4,3,0}, {0,0,0}, {5,0,0}, {2,0,0},
+    {3,0,3}, {3,0,0}, {1,0,0}, {5,0,0},
+    {2,0,0}, {1,1,6}, {4,0,0}, {6,1,6},
+    {0,0,2}, {5,0,0}, {6,1,6}, {3,0,0},
+    {4,0,0}, {6,0,0}, {2,0,0}, {1,0,0},
+    {5,0,0}, {7,0,0}, {4,3,0}, {3,3,0},
+    {6,0,0}, {1,0,2}, {7,1,0}, {6,0,2},
+    /* hat #1 in metatile #0 (type H) */
+    {1,1,0}, {1,1,4}, {7,1,1}, {6,1,4},
+    {0,1,2}, {0,1,0}, {5,1,0}, {2,1,0},
+    {7,1,1}, {3,1,0}, {1,1,0}, {5,1,0},
+    {2,1,0}, {4,1,1}, {4,1,0}, {0,3,0},
+    {2,3,0}, {5,1,0}, {0,3,0}, {3,1,0},
+    {4,1,0}, {6,1,0}, {2,1,0}, {1,1,0},
+    {5,1,0}, {7,1,0}, {0,1,2}, {7,0,2},
+    {6,1,0}, {3,3,0}, {6,0,2}, {7,0,0},
+    /* hat #2 in metatile #0 (type H) */
+    {1,2,0}, {1,1,5}, {7,1,3}, {6,1,5},
+    {3,0,1}, {0,2,0}, {5,2,0}, {2,2,0},
+    {7,1,3}, {3,2,0}, {1,2,0}, {5,2,0},
+    {2,2,0}, {4,1,3}, {4,2,0}, {6,3,0},
+    {1,3,0}, {5,2,0}, {6,3,0}, {3,2,0},
+    {4,2,0}, {6,2,0}, {2,2,0}, {1,2,0},
+    {5,2,0}, {7,2,0}, {3,0,1}, {4,0,1},
+    {6,2,0}, {0,3,0}, {3,1,1}, {4,1,1},
+    /* hat #3 in metatile #0 (type H) */
+    {7,2,0}, {1,3,0}, {3,1,0}, {4,1,0},
+    {0,3,0}, {4,2,0}, {2,3,0}, {5,3,0},
+    {3,3,0}, {4,1,0}, {5,3,0}, {1,3,0},
+    {7,1,0}, {2,3,0}, {6,0,0}, {4,3,0},
+    {5,3,0}, {1,0,0}, {3,3,0}, {6,0,0},
+    {6,3,0}, {4,3,0}, {1,3,0}, {2,3,0},
+    {7,3,0}, {5,3,0}, {3,2,0}, {4,2,0},
+    {0,0,0}, {6,3,0}, {3,1,3}, {4,1,3},
+    /* hat #0 in metatile #1 (type P) */
+    {1,0,1}, {-1,-1,-1}, {0,1,5}, {7,0,5},
+    {-1,-1,-1}, {0,0,1}, {5,0,1}, {2,0,1},
+    {0,1,5}, {3,0,1}, {1,0,1}, {5,0,1},
+    {2,0,1}, {1,2,0}, {4,0,1}, {6,2,0},
+    {3,1,1}, {5,0,1}, {6,2,0}, {3,0,1},
+    {4,0,1}, {6,0,1}, {2,0,1}, {1,0,1},
+    {5,0,1}, {7,0,1}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,1}, {2,1,1}, {-1,-1,-1}, {0,1,1},
+    /* hat #1 in metatile #1 (type P) */
+    {1,1,1}, {-1,-1,-1}, {7,0,1}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,1}, {5,1,1}, {2,1,1},
+    {7,0,1}, {3,1,1}, {1,1,1}, {5,1,1},
+    {2,1,1}, {4,0,1}, {4,1,1}, {7,2,0},
+    {3,1,0}, {5,1,1}, {7,2,0}, {3,1,1},
+    {4,1,1}, {6,1,1}, {2,1,1}, {1,1,1},
+    {5,1,1}, {7,1,1}, {-1,-1,-1}, {7,1,4},
+    {6,1,1}, {2,1,0}, {6,1,4}, {0,1,0},
+    /* hat #2 in metatile #1 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #1 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #2 (type P) */
+    {1,0,2}, {4,0,0}, {-1,-1,-1}, {7,1,6},
+    {7,0,0}, {0,0,2}, {5,0,2}, {2,0,2},
+    {-1,-1,-1}, {3,0,2}, {1,0,2}, {5,0,2},
+    {2,0,2}, {-1,-1,-1}, {4,0,2}, {-1,-1,-1},
+    {3,1,2}, {5,0,2}, {-1,-1,-1}, {3,0,2},
+    {4,0,2}, {6,0,2}, {2,0,2}, {1,0,2},
+    {5,0,2}, {7,0,2}, {7,0,0}, {7,1,0},
+    {6,0,2}, {2,1,2}, {6,1,0}, {0,1,2},
+    /* hat #1 in metatile #2 (type P) */
+    {1,1,2}, {1,1,0}, {7,0,2}, {6,1,0},
+    {0,1,4}, {0,1,2}, {5,1,2}, {2,1,2},
+    {7,0,2}, {3,1,2}, {1,1,2}, {5,1,2},
+    {2,1,2}, {4,0,2}, {4,1,2}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,2}, {-1,-1,-1}, {3,1,2},
+    {4,1,2}, {6,1,2}, {2,1,2}, {1,1,2},
+    {5,1,2}, {7,1,2}, {0,1,4}, {7,0,4},
+    {6,1,2}, {-1,-1,-1}, {6,0,4}, {-1,-1,-1},
+    /* hat #2 in metatile #2 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #2 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #3 (type P) */
+    {1,0,3}, {-1,-1,-1}, {0,1,6}, {7,0,6},
+    {-1,-1,-1}, {0,0,3}, {5,0,3}, {2,0,3},
+    {0,1,6}, {3,0,3}, {1,0,3}, {5,0,3},
+    {2,0,3}, {2,0,0}, {4,0,3}, {0,0,0},
+    {3,1,3}, {5,0,3}, {0,0,0}, {3,0,3},
+    {4,0,3}, {6,0,3}, {2,0,3}, {1,0,3},
+    {5,0,3}, {7,0,3}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,3}, {2,1,3}, {-1,-1,-1}, {0,1,3},
+    /* hat #1 in metatile #3 (type P) */
+    {1,1,3}, {-1,-1,-1}, {7,0,3}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,3}, {5,1,3}, {2,1,3},
+    {7,0,3}, {3,1,3}, {1,1,3}, {5,1,3},
+    {2,1,3}, {4,0,3}, {4,1,3}, {7,3,0},
+    {3,2,0}, {5,1,3}, {7,3,0}, {3,1,3},
+    {4,1,3}, {6,1,3}, {2,1,3}, {1,1,3},
+    {5,1,3}, {7,1,3}, {-1,-1,-1}, {7,1,5},
+    {6,1,3}, {2,2,0}, {6,1,5}, {0,2,0},
+    /* hat #2 in metatile #3 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #3 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #4 (type F) */
+    {1,0,4}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,4}, {5,0,4}, {2,0,4},
+    {-1,-1,-1}, {3,0,4}, {1,0,4}, {5,0,4},
+    {2,0,4}, {-1,-1,-1}, {4,0,4}, {-1,-1,-1},
+    {3,1,4}, {5,0,4}, {-1,-1,-1}, {3,0,4},
+    {4,0,4}, {6,0,4}, {2,0,4}, {1,0,4},
+    {5,0,4}, {7,0,4}, {-1,-1,-1}, {7,1,2},
+    {6,0,4}, {2,1,4}, {6,1,2}, {0,1,4},
+    /* hat #1 in metatile #4 (type F) */
+    {1,1,4}, {1,1,2}, {7,0,4}, {6,1,2},
+    {0,1,0}, {0,1,4}, {5,1,4}, {2,1,4},
+    {7,0,4}, {3,1,4}, {1,1,4}, {5,1,4},
+    {2,1,4}, {4,0,4}, {4,1,4}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,4}, {-1,-1,-1}, {3,1,4},
+    {4,1,4}, {6,1,4}, {2,1,4}, {1,1,4},
+    {5,1,4}, {7,1,4}, {0,1,0}, {7,1,1},
+    {6,1,4}, {-1,-1,-1}, {6,1,1}, {-1,-1,-1},
+    /* hat #2 in metatile #4 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #4 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #5 (type F) */
+    {1,0,5}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,5}, {5,0,5}, {2,0,5},
+    {-1,-1,-1}, {3,0,5}, {1,0,5}, {5,0,5},
+    {2,0,5}, {-1,-1,-1}, {4,0,5}, {-1,-1,-1},
+    {3,1,5}, {5,0,5}, {-1,-1,-1}, {3,0,5},
+    {4,0,5}, {6,0,5}, {2,0,5}, {1,0,5},
+    {5,0,5}, {7,0,5}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,5}, {2,1,5}, {0,0,1}, {0,1,5},
+    /* hat #1 in metatile #5 (type F) */
+    {1,1,5}, {2,0,1}, {7,0,5}, {0,0,1},
+    {0,2,0}, {0,1,5}, {5,1,5}, {2,1,5},
+    {7,0,5}, {3,1,5}, {1,1,5}, {5,1,5},
+    {2,1,5}, {4,0,5}, {4,1,5}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,5}, {-1,-1,-1}, {3,1,5},
+    {4,1,5}, {6,1,5}, {2,1,5}, {1,1,5},
+    {5,1,5}, {7,1,5}, {0,2,0}, {7,1,3},
+    {6,1,5}, {-1,-1,-1}, {6,1,3}, {-1,-1,-1},
+    /* hat #2 in metatile #5 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #5 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #6 (type F) */
+    {1,0,6}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,6}, {5,0,6}, {2,0,6},
+    {-1,-1,-1}, {3,0,6}, {1,0,6}, {5,0,6},
+    {2,0,6}, {-1,-1,-1}, {4,0,6}, {-1,-1,-1},
+    {3,1,6}, {5,0,6}, {-1,-1,-1}, {3,0,6},
+    {4,0,6}, {6,0,6}, {2,0,6}, {1,0,6},
+    {5,0,6}, {7,0,6}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,6}, {2,1,6}, {0,0,3}, {0,1,6},
+    /* hat #1 in metatile #6 (type F) */
+    {1,1,6}, {2,0,3}, {7,0,6}, {0,0,3},
+    {3,0,0}, {0,1,6}, {5,1,6}, {2,1,6},
+    {7,0,6}, {3,1,6}, {1,1,6}, {5,1,6},
+    {2,1,6}, {4,0,6}, {4,1,6}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,6}, {-1,-1,-1}, {3,1,6},
+    {4,1,6}, {6,1,6}, {2,1,6}, {1,1,6},
+    {5,1,6}, {7,1,6}, {3,0,0}, {4,0,0},
+    {6,1,6}, {-1,-1,-1}, {0,0,2}, {-1,-1,-1},
+    /* hat #2 in metatile #6 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #6 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+};
+static const KitemapEntry kitemap_P[] = {
+    /* hat #0 in metatile #0 (type H) */
+    {1,0,0}, {7,3,0}, {3,0,4}, {4,0,4},
+    {4,3,0}, {0,0,0}, {5,0,0}, {2,0,0},
+    {3,0,4}, {3,0,0}, {1,0,0}, {5,0,0},
+    {2,0,0}, {1,1,9}, {4,0,0}, {6,1,9},
+    {0,0,3}, {5,0,0}, {6,1,9}, {3,0,0},
+    {4,0,0}, {6,0,0}, {2,0,0}, {1,0,0},
+    {5,0,0}, {7,0,0}, {4,3,0}, {3,3,0},
+    {6,0,0}, {1,0,3}, {7,1,0}, {6,0,3},
+    /* hat #1 in metatile #0 (type H) */
+    {1,1,0}, {1,1,8}, {7,1,5}, {6,1,8},
+    {0,1,3}, {0,1,0}, {5,1,0}, {2,1,0},
+    {7,1,5}, {3,1,0}, {1,1,0}, {5,1,0},
+    {2,1,0}, {4,1,5}, {4,1,0}, {0,3,0},
+    {2,3,0}, {5,1,0}, {0,3,0}, {3,1,0},
+    {4,1,0}, {6,1,0}, {2,1,0}, {1,1,0},
+    {5,1,0}, {7,1,0}, {0,1,3}, {7,0,3},
+    {6,1,0}, {3,3,0}, {6,0,3}, {7,0,0},
+    /* hat #2 in metatile #0 (type H) */
+    {1,2,0}, {1,0,6}, {7,1,4}, {6,0,6},
+    {3,0,5}, {0,2,0}, {5,2,0}, {2,2,0},
+    {7,1,4}, {3,2,0}, {1,2,0}, {5,2,0},
+    {2,2,0}, {4,1,4}, {4,2,0}, {6,3,0},
+    {1,3,0}, {5,2,0}, {6,3,0}, {3,2,0},
+    {4,2,0}, {6,2,0}, {2,2,0}, {1,2,0},
+    {5,2,0}, {7,2,0}, {3,0,5}, {4,0,5},
+    {6,2,0}, {0,3,0}, {3,1,5}, {4,1,5},
+    /* hat #3 in metatile #0 (type H) */
+    {7,2,0}, {1,3,0}, {3,1,0}, {4,1,0},
+    {0,3,0}, {4,2,0}, {2,3,0}, {5,3,0},
+    {3,3,0}, {4,1,0}, {5,3,0}, {1,3,0},
+    {7,1,0}, {2,3,0}, {6,0,0}, {4,3,0},
+    {5,3,0}, {1,0,0}, {3,3,0}, {6,0,0},
+    {6,3,0}, {4,3,0}, {1,3,0}, {2,3,0},
+    {7,3,0}, {5,3,0}, {3,2,0}, {4,2,0},
+    {0,0,0}, {6,3,0}, {3,1,4}, {4,1,4},
+    /* hat #0 in metatile #1 (type H) */
+    {1,0,1}, {7,3,1}, {3,0,10}, {4,0,10},
+    {4,3,1}, {0,0,1}, {5,0,1}, {2,0,1},
+    {3,0,10}, {3,0,1}, {1,0,1}, {5,0,1},
+    {2,0,1}, {1,0,9}, {4,0,1}, {6,0,9},
+    {0,0,4}, {5,0,1}, {6,0,9}, {3,0,1},
+    {4,0,1}, {6,0,1}, {2,0,1}, {1,0,1},
+    {5,0,1}, {7,0,1}, {4,3,1}, {3,3,1},
+    {6,0,1}, {1,0,4}, {7,1,1}, {6,0,4},
+    /* hat #1 in metatile #1 (type H) */
+    {1,1,1}, {1,1,6}, {7,1,2}, {6,1,6},
+    {0,1,4}, {0,1,1}, {5,1,1}, {2,1,1},
+    {7,1,2}, {3,1,1}, {1,1,1}, {5,1,1},
+    {2,1,1}, {4,1,2}, {4,1,1}, {0,3,1},
+    {2,3,1}, {5,1,1}, {0,3,1}, {3,1,1},
+    {4,1,1}, {6,1,1}, {2,1,1}, {1,1,1},
+    {5,1,1}, {7,1,1}, {0,1,4}, {7,0,4},
+    {6,1,1}, {3,3,1}, {6,0,4}, {7,0,1},
+    /* hat #2 in metatile #1 (type H) */
+    {1,2,1}, {1,1,7}, {7,1,10}, {6,1,7},
+    {3,0,2}, {0,2,1}, {5,2,1}, {2,2,1},
+    {7,1,10}, {3,2,1}, {1,2,1}, {5,2,1},
+    {2,2,1}, {4,1,10}, {4,2,1}, {6,3,1},
+    {1,3,1}, {5,2,1}, {6,3,1}, {3,2,1},
+    {4,2,1}, {6,2,1}, {2,2,1}, {1,2,1},
+    {5,2,1}, {7,2,1}, {3,0,2}, {4,0,2},
+    {6,2,1}, {0,3,1}, {3,1,2}, {4,1,2},
+    /* hat #3 in metatile #1 (type H) */
+    {7,2,1}, {1,3,1}, {3,1,1}, {4,1,1},
+    {0,3,1}, {4,2,1}, {2,3,1}, {5,3,1},
+    {3,3,1}, {4,1,1}, {5,3,1}, {1,3,1},
+    {7,1,1}, {2,3,1}, {6,0,1}, {4,3,1},
+    {5,3,1}, {1,0,1}, {3,3,1}, {6,0,1},
+    {6,3,1}, {4,3,1}, {1,3,1}, {2,3,1},
+    {7,3,1}, {5,3,1}, {3,2,1}, {4,2,1},
+    {0,0,1}, {6,3,1}, {3,1,10}, {4,1,10},
+    /* hat #0 in metatile #2 (type P) */
+    {1,0,2}, {-1,-1,-1}, {0,1,7}, {7,0,7},
+    {-1,-1,-1}, {0,0,2}, {5,0,2}, {2,0,2},
+    {0,1,7}, {3,0,2}, {1,0,2}, {5,0,2},
+    {2,0,2}, {1,2,1}, {4,0,2}, {6,2,1},
+    {3,1,2}, {5,0,2}, {6,2,1}, {3,0,2},
+    {4,0,2}, {6,0,2}, {2,0,2}, {1,0,2},
+    {5,0,2}, {7,0,2}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,2}, {2,1,2}, {-1,-1,-1}, {0,1,2},
+    /* hat #1 in metatile #2 (type P) */
+    {1,1,2}, {-1,-1,-1}, {7,0,2}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,2}, {5,1,2}, {2,1,2},
+    {7,0,2}, {3,1,2}, {1,1,2}, {5,1,2},
+    {2,1,2}, {4,0,2}, {4,1,2}, {7,2,1},
+    {3,1,1}, {5,1,2}, {7,2,1}, {3,1,2},
+    {4,1,2}, {6,1,2}, {2,1,2}, {1,1,2},
+    {5,1,2}, {7,1,2}, {-1,-1,-1}, {7,1,6},
+    {6,1,2}, {2,1,1}, {6,1,6}, {0,1,1},
+    /* hat #2 in metatile #2 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #2 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #3 (type P) */
+    {1,0,3}, {4,0,0}, {-1,-1,-1}, {7,1,9},
+    {7,0,0}, {0,0,3}, {5,0,3}, {2,0,3},
+    {-1,-1,-1}, {3,0,3}, {1,0,3}, {5,0,3},
+    {2,0,3}, {-1,-1,-1}, {4,0,3}, {-1,-1,-1},
+    {3,1,3}, {5,0,3}, {-1,-1,-1}, {3,0,3},
+    {4,0,3}, {6,0,3}, {2,0,3}, {1,0,3},
+    {5,0,3}, {7,0,3}, {7,0,0}, {7,1,0},
+    {6,0,3}, {2,1,3}, {6,1,0}, {0,1,3},
+    /* hat #1 in metatile #3 (type P) */
+    {1,1,3}, {1,1,0}, {7,0,3}, {6,1,0},
+    {0,1,8}, {0,1,3}, {5,1,3}, {2,1,3},
+    {7,0,3}, {3,1,3}, {1,1,3}, {5,1,3},
+    {2,1,3}, {4,0,3}, {4,1,3}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,3}, {-1,-1,-1}, {3,1,3},
+    {4,1,3}, {6,1,3}, {2,1,3}, {1,1,3},
+    {5,1,3}, {7,1,3}, {0,1,8}, {7,0,8},
+    {6,1,3}, {-1,-1,-1}, {6,0,8}, {-1,-1,-1},
+    /* hat #2 in metatile #3 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #3 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #4 (type P) */
+    {1,0,4}, {4,0,1}, {0,1,9}, {7,0,9},
+    {7,0,1}, {0,0,4}, {5,0,4}, {2,0,4},
+    {0,1,9}, {3,0,4}, {1,0,4}, {5,0,4},
+    {2,0,4}, {2,0,0}, {4,0,4}, {0,0,0},
+    {3,1,4}, {5,0,4}, {0,0,0}, {3,0,4},
+    {4,0,4}, {6,0,4}, {2,0,4}, {1,0,4},
+    {5,0,4}, {7,0,4}, {7,0,1}, {7,1,1},
+    {6,0,4}, {2,1,4}, {6,1,1}, {0,1,4},
+    /* hat #1 in metatile #4 (type P) */
+    {1,1,4}, {1,1,1}, {7,0,4}, {6,1,1},
+    {0,1,6}, {0,1,4}, {5,1,4}, {2,1,4},
+    {7,0,4}, {3,1,4}, {1,1,4}, {5,1,4},
+    {2,1,4}, {4,0,4}, {4,1,4}, {7,3,0},
+    {3,2,0}, {5,1,4}, {7,3,0}, {3,1,4},
+    {4,1,4}, {6,1,4}, {2,1,4}, {1,1,4},
+    {5,1,4}, {7,1,4}, {0,1,6}, {7,0,6},
+    {6,1,4}, {2,2,0}, {6,0,6}, {0,2,0},
+    /* hat #2 in metatile #4 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #4 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #5 (type F) */
+    {1,0,5}, {-1,-1,-1}, {0,0,6}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,5}, {5,0,5}, {2,0,5},
+    {0,0,6}, {3,0,5}, {1,0,5}, {5,0,5},
+    {2,0,5}, {1,2,0}, {4,0,5}, {6,2,0},
+    {3,1,5}, {5,0,5}, {6,2,0}, {3,0,5},
+    {4,0,5}, {6,0,5}, {2,0,5}, {1,0,5},
+    {5,0,5}, {7,0,5}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,5}, {2,1,5}, {-1,-1,-1}, {0,1,5},
+    /* hat #1 in metatile #5 (type F) */
+    {1,1,5}, {-1,-1,-1}, {7,0,5}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,5}, {5,1,5}, {2,1,5},
+    {7,0,5}, {3,1,5}, {1,1,5}, {5,1,5},
+    {2,1,5}, {4,0,5}, {4,1,5}, {7,2,0},
+    {3,1,0}, {5,1,5}, {7,2,0}, {3,1,5},
+    {4,1,5}, {6,1,5}, {2,1,5}, {1,1,5},
+    {5,1,5}, {7,1,5}, {-1,-1,-1}, {7,1,8},
+    {6,1,5}, {2,1,0}, {6,1,8}, {0,1,0},
+    /* hat #2 in metatile #5 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #5 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #6 (type F) */
+    {1,0,6}, {2,0,5}, {-1,-1,-1}, {0,0,5},
+    {0,2,0}, {0,0,6}, {5,0,6}, {2,0,6},
+    {-1,-1,-1}, {3,0,6}, {1,0,6}, {5,0,6},
+    {2,0,6}, {-1,-1,-1}, {4,0,6}, {-1,-1,-1},
+    {3,1,6}, {5,0,6}, {-1,-1,-1}, {3,0,6},
+    {4,0,6}, {6,0,6}, {2,0,6}, {1,0,6},
+    {5,0,6}, {7,0,6}, {0,2,0}, {7,1,4},
+    {6,0,6}, {2,1,6}, {6,1,4}, {0,1,6},
+    /* hat #1 in metatile #6 (type F) */
+    {1,1,6}, {1,1,4}, {7,0,6}, {6,1,4},
+    {0,1,1}, {0,1,6}, {5,1,6}, {2,1,6},
+    {7,0,6}, {3,1,6}, {1,1,6}, {5,1,6},
+    {2,1,6}, {4,0,6}, {4,1,6}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,6}, {-1,-1,-1}, {3,1,6},
+    {4,1,6}, {6,1,6}, {2,1,6}, {1,1,6},
+    {5,1,6}, {7,1,6}, {0,1,1}, {7,1,2},
+    {6,1,6}, {-1,-1,-1}, {6,1,2}, {-1,-1,-1},
+    /* hat #2 in metatile #6 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #6 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #7 (type F) */
+    {1,0,7}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,7}, {5,0,7}, {2,0,7},
+    {-1,-1,-1}, {3,0,7}, {1,0,7}, {5,0,7},
+    {2,0,7}, {-1,-1,-1}, {4,0,7}, {-1,-1,-1},
+    {3,1,7}, {5,0,7}, {-1,-1,-1}, {3,0,7},
+    {4,0,7}, {6,0,7}, {2,0,7}, {1,0,7},
+    {5,0,7}, {7,0,7}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,7}, {2,1,7}, {0,0,2}, {0,1,7},
+    /* hat #1 in metatile #7 (type F) */
+    {1,1,7}, {2,0,2}, {7,0,7}, {0,0,2},
+    {0,2,1}, {0,1,7}, {5,1,7}, {2,1,7},
+    {7,0,7}, {3,1,7}, {1,1,7}, {5,1,7},
+    {2,1,7}, {4,0,7}, {4,1,7}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,7}, {-1,-1,-1}, {3,1,7},
+    {4,1,7}, {6,1,7}, {2,1,7}, {1,1,7},
+    {5,1,7}, {7,1,7}, {0,2,1}, {7,1,10},
+    {6,1,7}, {-1,-1,-1}, {6,1,10}, {-1,-1,-1},
+    /* hat #2 in metatile #7 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #7 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #8 (type F) */
+    {1,0,8}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,8}, {5,0,8}, {2,0,8},
+    {-1,-1,-1}, {3,0,8}, {1,0,8}, {5,0,8},
+    {2,0,8}, {-1,-1,-1}, {4,0,8}, {-1,-1,-1},
+    {3,1,8}, {5,0,8}, {-1,-1,-1}, {3,0,8},
+    {4,0,8}, {6,0,8}, {2,0,8}, {1,0,8},
+    {5,0,8}, {7,0,8}, {-1,-1,-1}, {7,1,3},
+    {6,0,8}, {2,1,8}, {6,1,3}, {0,1,8},
+    /* hat #1 in metatile #8 (type F) */
+    {1,1,8}, {1,1,3}, {7,0,8}, {6,1,3},
+    {0,1,0}, {0,1,8}, {5,1,8}, {2,1,8},
+    {7,0,8}, {3,1,8}, {1,1,8}, {5,1,8},
+    {2,1,8}, {4,0,8}, {4,1,8}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,8}, {-1,-1,-1}, {3,1,8},
+    {4,1,8}, {6,1,8}, {2,1,8}, {1,1,8},
+    {5,1,8}, {7,1,8}, {0,1,0}, {7,1,5},
+    {6,1,8}, {-1,-1,-1}, {6,1,5}, {-1,-1,-1},
+    /* hat #2 in metatile #8 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #8 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #9 (type F) */
+    {1,0,9}, {2,0,10}, {-1,-1,-1}, {0,0,10},
+    {3,0,1}, {0,0,9}, {5,0,9}, {2,0,9},
+    {-1,-1,-1}, {3,0,9}, {1,0,9}, {5,0,9},
+    {2,0,9}, {-1,-1,-1}, {4,0,9}, {-1,-1,-1},
+    {3,1,9}, {5,0,9}, {-1,-1,-1}, {3,0,9},
+    {4,0,9}, {6,0,9}, {2,0,9}, {1,0,9},
+    {5,0,9}, {7,0,9}, {3,0,1}, {4,0,1},
+    {6,0,9}, {2,1,9}, {0,0,4}, {0,1,9},
+    /* hat #1 in metatile #9 (type F) */
+    {1,1,9}, {2,0,4}, {7,0,9}, {0,0,4},
+    {3,0,0}, {0,1,9}, {5,1,9}, {2,1,9},
+    {7,0,9}, {3,1,9}, {1,1,9}, {5,1,9},
+    {2,1,9}, {4,0,9}, {4,1,9}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,9}, {-1,-1,-1}, {3,1,9},
+    {4,1,9}, {6,1,9}, {2,1,9}, {1,1,9},
+    {5,1,9}, {7,1,9}, {3,0,0}, {4,0,0},
+    {6,1,9}, {-1,-1,-1}, {0,0,3}, {-1,-1,-1},
+    /* hat #2 in metatile #9 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #9 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #10 (type F) */
+    {1,0,10}, {-1,-1,-1}, {0,0,9}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,10}, {5,0,10}, {2,0,10},
+    {0,0,9}, {3,0,10}, {1,0,10}, {5,0,10},
+    {2,0,10}, {2,0,1}, {4,0,10}, {0,0,1},
+    {3,1,10}, {5,0,10}, {0,0,1}, {3,0,10},
+    {4,0,10}, {6,0,10}, {2,0,10}, {1,0,10},
+    {5,0,10}, {7,0,10}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,10}, {2,1,10}, {-1,-1,-1}, {0,1,10},
+    /* hat #1 in metatile #10 (type F) */
+    {1,1,10}, {-1,-1,-1}, {7,0,10}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,10}, {5,1,10}, {2,1,10},
+    {7,0,10}, {3,1,10}, {1,1,10}, {5,1,10},
+    {2,1,10}, {4,0,10}, {4,1,10}, {7,3,1},
+    {3,2,1}, {5,1,10}, {7,3,1}, {3,1,10},
+    {4,1,10}, {6,1,10}, {2,1,10}, {1,1,10},
+    {5,1,10}, {7,1,10}, {-1,-1,-1}, {7,1,7},
+    {6,1,10}, {2,2,1}, {6,1,7}, {0,2,1},
+    /* hat #2 in metatile #10 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #10 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+};
+static const KitemapEntry kitemap_F[] = {
+    /* hat #0 in metatile #0 (type H) */
+    {1,0,0}, {7,3,0}, {3,0,3}, {4,0,3},
+    {4,3,0}, {0,0,0}, {5,0,0}, {2,0,0},
+    {3,0,3}, {3,0,0}, {1,0,0}, {5,0,0},
+    {2,0,0}, {1,1,9}, {4,0,0}, {6,1,9},
+    {0,0,2}, {5,0,0}, {6,1,9}, {3,0,0},
+    {4,0,0}, {6,0,0}, {2,0,0}, {1,0,0},
+    {5,0,0}, {7,0,0}, {4,3,0}, {3,3,0},
+    {6,0,0}, {1,0,2}, {7,1,0}, {6,0,2},
+    /* hat #1 in metatile #0 (type H) */
+    {1,1,0}, {1,1,8}, {7,1,4}, {6,1,8},
+    {0,1,2}, {0,1,0}, {5,1,0}, {2,1,0},
+    {7,1,4}, {3,1,0}, {1,1,0}, {5,1,0},
+    {2,1,0}, {4,1,4}, {4,1,0}, {0,3,0},
+    {2,3,0}, {5,1,0}, {0,3,0}, {3,1,0},
+    {4,1,0}, {6,1,0}, {2,1,0}, {1,1,0},
+    {5,1,0}, {7,1,0}, {0,1,2}, {7,0,2},
+    {6,1,0}, {3,3,0}, {6,0,2}, {7,0,0},
+    /* hat #2 in metatile #0 (type H) */
+    {1,2,0}, {1,0,5}, {7,1,3}, {6,0,5},
+    {3,0,4}, {0,2,0}, {5,2,0}, {2,2,0},
+    {7,1,3}, {3,2,0}, {1,2,0}, {5,2,0},
+    {2,2,0}, {4,1,3}, {4,2,0}, {6,3,0},
+    {1,3,0}, {5,2,0}, {6,3,0}, {3,2,0},
+    {4,2,0}, {6,2,0}, {2,2,0}, {1,2,0},
+    {5,2,0}, {7,2,0}, {3,0,4}, {4,0,4},
+    {6,2,0}, {0,3,0}, {3,1,4}, {4,1,4},
+    /* hat #3 in metatile #0 (type H) */
+    {7,2,0}, {1,3,0}, {3,1,0}, {4,1,0},
+    {0,3,0}, {4,2,0}, {2,3,0}, {5,3,0},
+    {3,3,0}, {4,1,0}, {5,3,0}, {1,3,0},
+    {7,1,0}, {2,3,0}, {6,0,0}, {4,3,0},
+    {5,3,0}, {1,0,0}, {3,3,0}, {6,0,0},
+    {6,3,0}, {4,3,0}, {1,3,0}, {2,3,0},
+    {7,3,0}, {5,3,0}, {3,2,0}, {4,2,0},
+    {0,0,0}, {6,3,0}, {3,1,3}, {4,1,3},
+    /* hat #0 in metatile #1 (type H) */
+    {1,0,1}, {7,3,1}, {3,0,10}, {4,0,10},
+    {4,3,1}, {0,0,1}, {5,0,1}, {2,0,1},
+    {3,0,10}, {3,0,1}, {1,0,1}, {5,0,1},
+    {2,0,1}, {1,0,9}, {4,0,1}, {6,0,9},
+    {0,0,3}, {5,0,1}, {6,0,9}, {3,0,1},
+    {4,0,1}, {6,0,1}, {2,0,1}, {1,0,1},
+    {5,0,1}, {7,0,1}, {4,3,1}, {3,3,1},
+    {6,0,1}, {1,0,3}, {7,1,1}, {6,0,3},
+    /* hat #1 in metatile #1 (type H) */
+    {1,1,1}, {1,1,5}, {7,1,6}, {6,1,5},
+    {0,1,3}, {0,1,1}, {5,1,1}, {2,1,1},
+    {7,1,6}, {3,1,1}, {1,1,1}, {5,1,1},
+    {2,1,1}, {4,1,6}, {4,1,1}, {0,3,1},
+    {2,3,1}, {5,1,1}, {0,3,1}, {3,1,1},
+    {4,1,1}, {6,1,1}, {2,1,1}, {1,1,1},
+    {5,1,1}, {7,1,1}, {0,1,3}, {7,0,3},
+    {6,1,1}, {3,3,1}, {6,0,3}, {7,0,1},
+    /* hat #2 in metatile #1 (type H) */
+    {1,2,1}, {1,0,7}, {7,1,10}, {6,0,7},
+    {3,0,6}, {0,2,1}, {5,2,1}, {2,2,1},
+    {7,1,10}, {3,2,1}, {1,2,1}, {5,2,1},
+    {2,2,1}, {4,1,10}, {4,2,1}, {6,3,1},
+    {1,3,1}, {5,2,1}, {6,3,1}, {3,2,1},
+    {4,2,1}, {6,2,1}, {2,2,1}, {1,2,1},
+    {5,2,1}, {7,2,1}, {3,0,6}, {4,0,6},
+    {6,2,1}, {0,3,1}, {3,1,6}, {4,1,6},
+    /* hat #3 in metatile #1 (type H) */
+    {7,2,1}, {1,3,1}, {3,1,1}, {4,1,1},
+    {0,3,1}, {4,2,1}, {2,3,1}, {5,3,1},
+    {3,3,1}, {4,1,1}, {5,3,1}, {1,3,1},
+    {7,1,1}, {2,3,1}, {6,0,1}, {4,3,1},
+    {5,3,1}, {1,0,1}, {3,3,1}, {6,0,1},
+    {6,3,1}, {4,3,1}, {1,3,1}, {2,3,1},
+    {7,3,1}, {5,3,1}, {3,2,1}, {4,2,1},
+    {0,0,1}, {6,3,1}, {3,1,10}, {4,1,10},
+    /* hat #0 in metatile #2 (type P) */
+    {1,0,2}, {4,0,0}, {-1,-1,-1}, {7,1,9},
+    {7,0,0}, {0,0,2}, {5,0,2}, {2,0,2},
+    {-1,-1,-1}, {3,0,2}, {1,0,2}, {5,0,2},
+    {2,0,2}, {-1,-1,-1}, {4,0,2}, {-1,-1,-1},
+    {3,1,2}, {5,0,2}, {-1,-1,-1}, {3,0,2},
+    {4,0,2}, {6,0,2}, {2,0,2}, {1,0,2},
+    {5,0,2}, {7,0,2}, {7,0,0}, {7,1,0},
+    {6,0,2}, {2,1,2}, {6,1,0}, {0,1,2},
+    /* hat #1 in metatile #2 (type P) */
+    {1,1,2}, {1,1,0}, {7,0,2}, {6,1,0},
+    {0,1,8}, {0,1,2}, {5,1,2}, {2,1,2},
+    {7,0,2}, {3,1,2}, {1,1,2}, {5,1,2},
+    {2,1,2}, {4,0,2}, {4,1,2}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,2}, {-1,-1,-1}, {3,1,2},
+    {4,1,2}, {6,1,2}, {2,1,2}, {1,1,2},
+    {5,1,2}, {7,1,2}, {0,1,8}, {7,0,8},
+    {6,1,2}, {-1,-1,-1}, {6,0,8}, {-1,-1,-1},
+    /* hat #2 in metatile #2 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #2 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #3 (type P) */
+    {1,0,3}, {4,0,1}, {0,1,9}, {7,0,9},
+    {7,0,1}, {0,0,3}, {5,0,3}, {2,0,3},
+    {0,1,9}, {3,0,3}, {1,0,3}, {5,0,3},
+    {2,0,3}, {2,0,0}, {4,0,3}, {0,0,0},
+    {3,1,3}, {5,0,3}, {0,0,0}, {3,0,3},
+    {4,0,3}, {6,0,3}, {2,0,3}, {1,0,3},
+    {5,0,3}, {7,0,3}, {7,0,1}, {7,1,1},
+    {6,0,3}, {2,1,3}, {6,1,1}, {0,1,3},
+    /* hat #1 in metatile #3 (type P) */
+    {1,1,3}, {1,1,1}, {7,0,3}, {6,1,1},
+    {0,1,5}, {0,1,3}, {5,1,3}, {2,1,3},
+    {7,0,3}, {3,1,3}, {1,1,3}, {5,1,3},
+    {2,1,3}, {4,0,3}, {4,1,3}, {7,3,0},
+    {3,2,0}, {5,1,3}, {7,3,0}, {3,1,3},
+    {4,1,3}, {6,1,3}, {2,1,3}, {1,1,3},
+    {5,1,3}, {7,1,3}, {0,1,5}, {7,0,5},
+    {6,1,3}, {2,2,0}, {6,0,5}, {0,2,0},
+    /* hat #2 in metatile #3 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #3 (type P) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #4 (type F) */
+    {1,0,4}, {-1,-1,-1}, {0,0,5}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,4}, {5,0,4}, {2,0,4},
+    {0,0,5}, {3,0,4}, {1,0,4}, {5,0,4},
+    {2,0,4}, {1,2,0}, {4,0,4}, {6,2,0},
+    {3,1,4}, {5,0,4}, {6,2,0}, {3,0,4},
+    {4,0,4}, {6,0,4}, {2,0,4}, {1,0,4},
+    {5,0,4}, {7,0,4}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,4}, {2,1,4}, {-1,-1,-1}, {0,1,4},
+    /* hat #1 in metatile #4 (type F) */
+    {1,1,4}, {-1,-1,-1}, {7,0,4}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,4}, {5,1,4}, {2,1,4},
+    {7,0,4}, {3,1,4}, {1,1,4}, {5,1,4},
+    {2,1,4}, {4,0,4}, {4,1,4}, {7,2,0},
+    {3,1,0}, {5,1,4}, {7,2,0}, {3,1,4},
+    {4,1,4}, {6,1,4}, {2,1,4}, {1,1,4},
+    {5,1,4}, {7,1,4}, {-1,-1,-1}, {7,1,8},
+    {6,1,4}, {2,1,0}, {6,1,8}, {0,1,0},
+    /* hat #2 in metatile #4 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #4 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #5 (type F) */
+    {1,0,5}, {2,0,4}, {-1,-1,-1}, {0,0,4},
+    {0,2,0}, {0,0,5}, {5,0,5}, {2,0,5},
+    {-1,-1,-1}, {3,0,5}, {1,0,5}, {5,0,5},
+    {2,0,5}, {-1,-1,-1}, {4,0,5}, {-1,-1,-1},
+    {3,1,5}, {5,0,5}, {-1,-1,-1}, {3,0,5},
+    {4,0,5}, {6,0,5}, {2,0,5}, {1,0,5},
+    {5,0,5}, {7,0,5}, {0,2,0}, {7,1,3},
+    {6,0,5}, {2,1,5}, {6,1,3}, {0,1,5},
+    /* hat #1 in metatile #5 (type F) */
+    {1,1,5}, {1,1,3}, {7,0,5}, {6,1,3},
+    {0,1,1}, {0,1,5}, {5,1,5}, {2,1,5},
+    {7,0,5}, {3,1,5}, {1,1,5}, {5,1,5},
+    {2,1,5}, {4,0,5}, {4,1,5}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,5}, {-1,-1,-1}, {3,1,5},
+    {4,1,5}, {6,1,5}, {2,1,5}, {1,1,5},
+    {5,1,5}, {7,1,5}, {0,1,1}, {7,1,6},
+    {6,1,5}, {-1,-1,-1}, {6,1,6}, {-1,-1,-1},
+    /* hat #2 in metatile #5 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #5 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #6 (type F) */
+    {1,0,6}, {-1,-1,-1}, {0,0,7}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,6}, {5,0,6}, {2,0,6},
+    {0,0,7}, {3,0,6}, {1,0,6}, {5,0,6},
+    {2,0,6}, {1,2,1}, {4,0,6}, {6,2,1},
+    {3,1,6}, {5,0,6}, {6,2,1}, {3,0,6},
+    {4,0,6}, {6,0,6}, {2,0,6}, {1,0,6},
+    {5,0,6}, {7,0,6}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,6}, {2,1,6}, {-1,-1,-1}, {0,1,6},
+    /* hat #1 in metatile #6 (type F) */
+    {1,1,6}, {-1,-1,-1}, {7,0,6}, {-1,-1,-1},
+    {-1,-1,-1}, {0,1,6}, {5,1,6}, {2,1,6},
+    {7,0,6}, {3,1,6}, {1,1,6}, {5,1,6},
+    {2,1,6}, {4,0,6}, {4,1,6}, {7,2,1},
+    {3,1,1}, {5,1,6}, {7,2,1}, {3,1,6},
+    {4,1,6}, {6,1,6}, {2,1,6}, {1,1,6},
+    {5,1,6}, {7,1,6}, {-1,-1,-1}, {7,1,5},
+    {6,1,6}, {2,1,1}, {6,1,5}, {0,1,1},
+    /* hat #2 in metatile #6 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #6 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #7 (type F) */
+    {1,0,7}, {2,0,6}, {-1,-1,-1}, {0,0,6},
+    {0,2,1}, {0,0,7}, {5,0,7}, {2,0,7},
+    {-1,-1,-1}, {3,0,7}, {1,0,7}, {5,0,7},
+    {2,0,7}, {-1,-1,-1}, {4,0,7}, {-1,-1,-1},
+    {3,1,7}, {5,0,7}, {-1,-1,-1}, {3,0,7},
+    {4,0,7}, {6,0,7}, {2,0,7}, {1,0,7},
+    {5,0,7}, {7,0,7}, {0,2,1}, {7,1,10},
+    {6,0,7}, {2,1,7}, {6,1,10}, {0,1,7},
+    /* hat #1 in metatile #7 (type F) */
+    {1,1,7}, {1,1,10}, {7,0,7}, {6,1,10},
+    {-1,-1,-1}, {0,1,7}, {5,1,7}, {2,1,7},
+    {7,0,7}, {3,1,7}, {1,1,7}, {5,1,7},
+    {2,1,7}, {4,0,7}, {4,1,7}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,7}, {-1,-1,-1}, {3,1,7},
+    {4,1,7}, {6,1,7}, {2,1,7}, {1,1,7},
+    {5,1,7}, {7,1,7}, {-1,-1,-1}, {-1,-1,-1},
+    {6,1,7}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #2 in metatile #7 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #7 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #8 (type F) */
+    {1,0,8}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,8}, {5,0,8}, {2,0,8},
+    {-1,-1,-1}, {3,0,8}, {1,0,8}, {5,0,8},
+    {2,0,8}, {-1,-1,-1}, {4,0,8}, {-1,-1,-1},
+    {3,1,8}, {5,0,8}, {-1,-1,-1}, {3,0,8},
+    {4,0,8}, {6,0,8}, {2,0,8}, {1,0,8},
+    {5,0,8}, {7,0,8}, {-1,-1,-1}, {7,1,2},
+    {6,0,8}, {2,1,8}, {6,1,2}, {0,1,8},
+    /* hat #1 in metatile #8 (type F) */
+    {1,1,8}, {1,1,2}, {7,0,8}, {6,1,2},
+    {0,1,0}, {0,1,8}, {5,1,8}, {2,1,8},
+    {7,0,8}, {3,1,8}, {1,1,8}, {5,1,8},
+    {2,1,8}, {4,0,8}, {4,1,8}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,8}, {-1,-1,-1}, {3,1,8},
+    {4,1,8}, {6,1,8}, {2,1,8}, {1,1,8},
+    {5,1,8}, {7,1,8}, {0,1,0}, {7,1,4},
+    {6,1,8}, {-1,-1,-1}, {6,1,4}, {-1,-1,-1},
+    /* hat #2 in metatile #8 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #8 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #9 (type F) */
+    {1,0,9}, {2,0,10}, {-1,-1,-1}, {0,0,10},
+    {3,0,1}, {0,0,9}, {5,0,9}, {2,0,9},
+    {-1,-1,-1}, {3,0,9}, {1,0,9}, {5,0,9},
+    {2,0,9}, {-1,-1,-1}, {4,0,9}, {-1,-1,-1},
+    {3,1,9}, {5,0,9}, {-1,-1,-1}, {3,0,9},
+    {4,0,9}, {6,0,9}, {2,0,9}, {1,0,9},
+    {5,0,9}, {7,0,9}, {3,0,1}, {4,0,1},
+    {6,0,9}, {2,1,9}, {0,0,3}, {0,1,9},
+    /* hat #1 in metatile #9 (type F) */
+    {1,1,9}, {2,0,3}, {7,0,9}, {0,0,3},
+    {3,0,0}, {0,1,9}, {5,1,9}, {2,1,9},
+    {7,0,9}, {3,1,9}, {1,1,9}, {5,1,9},
+    {2,1,9}, {4,0,9}, {4,1,9}, {-1,-1,-1},
+    {-1,-1,-1}, {5,1,9}, {-1,-1,-1}, {3,1,9},
+    {4,1,9}, {6,1,9}, {2,1,9}, {1,1,9},
+    {5,1,9}, {7,1,9}, {3,0,0}, {4,0,0},
+    {6,1,9}, {-1,-1,-1}, {0,0,2}, {-1,-1,-1},
+    /* hat #2 in metatile #9 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #9 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #0 in metatile #10 (type F) */
+    {1,0,10}, {-1,-1,-1}, {0,0,9}, {-1,-1,-1},
+    {-1,-1,-1}, {0,0,10}, {5,0,10}, {2,0,10},
+    {0,0,9}, {3,0,10}, {1,0,10}, {5,0,10},
+    {2,0,10}, {2,0,1}, {4,0,10}, {0,0,1},
+    {3,1,10}, {5,0,10}, {0,0,1}, {3,0,10},
+    {4,0,10}, {6,0,10}, {2,0,10}, {1,0,10},
+    {5,0,10}, {7,0,10}, {-1,-1,-1}, {-1,-1,-1},
+    {6,0,10}, {2,1,10}, {-1,-1,-1}, {0,1,10},
+    /* hat #1 in metatile #10 (type F) */
+    {1,1,10}, {-1,-1,-1}, {7,0,10}, {-1,-1,-1},
+    {0,1,7}, {0,1,10}, {5,1,10}, {2,1,10},
+    {7,0,10}, {3,1,10}, {1,1,10}, {5,1,10},
+    {2,1,10}, {4,0,10}, {4,1,10}, {7,3,1},
+    {3,2,1}, {5,1,10}, {7,3,1}, {3,1,10},
+    {4,1,10}, {6,1,10}, {2,1,10}, {1,1,10},
+    {5,1,10}, {7,1,10}, {0,1,7}, {7,0,7},
+    {6,1,10}, {2,2,1}, {6,0,7}, {0,2,1},
+    /* hat #2 in metatile #10 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    /* hat #3 in metatile #10 (type F) does not exist */
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+    {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1}, {-1,-1,-1},
+};
+static const KitemapEntry *const kitemap[] = {
+    kitemap_H,
+    kitemap_T,
+    kitemap_P,
+    kitemap_F,
+};
+
+static const MetamapEntry metamap_H[] = {
+    /* 0, 0 -> */ {0, 0}, /* no alternatives */
+    /* 1, 0 -> */ {1, 0}, /* no alternatives */
+    /* 2, 0 -> */ {2, 0}, /* no alternatives */
+    /* 3, 0 -> */ {3, 0}, /* no alternatives */
+    /* 4, 0 -> */ {3, 4},
+    /* 5, 0 -> */ {2, 8},
+    /* 6, 0 -> */ {3, 3},
+    /* 7, 0 -> */ {8, 4},
+    /* 8, 0 -> */ {9, 8},
+    /* 9, 0 -> */ {9, 4},
+    /* 10, 0 -> */ {8, 1},
+    /* 11, 0 -> */ {10, 5},
+    /* 12, 0 -> */ {5, 3},
+    /* 0, 1 -> */ {0, 1}, /* no alternatives */
+    /* 1, 1 -> */ {1, 1}, /* no alternatives */
+    /* 2, 1 -> */ {2, 1}, /* no alternatives */
+    /* 3, 1 -> */ {3, 1}, /* no alternatives */
+    /* 4, 1 -> */ {2, 9},
+    /* 5, 1 -> */ {2, 3},
+    /* 6, 1 -> */ {2, 6},
+    /* 7, 1 -> */ {10, 4},
+    /* 8, 1 -> */ {6, 3},
+    /* 9, 1 -> */ {9, 9},
+    /* 10, 1 -> */ {6, 10},
+    /* 11, 1 -> */ {4, 3},
+    /* 12, 1 -> */ {6, 6},
+    /* 0, 2 -> */ {0, 2}, /* no alternatives */
+    /* 1, 2 -> */ {1, 2}, /* no alternatives */
+    /* 2, 2 -> */ {2, 2}, /* no alternatives */
+    /* 3, 2 -> */ {3, 2}, /* no alternatives */
+    /* 4, 2 -> */ {3, 5},
+    /* 5, 2 -> */ {2, 12},
+    /* 6, 2 -> */ {1, 3},
+    /* 7, 2 -> */ {8, 5},
+    /* 8, 2 -> */ {9, 12},
+    /* 9, 2 -> */ {9, 5},
+    /* 10, 2 -> */ {12, 0},
+    /* 11, 2 -> */ {5, 6},
+    /* 12, 2 -> */ {11, 1},
+    /* 0, 3 -> */ {0, 3}, /* no alternatives */
+    /* 1, 3 -> */ {6, 2},
+    /* 2, 3 -> */ {5, 1},
+    /* 3, 3 -> */ {6, 0},
+    /* 4, 3 -> */ {12, 2},
+    /* 5, 3 -> */ {10, 2},
+    /* 6, 3 -> */ {10, 0},
+    /* 7, 3 -> */ {-1,-1}, /* does not exist */
+    /* 8, 3 -> */ {-1,-1}, /* does not exist */
+    /* 9, 3 -> */ {-1,-1}, /* does not exist */
+    /* 10, 3 -> */ {-1,-1}, /* does not exist */
+    /* 11, 3 -> */ {-1,-1}, /* does not exist */
+    /* 12, 3 -> */ {-1,-1}, /* does not exist */
+    /* 0, 4 -> */ {0, 4}, /* no alternatives */
+    /* 1, 4 -> */ {1, 4}, /* no alternatives */
+    /* 2, 4 -> */ {2, 4}, /* no alternatives */
+    /* 3, 4 -> */ {4, 0},
+    /* 4, 4 -> */ {4, 4}, /* no alternatives */
+    /* 5, 4 -> */ {5, 7},
+    /* 6, 4 -> */ {6, 4}, /* no alternatives */
+    /* 7, 4 -> */ {4, 9},
+    /* 8, 4 -> */ {6, 7},
+    /* 9, 4 -> */ {9, 0},
+    /* 10, 4 -> */ {8, 9},
+    /* 11, 4 -> */ {-1,-1}, /* does not exist */
+    /* 12, 4 -> */ {-1,-1}, /* does not exist */
+    /* 0, 5 -> */ {0, 5}, /* no alternatives */
+    /* 1, 5 -> */ {1, 5}, /* no alternatives */
+    /* 2, 5 -> */ {2, 5}, /* no alternatives */
+    /* 3, 5 -> */ {4, 2},
+    /* 4, 5 -> */ {4, 5}, /* no alternatives */
+    /* 5, 5 -> */ {5, 11},
+    /* 6, 5 -> */ {6, 5}, /* no alternatives */
+    /* 7, 5 -> */ {4, 8},
+    /* 8, 5 -> */ {6, 11},
+    /* 9, 5 -> */ {9, 2},
+    /* 10, 5 -> */ {8, 8},
+    /* 11, 5 -> */ {-1,-1}, /* does not exist */
+    /* 12, 5 -> */ {-1,-1}, /* does not exist */
+    /* 0, 6 -> */ {0, 6}, /* no alternatives */
+    /* 1, 6 -> */ {1, 6}, /* no alternatives */
+    /* 2, 6 -> */ {6, 1},
+    /* 3, 6 -> */ {3, 6}, /* no alternatives */
+    /* 4, 6 -> */ {4, 6}, /* no alternatives */
+    /* 5, 6 -> */ {8, 12},
+    /* 6, 6 -> */ {12, 1},
+    /* 7, 6 -> */ {10, 1},
+    /* 8, 6 -> */ {4, 12},
+    /* 9, 6 -> */ {9, 6}, /* no alternatives */
+    /* 10, 6 -> */ {5, 10},
+    /* 11, 6 -> */ {-1,-1}, /* does not exist */
+    /* 12, 6 -> */ {-1,-1}, /* does not exist */
+    /* 0, 7 -> */ {0, 7}, /* no alternatives */
+    /* 1, 7 -> */ {1, 7}, /* no alternatives */
+    /* 2, 7 -> */ {2, 7}, /* no alternatives */
+    /* 3, 7 -> */ {3, 7}, /* no alternatives */
+    /* 4, 7 -> */ {4, 7}, /* no alternatives */
+    /* 5, 7 -> */ {5, 4},
+    /* 6, 7 -> */ {7, 0},
+    /* 7, 7 -> */ {10, 8},
+    /* 8, 7 -> */ {8, 7}, /* no alternatives */
+    /* 9, 7 -> */ {9, 7}, /* no alternatives */
+    /* 10, 7 -> */ {10, 7}, /* no alternatives */
+    /* 11, 7 -> */ {-1,-1}, /* does not exist */
+    /* 12, 7 -> */ {-1,-1}, /* does not exist */
+    /* 0, 8 -> */ {0, 8}, /* no alternatives */
+    /* 1, 8 -> */ {1, 8}, /* no alternatives */
+    /* 2, 8 -> */ {5, 0},
+    /* 3, 8 -> */ {3, 8}, /* no alternatives */
+    /* 4, 8 -> */ {7, 5},
+    /* 5, 8 -> */ {5, 8}, /* no alternatives */
+    /* 6, 8 -> */ {6, 8}, /* no alternatives */
+    /* 7, 8 -> */ {7, 8}, /* no alternatives */
+    /* 8, 8 -> */ {11, 0},
+    /* 9, 8 -> */ {8, 0},
+    /* 10, 8 -> */ {7, 7},
+    /* 11, 8 -> */ {-1,-1}, /* does not exist */
+    /* 12, 8 -> */ {-1,-1}, /* does not exist */
+    /* 0, 9 -> */ {0, 9}, /* no alternatives */
+    /* 1, 9 -> */ {1, 9}, /* no alternatives */
+    /* 2, 9 -> */ {4, 1},
+    /* 3, 9 -> */ {3, 9}, /* no alternatives */
+    /* 4, 9 -> */ {7, 4},
+    /* 5, 9 -> */ {5, 9}, /* no alternatives */
+    /* 6, 9 -> */ {6, 9}, /* no alternatives */
+    /* 7, 9 -> */ {7, 9}, /* no alternatives */
+    /* 8, 9 -> */ {7, 1},
+    /* 9, 9 -> */ {9, 1},
+    /* 10, 9 -> */ {7, 10},
+    /* 11, 9 -> */ {-1,-1}, /* does not exist */
+    /* 12, 9 -> */ {-1,-1}, /* does not exist */
+    /* 0, 10 -> */ {0, 10}, /* no alternatives */
+    /* 1, 10 -> */ {1, 10}, /* no alternatives */
+    /* 2, 10 -> */ {2, 10}, /* no alternatives */
+    /* 3, 10 -> */ {3, 10}, /* no alternatives */
+    /* 4, 10 -> */ {4, 10}, /* no alternatives */
+    /* 5, 10 -> */ {10, 6},
+    /* 6, 10 -> */ {7, 6},
+    /* 7, 10 -> */ {10, 9},
+    /* 8, 10 -> */ {8, 10}, /* no alternatives */
+    /* 9, 10 -> */ {9, 10}, /* no alternatives */
+    /* 10, 10 -> */ {10, 10}, /* no alternatives */
+    /* 11, 10 -> */ {-1,-1}, /* does not exist */
+    /* 12, 10 -> */ {-1,-1}, /* does not exist */
+    /* 0, 11 -> */ {0, 11}, /* no alternatives */
+    /* 1, 11 -> */ {1, 11}, /* no alternatives */
+    /* 2, 11 -> */ {2, 11}, /* no alternatives */
+    /* 3, 11 -> */ {3, 11}, /* no alternatives */
+    /* 4, 11 -> */ {4, 11}, /* no alternatives */
+    /* 5, 11 -> */ {5, 5},
+    /* 6, 11 -> */ {7, 2},
+    /* 7, 11 -> */ {10, 12},
+    /* 8, 11 -> */ {8, 11}, /* no alternatives */
+    /* 9, 11 -> */ {9, 11}, /* no alternatives */
+    /* 10, 11 -> */ {10, 11}, /* no alternatives */
+    /* 11, 11 -> */ {-1,-1}, /* does not exist */
+    /* 12, 11 -> */ {-1,-1}, /* does not exist */
+    /* 0, 12 -> */ {0, 12}, /* no alternatives */
+    /* 1, 12 -> */ {1, 12}, /* no alternatives */
+    /* 2, 12 -> */ {5, 2},
+    /* 3, 12 -> */ {3, 12}, /* no alternatives */
+    /* 4, 12 -> */ {8, 6},
+    /* 5, 12 -> */ {5, 12}, /* no alternatives */
+    /* 6, 12 -> */ {6, 12}, /* no alternatives */
+    /* 7, 12 -> */ {7, 12}, /* no alternatives */
+    /* 8, 12 -> */ {11, 2},
+    /* 9, 12 -> */ {8, 2},
+    /* 10, 12 -> */ {7, 11},
+    /* 11, 12 -> */ {-1,-1}, /* does not exist */
+    /* 12, 12 -> */ {-1,-1}, /* does not exist */
+};
+static const MetamapEntry metamap_T[] = {
+    /* 0, 0 -> */ {0, 0}, /* no alternatives */
+    /* 1, 0 -> */ {1, 0}, /* no alternatives */
+    /* 2, 0 -> */ {2, 0}, /* no alternatives */
+    /* 3, 0 -> */ {3, 0}, /* no alternatives */
+    /* 4, 0 -> */ {3, 3},
+    /* 5, 0 -> */ {3, 1},
+    /* 6, 0 -> */ {2, 2},
+    /* 7, 0 -> */ {8, 3},
+    /* 8, 0 -> */ {9, 1},
+    /* 9, 0 -> */ {9, 3},
+    /* 10, 0 -> */ {4, 6},
+    /* 11, 0 -> */ {4, 4},
+    /* 12, 0 -> */ {6, 2},
+    /* 0, 1 -> */ {0, 1}, /* no alternatives */
+    /* 1, 1 -> */ {1, 1}, /* no alternatives */
+    /* 2, 1 -> */ {2, 1}, /* no alternatives */
+    /* 3, 1 -> */ {5, 0},
+    /* 4, 1 -> */ {4, 1}, /* no alternatives */
+    /* 5, 1 -> */ {8, 4},
+    /* 6, 1 -> */ {6, 1}, /* no alternatives */
+    /* 7, 1 -> */ {6, 5},
+    /* 8, 1 -> */ {11, 0},
+    /* 9, 1 -> */ {8, 0},
+    /* 10, 1 -> */ {5, 5},
+    /* 11, 1 -> */ {-1,-1}, /* does not exist */
+    /* 12, 1 -> */ {-1,-1}, /* does not exist */
+    /* 0, 2 -> */ {0, 2}, /* no alternatives */
+    /* 1, 2 -> */ {1, 2}, /* no alternatives */
+    /* 2, 2 -> */ {6, 0},
+    /* 3, 2 -> */ {3, 2}, /* no alternatives */
+    /* 4, 2 -> */ {4, 2}, /* no alternatives */
+    /* 5, 2 -> */ {5, 4},
+    /* 6, 2 -> */ {12, 0},
+    /* 7, 2 -> */ {10, 0},
+    /* 8, 2 -> */ {6, 4},
+    /* 9, 2 -> */ {9, 2}, /* no alternatives */
+    /* 10, 2 -> */ {8, 6},
+    /* 11, 2 -> */ {-1,-1}, /* does not exist */
+    /* 12, 2 -> */ {-1,-1}, /* does not exist */
+    /* 0, 3 -> */ {0, 3}, /* no alternatives */
+    /* 1, 3 -> */ {1, 3}, /* no alternatives */
+    /* 2, 3 -> */ {2, 3}, /* no alternatives */
+    /* 3, 3 -> */ {4, 0},
+    /* 4, 3 -> */ {4, 3}, /* no alternatives */
+    /* 5, 3 -> */ {8, 5},
+    /* 6, 3 -> */ {6, 3}, /* no alternatives */
+    /* 7, 3 -> */ {6, 6},
+    /* 8, 3 -> */ {4, 5},
+    /* 9, 3 -> */ {9, 0},
+    /* 10, 3 -> */ {5, 6},
+    /* 11, 3 -> */ {-1,-1}, /* does not exist */
+    /* 12, 3 -> */ {-1,-1}, /* does not exist */
+    /* 0, 4 -> */ {0, 4}, /* no alternatives */
+    /* 1, 4 -> */ {1, 4}, /* no alternatives */
+    /* 2, 4 -> */ {2, 4}, /* no alternatives */
+    /* 3, 4 -> */ {3, 4}, /* no alternatives */
+    /* 4, 4 -> */ {8, 1},
+    /* 5, 4 -> */ {5, 2},
+    /* 6, 4 -> */ {8, 2},
+    /* 7, 4 -> */ {7, 4}, /* no alternatives */
+    /* 8, 4 -> */ {5, 1},
+    /* 9, 4 -> */ {9, 4}, /* no alternatives */
+    /* 10, 4 -> */ {10, 4}, /* no alternatives */
+    /* 11, 4 -> */ {-1,-1}, /* does not exist */
+    /* 12, 4 -> */ {-1,-1}, /* does not exist */
+    /* 0, 5 -> */ {0, 5}, /* no alternatives */
+    /* 1, 5 -> */ {1, 5}, /* no alternatives */
+    /* 2, 5 -> */ {2, 5}, /* no alternatives */
+    /* 3, 5 -> */ {3, 5}, /* no alternatives */
+    /* 4, 5 -> */ {7, 0},
+    /* 5, 5 -> */ {10, 1},
+    /* 6, 5 -> */ {7, 1},
+    /* 7, 5 -> */ {7, 5}, /* no alternatives */
+    /* 8, 5 -> */ {5, 3},
+    /* 9, 5 -> */ {9, 5}, /* no alternatives */
+    /* 10, 5 -> */ {10, 5}, /* no alternatives */
+    /* 11, 5 -> */ {-1,-1}, /* does not exist */
+    /* 12, 5 -> */ {-1,-1}, /* does not exist */
+    /* 0, 6 -> */ {0, 6}, /* no alternatives */
+    /* 1, 6 -> */ {1, 6}, /* no alternatives */
+    /* 2, 6 -> */ {2, 6}, /* no alternatives */
+    /* 3, 6 -> */ {3, 6}, /* no alternatives */
+    /* 4, 6 -> */ {7, 2},
+    /* 5, 6 -> */ {10, 3},
+    /* 6, 6 -> */ {7, 3},
+    /* 7, 6 -> */ {7, 6}, /* no alternatives */
+    /* 8, 6 -> */ {10, 2},
+    /* 9, 6 -> */ {9, 6}, /* no alternatives */
+    /* 10, 6 -> */ {10, 6}, /* no alternatives */
+    /* 11, 6 -> */ {-1,-1}, /* does not exist */
+    /* 12, 6 -> */ {-1,-1}, /* does not exist */
+};
+static const MetamapEntry metamap_P[] = {
+    /* 0, 0 -> */ {0, 0}, /* no alternatives */
+    /* 1, 0 -> */ {1, 0}, /* no alternatives */
+    /* 2, 0 -> */ {2, 0}, /* no alternatives */
+    /* 3, 0 -> */ {3, 0}, /* no alternatives */
+    /* 4, 0 -> */ {3, 4},
+    /* 5, 0 -> */ {2, 5},
+    /* 6, 0 -> */ {2, 3},
+    /* 7, 0 -> */ {8, 4},
+    /* 8, 0 -> */ {9, 5},
+    /* 9, 0 -> */ {9, 4},
+    /* 10, 0 -> */ {4, 9},
+    /* 11, 0 -> */ {4, 8},
+    /* 12, 0 -> */ {6, 3},
+    /* 0, 1 -> */ {0, 1}, /* no alternatives */
+    /* 1, 1 -> */ {1, 1}, /* no alternatives */
+    /* 2, 1 -> */ {2, 1}, /* no alternatives */
+    /* 3, 1 -> */ {3, 1}, /* no alternatives */
+    /* 4, 1 -> */ {2, 10},
+    /* 5, 1 -> */ {3, 2},
+    /* 6, 1 -> */ {2, 4},
+    /* 7, 1 -> */ {8, 10},
+    /* 8, 1 -> */ {9, 2},
+    /* 9, 1 -> */ {9, 10},
+    /* 10, 1 -> */ {7, 4},
+    /* 11, 1 -> */ {8, 2},
+    /* 12, 1 -> */ {6, 4},
+    /* 0, 2 -> */ {0, 2}, /* no alternatives */
+    /* 1, 2 -> */ {1, 2}, /* no alternatives */
+    /* 2, 2 -> */ {2, 2}, /* no alternatives */
+    /* 3, 2 -> */ {5, 1},
+    /* 4, 2 -> */ {4, 2}, /* no alternatives */
+    /* 5, 2 -> */ {8, 6},
+    /* 6, 2 -> */ {6, 2}, /* no alternatives */
+    /* 7, 2 -> */ {6, 7},
+    /* 8, 2 -> */ {4, 6},
+    /* 9, 2 -> */ {8, 1},
+    /* 10, 2 -> */ {5, 7},
+    /* 11, 2 -> */ {-1,-1}, /* does not exist */
+    /* 12, 2 -> */ {-1,-1}, /* does not exist */
+    /* 0, 3 -> */ {0, 3}, /* no alternatives */
+    /* 1, 3 -> */ {1, 3}, /* no alternatives */
+    /* 2, 3 -> */ {6, 0},
+    /* 3, 3 -> */ {3, 3}, /* no alternatives */
+    /* 4, 3 -> */ {4, 3}, /* no alternatives */
+    /* 5, 3 -> */ {5, 8},
+    /* 6, 3 -> */ {12, 0},
+    /* 7, 3 -> */ {10, 0},
+    /* 8, 3 -> */ {6, 8},
+    /* 9, 3 -> */ {9, 3}, /* no alternatives */
+    /* 10, 3 -> */ {8, 9},
+    /* 11, 3 -> */ {-1,-1}, /* does not exist */
+    /* 12, 3 -> */ {-1,-1}, /* does not exist */
+    /* 0, 4 -> */ {0, 4}, /* no alternatives */
+    /* 1, 4 -> */ {1, 4}, /* no alternatives */
+    /* 2, 4 -> */ {6, 1},
+    /* 3, 4 -> */ {4, 0},
+    /* 4, 4 -> */ {4, 4}, /* no alternatives */
+    /* 5, 4 -> */ {5, 6},
+    /* 6, 4 -> */ {12, 1},
+    /* 7, 4 -> */ {6, 9},
+    /* 8, 4 -> */ {6, 6},
+    /* 9, 4 -> */ {9, 0},
+    /* 10, 4 -> */ {5, 9},
+    /* 11, 4 -> */ {-1,-1}, /* does not exist */
+    /* 12, 4 -> */ {-1,-1}, /* does not exist */
+    /* 0, 5 -> */ {0, 5}, /* no alternatives */
+    /* 1, 5 -> */ {1, 5}, /* no alternatives */
+    /* 2, 5 -> */ {5, 0},
+    /* 3, 5 -> */ {3, 5}, /* no alternatives */
+    /* 4, 5 -> */ {8, 8},
+    /* 5, 5 -> */ {5, 5}, /* no alternatives */
+    /* 6, 5 -> */ {6, 5}, /* no alternatives */
+    /* 7, 5 -> */ {7, 5}, /* no alternatives */
+    /* 8, 5 -> */ {11, 0},
+    /* 9, 5 -> */ {8, 0},
+    /* 10, 5 -> */ {7, 6},
+    /* 11, 5 -> */ {-1,-1}, /* does not exist */
+    /* 12, 5 -> */ {-1,-1}, /* does not exist */
+    /* 0, 6 -> */ {0, 6}, /* no alternatives */
+    /* 1, 6 -> */ {1, 6}, /* no alternatives */
+    /* 2, 6 -> */ {2, 6}, /* no alternatives */
+    /* 3, 6 -> */ {3, 6}, /* no alternatives */
+    /* 4, 6 -> */ {11, 1},
+    /* 5, 6 -> */ {5, 4},
+    /* 6, 6 -> */ {7, 0},
+    /* 7, 6 -> */ {10, 5},
+    /* 8, 6 -> */ {5, 2},
+    /* 9, 6 -> */ {9, 6}, /* no alternatives */
+    /* 10, 6 -> */ {10, 6}, /* no alternatives */
+    /* 11, 6 -> */ {-1,-1}, /* does not exist */
+    /* 12, 6 -> */ {-1,-1}, /* does not exist */
+    /* 0, 7 -> */ {0, 7}, /* no alternatives */
+    /* 1, 7 -> */ {1, 7}, /* no alternatives */
+    /* 2, 7 -> */ {2, 7}, /* no alternatives */
+    /* 3, 7 -> */ {3, 7}, /* no alternatives */
+    /* 4, 7 -> */ {7, 1},
+    /* 5, 7 -> */ {10, 2},
+    /* 6, 7 -> */ {7, 2},
+    /* 7, 7 -> */ {7, 7}, /* no alternatives */
+    /* 8, 7 -> */ {4, 10},
+    /* 9, 7 -> */ {9, 7}, /* no alternatives */
+    /* 10, 7 -> */ {10, 7}, /* no alternatives */
+    /* 11, 7 -> */ {-1,-1}, /* does not exist */
+    /* 12, 7 -> */ {-1,-1}, /* does not exist */
+    /* 0, 8 -> */ {0, 8}, /* no alternatives */
+    /* 1, 8 -> */ {1, 8}, /* no alternatives */
+    /* 2, 8 -> */ {2, 8}, /* no alternatives */
+    /* 3, 8 -> */ {3, 8}, /* no alternatives */
+    /* 4, 8 -> */ {8, 5},
+    /* 5, 8 -> */ {5, 3},
+    /* 6, 8 -> */ {8, 3},
+    /* 7, 8 -> */ {7, 8}, /* no alternatives */
+    /* 8, 8 -> */ {4, 5},
+    /* 9, 8 -> */ {9, 8}, /* no alternatives */
+    /* 10, 8 -> */ {10, 8}, /* no alternatives */
+    /* 11, 8 -> */ {-1,-1}, /* does not exist */
+    /* 12, 8 -> */ {-1,-1}, /* does not exist */
+    /* 0, 9 -> */ {0, 9}, /* no alternatives */
+    /* 1, 9 -> */ {1, 9}, /* no alternatives */
+    /* 2, 9 -> */ {2, 9}, /* no alternatives */
+    /* 3, 9 -> */ {3, 9}, /* no alternatives */
+    /* 4, 9 -> */ {7, 3},
+    /* 5, 9 -> */ {10, 4},
+    /* 6, 9 -> */ {10, 1},
+    /* 7, 9 -> */ {10, 10},
+    /* 8, 9 -> */ {10, 3},
+    /* 9, 9 -> */ {9, 9}, /* no alternatives */
+    /* 10, 9 -> */ {10, 9}, /* no alternatives */
+    /* 11, 9 -> */ {-1,-1}, /* does not exist */
+    /* 12, 9 -> */ {-1,-1}, /* does not exist */
+    /* 0, 10 -> */ {0, 10}, /* no alternatives */
+    /* 1, 10 -> */ {1, 10}, /* no alternatives */
+    /* 2, 10 -> */ {4, 1},
+    /* 3, 10 -> */ {3, 10}, /* no alternatives */
+    /* 4, 10 -> */ {8, 7},
+    /* 5, 10 -> */ {5, 10}, /* no alternatives */
+    /* 6, 10 -> */ {6, 10}, /* no alternatives */
+    /* 7, 10 -> */ {7, 10}, /* no alternatives */
+    /* 8, 10 -> */ {4, 7},
+    /* 9, 10 -> */ {9, 1},
+    /* 10, 10 -> */ {7, 9},
+    /* 11, 10 -> */ {-1,-1}, /* does not exist */
+    /* 12, 10 -> */ {-1,-1}, /* does not exist */
+};
+static const MetamapEntry metamap_F[] = {
+    /* 0, 0 -> */ {0, 0}, /* no alternatives */
+    /* 1, 0 -> */ {1, 0}, /* no alternatives */
+    /* 2, 0 -> */ {2, 0}, /* no alternatives */
+    /* 3, 0 -> */ {3, 0}, /* no alternatives */
+    /* 4, 0 -> */ {3, 3},
+    /* 5, 0 -> */ {2, 4},
+    /* 6, 0 -> */ {2, 2},
+    /* 7, 0 -> */ {8, 3},
+    /* 8, 0 -> */ {9, 4},
+    /* 9, 0 -> */ {9, 3},
+    /* 10, 0 -> */ {4, 9},
+    /* 11, 0 -> */ {4, 8},
+    /* 12, 0 -> */ {6, 2},
+    /* 0, 1 -> */ {0, 1}, /* no alternatives */
+    /* 1, 1 -> */ {1, 1}, /* no alternatives */
+    /* 2, 1 -> */ {2, 1}, /* no alternatives */
+    /* 3, 1 -> */ {3, 1}, /* no alternatives */
+    /* 4, 1 -> */ {2, 10},
+    /* 5, 1 -> */ {2, 6},
+    /* 6, 1 -> */ {2, 3},
+    /* 7, 1 -> */ {8, 10},
+    /* 8, 1 -> */ {9, 6},
+    /* 9, 1 -> */ {9, 10},
+    /* 10, 1 -> */ {7, 3},
+    /* 11, 1 -> */ {8, 6},
+    /* 12, 1 -> */ {6, 3},
+    /* 0, 2 -> */ {0, 2}, /* no alternatives */
+    /* 1, 2 -> */ {1, 2}, /* no alternatives */
+    /* 2, 2 -> */ {6, 0},
+    /* 3, 2 -> */ {3, 2}, /* no alternatives */
+    /* 4, 2 -> */ {4, 2}, /* no alternatives */
+    /* 5, 2 -> */ {5, 8},
+    /* 6, 2 -> */ {12, 0},
+    /* 7, 2 -> */ {10, 0},
+    /* 8, 2 -> */ {6, 8},
+    /* 9, 2 -> */ {9, 2}, /* no alternatives */
+    /* 10, 2 -> */ {8, 9},
+    /* 11, 2 -> */ {-1,-1}, /* does not exist */
+    /* 12, 2 -> */ {-1,-1}, /* does not exist */
+    /* 0, 3 -> */ {0, 3}, /* no alternatives */
+    /* 1, 3 -> */ {1, 3}, /* no alternatives */
+    /* 2, 3 -> */ {6, 1},
+    /* 3, 3 -> */ {4, 0},
+    /* 4, 3 -> */ {4, 3}, /* no alternatives */
+    /* 5, 3 -> */ {5, 5},
+    /* 6, 3 -> */ {12, 1},
+    /* 7, 3 -> */ {6, 9},
+    /* 8, 3 -> */ {6, 5},
+    /* 9, 3 -> */ {9, 0},
+    /* 10, 3 -> */ {5, 9},
+    /* 11, 3 -> */ {-1,-1}, /* does not exist */
+    /* 12, 3 -> */ {-1,-1}, /* does not exist */
+    /* 0, 4 -> */ {0, 4}, /* no alternatives */
+    /* 1, 4 -> */ {1, 4}, /* no alternatives */
+    /* 2, 4 -> */ {5, 0},
+    /* 3, 4 -> */ {3, 4}, /* no alternatives */
+    /* 4, 4 -> */ {8, 8},
+    /* 5, 4 -> */ {5, 4}, /* no alternatives */
+    /* 6, 4 -> */ {6, 4}, /* no alternatives */
+    /* 7, 4 -> */ {7, 4}, /* no alternatives */
+    /* 8, 4 -> */ {11, 0},
+    /* 9, 4 -> */ {8, 0},
+    /* 10, 4 -> */ {7, 5},
+    /* 11, 4 -> */ {-1,-1}, /* does not exist */
+    /* 12, 4 -> */ {-1,-1}, /* does not exist */
+    /* 0, 5 -> */ {0, 5}, /* no alternatives */
+    /* 1, 5 -> */ {1, 5}, /* no alternatives */
+    /* 2, 5 -> */ {2, 5}, /* no alternatives */
+    /* 3, 5 -> */ {3, 5}, /* no alternatives */
+    /* 4, 5 -> */ {11, 1},
+    /* 5, 5 -> */ {5, 3},
+    /* 6, 5 -> */ {7, 0},
+    /* 7, 5 -> */ {10, 4},
+    /* 8, 5 -> */ {4, 6},
+    /* 9, 5 -> */ {9, 5}, /* no alternatives */
+    /* 10, 5 -> */ {10, 5}, /* no alternatives */
+    /* 11, 5 -> */ {-1,-1}, /* does not exist */
+    /* 12, 5 -> */ {-1,-1}, /* does not exist */
+    /* 0, 6 -> */ {0, 6}, /* no alternatives */
+    /* 1, 6 -> */ {1, 6}, /* no alternatives */
+    /* 2, 6 -> */ {5, 1},
+    /* 3, 6 -> */ {3, 6}, /* no alternatives */
+    /* 4, 6 -> */ {8, 5},
+    /* 5, 6 -> */ {5, 6}, /* no alternatives */
+    /* 6, 6 -> */ {6, 6}, /* no alternatives */
+    /* 7, 6 -> */ {7, 6}, /* no alternatives */
+    /* 8, 6 -> */ {4, 5},
+    /* 9, 6 -> */ {8, 1},
+    /* 10, 6 -> */ {7, 7},
+    /* 11, 6 -> */ {-1,-1}, /* does not exist */
+    /* 12, 6 -> */ {-1,-1}, /* does not exist */
+    /* 0, 7 -> */ {0, 7}, /* no alternatives */
+    /* 1, 7 -> */ {1, 7}, /* no alternatives */
+    /* 2, 7 -> */ {2, 7}, /* no alternatives */
+    /* 3, 7 -> */ {3, 7}, /* no alternatives */
+    /* 4, 7 -> */ {4, 7}, /* no alternatives */
+    /* 5, 7 -> */ {4, 10},
+    /* 6, 7 -> */ {7, 1},
+    /* 7, 7 -> */ {10, 6},
+    /* 8, 7 -> */ {8, 7}, /* no alternatives */
+    /* 9, 7 -> */ {9, 7}, /* no alternatives */
+    /* 10, 7 -> */ {10, 7}, /* no alternatives */
+    /* 11, 7 -> */ {-1,-1}, /* does not exist */
+    /* 12, 7 -> */ {-1,-1}, /* does not exist */
+    /* 0, 8 -> */ {0, 8}, /* no alternatives */
+    /* 1, 8 -> */ {1, 8}, /* no alternatives */
+    /* 2, 8 -> */ {2, 8}, /* no alternatives */
+    /* 3, 8 -> */ {3, 8}, /* no alternatives */
+    /* 4, 8 -> */ {8, 4},
+    /* 5, 8 -> */ {5, 2},
+    /* 6, 8 -> */ {8, 2},
+    /* 7, 8 -> */ {7, 8}, /* no alternatives */
+    /* 8, 8 -> */ {4, 4},
+    /* 9, 8 -> */ {9, 8}, /* no alternatives */
+    /* 10, 8 -> */ {10, 8}, /* no alternatives */
+    /* 11, 8 -> */ {-1,-1}, /* does not exist */
+    /* 12, 8 -> */ {-1,-1}, /* does not exist */
+    /* 0, 9 -> */ {0, 9}, /* no alternatives */
+    /* 1, 9 -> */ {1, 9}, /* no alternatives */
+    /* 2, 9 -> */ {2, 9}, /* no alternatives */
+    /* 3, 9 -> */ {3, 9}, /* no alternatives */
+    /* 4, 9 -> */ {7, 2},
+    /* 5, 9 -> */ {10, 3},
+    /* 6, 9 -> */ {10, 1},
+    /* 7, 9 -> */ {10, 10},
+    /* 8, 9 -> */ {10, 2},
+    /* 9, 9 -> */ {9, 9}, /* no alternatives */
+    /* 10, 9 -> */ {10, 9}, /* no alternatives */
+    /* 11, 9 -> */ {-1,-1}, /* does not exist */
+    /* 12, 9 -> */ {-1,-1}, /* does not exist */
+    /* 0, 10 -> */ {0, 10}, /* no alternatives */
+    /* 1, 10 -> */ {1, 10}, /* no alternatives */
+    /* 2, 10 -> */ {4, 1},
+    /* 3, 10 -> */ {3, 10}, /* no alternatives */
+    /* 4, 10 -> */ {5, 7},
+    /* 5, 10 -> */ {5, 10}, /* no alternatives */
+    /* 6, 10 -> */ {6, 10}, /* no alternatives */
+    /* 7, 10 -> */ {7, 10}, /* no alternatives */
+    /* 8, 10 -> */ {6, 7},
+    /* 9, 10 -> */ {9, 1},
+    /* 10, 10 -> */ {7, 9},
+    /* 11, 10 -> */ {-1,-1}, /* does not exist */
+    /* 12, 10 -> */ {-1,-1}, /* does not exist */
+};
+static const MetamapEntry *const metamap[] = {
+    metamap_H,
+    metamap_T,
+    metamap_P,
+    metamap_F,
+};