geom/m44750: occupancy context maps with on-the-fly update

Bitwise geometry occupancy coding uses a mapping table to select entropy
contexts.  This commit employs a dynamic mapping which is updated after
each coding operation, replacing the previous static mapping tables.

NB: the proposed version used a context with a halving period
(max_count) of 64 symbols.  However, this conflicts with another
adoption (512 symbols), and a wholesale replacement of the arithmetic
codec and context model.  To resolve the conflict, the existing halving
period (128) is used.

cfg/octree-liftt-ctc-lossless-geom-lossy-attrs.yaml

@@ -11,6 +11,7 @@ categories:
      #  - preserve lossless geometry property
      - geometryCodec: 1
      - mergeDuplicatedPoints: 0
+     - ctxOccupancyReductionFactor: 3
      - neighbourAvailBoundaryLog2: 9
      - positionQuantizationScale: 1
 

cfg/octree-liftt-ctc-lossy-geom-lossy-attrs.yaml

@@ -10,6 +10,7 @@ categories:
      # geometry parameters (octree)
      - geometryCodec: 1
      - mergeDuplicatedPoints: 1
+     - ctxOccupancyReductionFactor: 3
      - neighbourAvailBoundaryLog2: 9
      - positionQuantizationScale:
          r01: '$eval{ $rp = 5; $gp = ${src-geometry-precision}; $p_min = max(gp - 9, 7); $start = min(1, $gp - ($p_min + 6)); $step = max(1, (min($gp - 1, $p_min + 7) - $p_min) / 5); $y = $start + round($rp * $step); $div = 1 << (abs($y) + 1); ((1 - 2*signbit($y)) % $div) / $div }'

cfg/octree-predt-ctc-lossless-geom-lossless-attrs.yaml

@@ -14,6 +14,7 @@ categories:
      # geometry parameters (octree)
      - geometryCodec: 1
      - neighbourAvailBoundaryLog2: 9
+     - ctxOccupancyReductionFactor: 3
 
      ####
      # attribute coding (common options -- relies on option ordering)

cfg/octree-predt-ctc-lossless-geom-nearlossless-attrs.yaml

@@ -14,6 +14,7 @@ categories:
      # geometry parameters (octree)
      - geometryCodec: 1
      - neighbourAvailBoundaryLog2: 9
+     - ctxOccupancyReductionFactor: 3
 
      ####
      # attribute coding (common options -- relies on option ordering)

cfg/octree-raht-ctc-lossless-geom-lossy-attrs.yaml

@@ -11,6 +11,7 @@ categories:
      #  - preserve lossless geometry property
      - geometryCodec: 1
      - mergeDuplicatedPoints: 0
+     - ctxOccupancyReductionFactor: 3
      - neighbourAvailBoundaryLog2: 9
      - positionQuantizationScale: 1
 

cfg/octree-raht-ctc-lossy-geom-lossy-attrs.yaml

@@ -10,6 +10,7 @@ categories:
      # geometry parameters (octree)
      - geometryCodec: 1
      - mergeDuplicatedPoints: 1
+     - ctxOccupancyReductionFactor: 3
      - neighbourAvailBoundaryLog2: 9
      - positionQuantizationScale:
          r01: '$eval{ $rp = 5; $gp = ${src-geometry-precision}; $p_min = max(gp - 9, 7); $start = min(1, $gp - ($p_min + 6)); $step = max(1, (min($gp - 1, $p_min + 7) - $p_min) / 5); $y = $start + round($rp * $step); $div = 1 << (abs($y) + 1); ((1 - 2*signbit($y)) % $div) / $div }'

cfg/trisoup-liftt-ctc-lossy-geom-lossy-attrs.yaml

@@ -10,6 +10,7 @@ categories:
      ##
      # geometry parameters (trisoup)
      - geometryCodec: 2
+     - ctxOccupancyReductionFactor: 3
      - neighbourAvailBoundaryLog2: 9
      - inferredDirectCodingMode: 0
      - triSoupDepth: ${test-depth}

cfg/trisoup-raht-ctc-lossy-geom-lossy-attrs.yaml

@@ -10,6 +10,7 @@ categories:
      ##
      # geometry parameters (trisoup)
      - geometryCodec: 2
+     - ctxOccupancyReductionFactor: 3
      - neighbourAvailBoundaryLog2: 9
      - inferredDirectCodingMode: 0
      - triSoupDepth: ${test-depth}

tmc3/TMC3.cpp

@@ -323,6 +323,10 @@ ParseParameters(int argc, char* argv[], Parameters& params)
     params.encoder.gps.inferred_direct_coding_mode_enabled_flag, true,
     "Permits early termination of the geometry octree for isolated points")
 
+  ("ctxOccupancyReductionFactor",
+     params.encoder.gps.geom_occupancy_ctx_reduction_factor, 3,
+     "Adjusts the number of contexts used in occupancy coding")
+
   // (trisoup) geometry parameters
   ("triSoupDepth",  // log2(maxBB+1), where maxBB+1 is analogous to image width
     params.encoder.gps.trisoup_depth, 10,

tmc3/geometry_octree.cpp

@@ -198,4 +198,29 @@ updateGeometryNeighState(
 
 //============================================================================
 
+CtxMapOctreeOccupancy::CtxMapOctreeOccupancy()
+{
+  map.reset(new CtxIdxMap);
+  b[0] = map->b0;
+  b[1] = map->b1;
+  b[2] = map->b2;
+  b[3] = map->b3;
+  b[4] = map->b4;
+  b[5] = map->b5;
+  b[6] = map->b6;
+  b[7] = map->b7;
+
+  using namespace std;
+  fill(begin(map->b0), end(map->b0), 127);
+  fill(begin(map->b1), end(map->b1), 127);
+  fill(begin(map->b2), end(map->b2), 127);
+  fill(begin(map->b3), end(map->b3), 127);
+  fill(begin(map->b4), end(map->b4), 127);
+  fill(begin(map->b5), end(map->b5), 127);
+  fill(begin(map->b6), end(map->b6), 127);
+  fill(begin(map->b7), end(map->b7), 127);
+}
+
+//============================================================================
+
 }  // namespace pcc

tmc3/geometry_octree.h

@@ -42,6 +42,7 @@
 #include "PCCPointSet.h"
 #include "hls.h"
 #include "ringbuf.h"
+#include "tables.h"
 
 namespace pcc {
 
@@ -130,32 +131,63 @@ isDirectModeEligible(
 //---------------------------------------------------------------------------
 
 struct CtxModelOctreeOccupancy {
-  o3dgc::Adaptive_Bit_Model_Fast b0[10];
-  o3dgc::Adaptive_Bit_Model_Fast b1[2 * 10];
-  o3dgc::Adaptive_Bit_Model_Fast b2[4 * 10];
-  o3dgc::Adaptive_Bit_Model_Fast b3[8 * 10];
-  o3dgc::Adaptive_Bit_Model_Fast b4[75];
-  o3dgc::Adaptive_Bit_Model_Fast b5[112];
-  o3dgc::Adaptive_Bit_Model_Fast b6[117];
-  o3dgc::Adaptive_Bit_Model_Fast b7[127];
-
-  o3dgc::Adaptive_Bit_Model* operator[](int bit_pos)
+  o3dgc::Adaptive_Bit_Model_Fast contexts[256];
+  int ctxFactorShift;
+
+  CtxModelOctreeOccupancy(int ctxFactorShift) : ctxFactorShift(ctxFactorShift)
+  {}
+
+  o3dgc::Adaptive_Bit_Model& operator[](int idx)
   {
-    assert(unsigned(bit_pos) < 8);
-    switch (bit_pos) {
-    case 0: return b0;
-    case 1: return b1;
-    case 2: return b2;
-    case 3: return b3;
-    case 4: return b4;
-    case 5: return b5;
-    case 6: return b6;
-    case 7: return b7;
-    default: return nullptr;
-    }
+    return contexts[idx >> ctxFactorShift];
   }
 };
 
+//---------------------------------------------------------------------------
+// Encapsulates the derivation of ctxIdx for occupancy coding.
+
+class CtxMapOctreeOccupancy {
+public:
+  struct CtxIdxMap {
+    uint8_t b0[10];
+    uint8_t b1[20];
+    uint8_t b2[39];
+    uint8_t b3[76];
+    uint8_t b4[149];
+    uint8_t b5[294];
+    uint8_t b6[391];
+    uint8_t b7[520];
+  };
+
+  CtxMapOctreeOccupancy();
+
+  const uint8_t* operator[](int bit) const { return b[bit]; }
+
+  uint8_t* operator[](int bit) { return b[bit]; }
+
+  // return *ctxIdx and update *ctxIdx according to bit
+  static uint8_t evolve(bool bit, uint8_t* ctxIdx);
+
+private:
+  std::unique_ptr<CtxIdxMap> map;
+  uint8_t* b[8];
+};
+
+//----------------------------------------------------------------------------
+
+inline uint8_t
+CtxMapOctreeOccupancy::evolve(bool bit, uint8_t* ctxIdx)
+{
+  uint8_t retval = *ctxIdx;
+
+  if (bit)
+    *ctxIdx = kCtxMapOctreeOccupancyEvolutionOn1[*ctxIdx];
+  else
+    *ctxIdx = kCtxMapOctreeOccupancyEvolutionOn0[*ctxIdx];
+
+  return retval;
+}
+
 //---------------------------------------------------------------------------
 
 }  // namespace pcc

tmc3/geometry_octree_decoder.cpp

@@ -85,6 +85,7 @@ private:
 
   // For bitwise occupancy coding
   CtxModelOctreeOccupancy _ctxOccupancy;
+  CtxMapOctreeOccupancy _ctxIdxMap;
 
   // For bytewise occupancy coding
   DualLutCoder<true> _bytewiseOccupancyCoder[10];
@@ -96,6 +97,7 @@ GeometryOctreeDecoder::GeometryOctreeDecoder(
   const GeometryParameterSet& gps, o3dgc::Arithmetic_Codec* arithmeticDecoder)
   : _useBitwiseOccupancyCoder(gps.bitwise_occupancy_coding_flag)
   , _arithmeticDecoder(arithmeticDecoder)
+  , _ctxOccupancy(gps.geom_occupancy_ctx_reduction_factor)
 {
   if (!_useBitwiseOccupancyCoder) {
     for (int i = 0; i < 10; i++)
@@ -146,9 +148,10 @@ GeometryOctreeDecoder::decodeOccupancyNeighZ()
     // NB: There must be at least two occupied child nodes
     //  -- avoid coding the occupancy bit if it is implied.
     if (numOccupiedAcc >= minOccupied + i - 7) {
-      int idx = numOccupiedAcc;
-      bit = _arithmeticDecoder->decode(_ctxOccupancy[i][idx]);
+      int ctxIdx = _ctxIdxMap[i][numOccupiedAcc];
+      bit = _arithmeticDecoder->decode(_ctxOccupancy[ctxIdx]);
     }
+    _ctxIdxMap.evolve(bit, &_ctxIdxMap[i][numOccupiedAcc]);
     numOccupiedAcc += bit;
     occupancy |= bit << occupancyCodingOrder[i];
   }
@@ -173,30 +176,26 @@ GeometryOctreeDecoder::decodeOccupancyNeighNZ(int neighPattern10)
   // NB: it is impossible for pattern to be 0 (handled in Z case).
   // NB: offsets are added since ctxIdxMap is shared between Z and NZ cases.
   for (int i = 0; i < 8; i++) {
-    int idx, bit;
-    if (i < 4) {
-      idx = (neighPattern10 << i) + partialOccupancy;
-    } else if (i == 4) {
-      idx = ((neighPattern10 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit4CtxIdx[idx] + i;
-    } else if (i == 5) {
-      idx = ((neighPattern10 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit5CtxIdx[idx] + i;
+    int idx;
+    if (i < 6) {
+      idx = ((neighPattern10 - 1) << i) + partialOccupancy + i + 1;
     } else if (i == 6) {
-      idx = ((neighPattern7 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit6CtxIdx[idx] + i;
+      idx = ((neighPattern7 - 1) << i) + partialOccupancy + i + 1;
     } else if (i == 7) {
-      idx = ((neighPattern5 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit7CtxIdx[idx] + i;
-      bit = 1;
+      idx = ((neighPattern5 - 1) << i) + partialOccupancy + i + 1;
     } else {
       // work around clang -Wsometimes-uninitialized fault
       break;
     }
 
     // NB: if firt 7 bits are 0, then the last is implicitly 1.
-    if (i < 7 || partialOccupancy)
-      bit = _arithmeticDecoder->decode(_ctxOccupancy[i][idx]);
+    int bit = 1;
+    if (i < 7 || partialOccupancy) {
+      int ctxIdx = _ctxIdxMap[i][idx];
+      bit = _arithmeticDecoder->decode(_ctxOccupancy[ctxIdx]);
+    }
+
+    _ctxIdxMap.evolve(bit, &_ctxIdxMap[i][idx]);
     partialOccupancy |= bit << i;
     occupancy |= bit << occupancyCodingOrder[i];
   }

tmc3/geometry_octree_encoder.cpp

@@ -86,6 +86,7 @@ private:
 
   // For bitwise occupancy coding
   CtxModelOctreeOccupancy _ctxOccupancy;
+  CtxMapOctreeOccupancy _ctxIdxMap;
 
   // For bytewise occupancy coding
   DualLutCoder<true> _bytewiseOccupancyCoder[10];
@@ -97,6 +98,7 @@ GeometryOctreeEncoder::GeometryOctreeEncoder(
   const GeometryParameterSet& gps, o3dgc::Arithmetic_Codec* arithmeticEncoder)
   : _useBitwiseOccupancyCoder(gps.bitwise_occupancy_coding_flag)
   , _arithmeticEncoder(arithmeticEncoder)
+  , _ctxOccupancy(gps.geom_occupancy_ctx_reduction_factor)
 {
   if (!_useBitwiseOccupancyCoder) {
     for (int i = 0; i < 10; i++)
@@ -142,16 +144,17 @@ GeometryOctreeEncoder::encodeOccupancyNeighZ(int mappedOccupancy)
   int numOccupiedAcc = 0;
 
   for (int i = 0; i < 8; i++) {
+    int occupancyBit = (mappedOccupancy >> occupancyCodingOrder[i]) & 1;
+
+    int idx = numOccupiedAcc;
+    int ctxIdx = _ctxIdxMap.evolve(occupancyBit, &_ctxIdxMap[i][idx]);
+
     // NB: There must be at least minOccupied child nodes
     //  -- avoid coding the occupancyBit if it is implied.
-    if (numOccupiedAcc < minOccupied + i - 7) {
-      assert(i >= 6);
-      break;
+    if (numOccupiedAcc >= minOccupied + i - 7) {
+      _arithmeticEncoder->encode(occupancyBit, _ctxOccupancy[ctxIdx]);
     }
 
-    int occupancyBit = (mappedOccupancy >> occupancyCodingOrder[i]) & 1;
-    int idx = numOccupiedAcc;
-    _arithmeticEncoder->encode(occupancyBit, _ctxOccupancy[i][idx]);
     numOccupiedAcc += occupancyBit;
   }
 }
@@ -175,29 +178,23 @@ GeometryOctreeEncoder::encodeOccupancyNeighNZ(
     int occupancyBit = (mappedOccupancy >> occupancyCodingOrder[i]) & 1;
 
     int idx;
-    if (i < 4)
-      idx = (neighPattern10 << i) + partialOccupancy;
-    else if (i == 4) {
-      idx = ((neighPattern10 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit4CtxIdx[idx] + i;
-    } else if (i == 5) {
-      idx = ((neighPattern10 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit5CtxIdx[idx] + i;
+    if (i < 6) {
+      idx = ((neighPattern10 - 1) << i) + partialOccupancy + i + 1;
     } else if (i == 6) {
-      idx = ((neighPattern7 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit6CtxIdx[idx] + i;
+      idx = ((neighPattern7 - 1) << i) + partialOccupancy + i + 1;
     } else if (i == 7) {
-      // NB: if firt 7 bits are 0, then the last is implicitly 1.
-      if (!partialOccupancy)
-        break;
-      idx = ((neighPattern5 - 1) << i) + partialOccupancy;
-      idx = kOccMapBit7CtxIdx[idx] + i;
+      idx = ((neighPattern5 - 1) << i) + partialOccupancy + i + 1;
     } else {
       // work around clang -Wsometimes-uninitialized fault
       break;
     }
 
-    _arithmeticEncoder->encode(occupancyBit, _ctxOccupancy[i][idx]);
+    int ctxIdx = _ctxIdxMap.evolve(occupancyBit, &_ctxIdxMap[i][idx]);
+
+    // NB: if firt 7 bits are 0, then the last is implicitly 1.
+    if (i < 7 || partialOccupancy)
+      _arithmeticEncoder->encode(occupancyBit, _ctxOccupancy[ctxIdx]);
+
     partialOccupancy |= occupancyBit << i;
   }
 }

tmc3/hls.h

@@ -207,6 +207,10 @@ struct GeometryParameterSet {
   // Selects between bitwise and bytewise occupancy coding
   bool bitwise_occupancy_coding_flag;
 
+  // Experimental knob to control the number of contexts used
+  // for occupancy coding.
+  int geom_occupancy_ctx_reduction_factor;
+
   // depth of voxels (reconstructed points) in trisoup geometry
   int trisoup_depth;
 

tmc3/io_hls.cpp

@@ -193,6 +193,7 @@ write(const GeometryParameterSet& gps)
   bs.write(gps.neighbour_context_restriction_flag);
   bs.write(gps.inferred_direct_coding_mode_enabled_flag);
   bs.write(gps.bitwise_occupancy_coding_flag);
+  bs.writeUe(gps.geom_occupancy_ctx_reduction_factor);
   bs.writeUe(gps.neighbour_avail_boundary_log2);
 
   if (gps.geom_codec_type == GeometryCodecType::kTriSoup) {
@@ -224,6 +225,7 @@ parseGps(const PayloadBuffer& buf)
   bs.read(&gps.neighbour_context_restriction_flag);
   bs.read(&gps.inferred_direct_coding_mode_enabled_flag);
   bs.read(&gps.bitwise_occupancy_coding_flag);
+  bs.readUe(&gps.geom_occupancy_ctx_reduction_factor);
   bs.readUe(&gps.neighbour_avail_boundary_log2);
 
   if (gps.geom_codec_type == GeometryCodecType::kTriSoup) {

tmc3/tables.cpp

@@ -247,96 +247,48 @@ const uint8_t pcc::kOccMapRotateZ090[256] = {
   50, 54, 58, 62, 114, 118, 122, 126, 178, 182, 186, 190, 242, 246, 250, 254,
   51, 55, 59, 63, 115, 119, 123, 127, 179, 183, 187, 191, 243, 247, 251, 255};
 
-const uint8_t pcc::kOccMapBit4CtxIdx[16 * 9] = {
-  1,  3,  3,  3,  3,  4,  5,  6,  7,  6,  8,  4,  3,  9,  10, 11, 12, 13,
-  14, 15, 13, 16, 13, 17, 5,  18, 19, 18, 20, 21, 22, 16, 23, 20, 4,  4,
-  5,  4,  9,  24, 4,  4,  25, 26, 4,  9,  13, 25, 27, 28, 29, 19, 24, 30,
-  17, 31, 26, 32, 33, 34, 9,  23, 35, 36, 37, 13, 38, 3,  33, 39, 40, 9,
-  13, 41, 18, 6,  7,  9,  29, 20, 11, 9,  8,  24, 4,  24, 6,  22, 15, 34,
-  18, 23, 33, 42, 43, 23, 44, 28, 43, 16, 39, 11, 12, 45, 33, 41, 46, 45,
-  47, 48, 49, 50, 51, 11, 32, 30, 41, 2,  41, 52, 17, 53, 27, 54, 42, 55,
-  36, 48, 56, 57, 54, 49, 58, 59, 60, 37, 61, 62, 63, 64, 65, 66, 67, 68};
-
-const uint8_t pcc::kOccMapBit5CtxIdx[32 * 9] = {
-  1,  3,   3,  4,  5,   6,   7,   8,   9,   10, 4,   11, 9,   12,  13, 14,  15,
-  16, 15,  17, 18, 7,   19,  20,  21,  8,   19, 22,  22, 23,  24,  25, 26,  6,
-  27, 28,  5,  29, 30,  14,  31,  21,  32,  33, 34,  15, 11,  35,  36, 8,   6,
-  37, 38,  7,  29, 39,  40,  41,  42,  43,  44, 45,  46, 47,  48,  5,  27,  11,
-  37, 11,  49, 7,  10,  20,  18,  50,  51,  52, 17,  47, 53,  17,  54, 55,  56,
-  19, 57,  36, 40, 50,  54,  58,  36,  59,  60, 61,  62, 35,  16,  63, 27,  15,
-  4,  16,  15, 12, 33,  64,  4,   15,  10,  65, 47,  66, 67,  15,  12, 36,  68,
-  65, 19,  47, 69, 44,  70,  57,  71,  33,  61, 64,  15, 72,  31,  30, 13,  28,
-  73, 26,  42, 74, 3,   17,  5,   15,  75,  76, 77,  78, 61,  79,  25, 80,  81,
-  82, 83,  84, 80, 84,  85,  26,  47,  35,  5,  12,  68, 55,  42,  70, 38,  41,
-  38, 7,   7,  54, 86,  19,  43,  14,  69,  87, 22,  59, 79,  62,  86, 88,  56,
-  45, 77,  25, 89, 25,  57,  37,  29,  15,  17, 40,  88, 55,  5,   90, 33,  32,
-  64, 33,  42, 39, 41,  7,   87,  35,  19,  91, 23,  88, 92,  31,  43, 35,  61,
-  59, 93,  67, 25, 73,  88,  94,  95,  59,  24, 2,   70, 46,  96,  97, 44,  24,
-  48, 57,  62, 57, 57,  98,  60,  77,  99,  79, 100, 2,  101, 100, 2,  60,  79,
-  79, 85,  62, 62, 60,  60,  89,  89,  102, 57, 100, 61, 103, 100, 89, 103, 75,
-  61, 101, 93, 25, 104, 105, 105, 106, 78,  25, 60,  85, 85,  76,  81, 102};
+//============================================================================
 
-const uint8_t pcc::kOccMapBit6CtxIdx[64 * 6] = {
-  1,  3,   4,  5,  4,   6,   7,   8,   9,  10,  11, 12,  13, 12,  14,  12, 15,
-  16, 7,   17, 18, 19,  20,  21,  8,   18, 22,  23, 24,  20, 20,  25,  26, 27,
-  28, 29,  8,  29, 30,  31,  10,  28,  32, 33,  34, 24,  21, 35,  34,  36, 37,
-  38, 39,  33, 40, 41,  39,  21,  33,  42, 43,  19, 44,  45, 23,  34,  6,  15,
-  7,  46,  47, 18, 48,  18,  10,  49,  50, 51,  14, 18,  52, 24,  53,  33, 54,
-  55, 56,  25, 57, 24,  40,  25,  58,  59, 60,  61, 10,  62, 34,  63,  46, 46,
-  20, 64,  65, 49, 47,  66,  52,  8,   7,  63,  12, 67,  56, 31,  57,  68, 2,
-  60, 33,  69, 2,  70,  21,  71,  72,  73, 74,  11, 36,  8,  62,  75,  76, 39,
-  34, 47,  56, 77, 54,  21,  66,  63,  36, 29,  30, 78,  17, 21,  31,  58, 37,
-  63, 19,  79, 38, 70,  71,  68,  47,  49, 44,  56, 37,  56, 72,  2,   39, 31,
+// transition tables L= 10; 256 ctx
+const uint8_t pcc::kCtxMapOctreeOccupancyEvolutionOn0[256] = {
+  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   9,   10,  11,  12,  13,
+  14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,  28,
+  29,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,  42,
+  43,  44,  45,  46,  47,  48,  48,  49,  50,  51,  52,  53,  54,  55,  56,
+  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  66,  67,  68,  69,  70,
+  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  82,  83,  84,
+  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  96,  97,  98,
+  99,  100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 109, 110, 111, 112,
+  113, 114, 115, 116, 117, 118, 119, 120, 120, 121, 122, 123, 124, 125, 126,