From badfdf60612bc0019033b47db02dc9d0dc07b536 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Alexandre=20Delano=C3=AB?= <devel+git@delanoe.org>
Date: Fri, 26 Mar 2021 11:55:57 +0100
Subject: [PATCH] [FEAT] Distributional Measure Similarity in Graph Flow (WIP)
---
src/Gargantext/Core/Methods/Distances.hs | 10 +--
.../Distances/Accelerate/Distributional.hs | 10 ++-
.../Core/Methods/Distances/Conditional.hs | 14 +---
.../Core/Methods/Matrix/Accelerate/Utils.hs | 2 +-
src/Gargantext/Core/Text/Examples.hs | 4 +-
src/Gargantext/Core/Text/Metrics.hs | 4 +-
src/Gargantext/Core/Viz/Graph/API.hs | 59 ++++++++-------
src/Gargantext/Core/Viz/Graph/Index.hs | 37 ++++++----
src/Gargantext/Core/Viz/Graph/Tools.hs | 71 +++++++++++++------
9 files changed, 129 insertions(+), 82 deletions(-)
diff --git a/src/Gargantext/Core/Methods/Distances.hs b/src/Gargantext/Core/Methods/Distances.hs
index 152bfdb6..6118bba0 100644
--- a/src/Gargantext/Core/Methods/Distances.hs
+++ b/src/Gargantext/Core/Methods/Distances.hs
@@ -18,10 +18,10 @@ import Data.Aeson
import Data.Array.Accelerate (Matrix)
import Data.Swagger
import GHC.Generics (Generic)
+import Gargantext.Core.Methods.Distances.Accelerate.Conditional (measureConditional)
+import Gargantext.Core.Methods.Distances.Accelerate.Distributional (logDistributional)
import Gargantext.Prelude (Ord, Eq, Int, Double)
import Gargantext.Prelude (Show)
-import Gargantext.Core.Methods.Distances.Accelerate.Conditional (measureConditional)
-import Gargantext.Core.Methods.Distances.Accelerate.Distributional (distributional)
import Prelude (Enum, Bounded, minBound, maxBound)
import Test.QuickCheck (elements)
import Test.QuickCheck.Arbitrary
@@ -32,12 +32,12 @@ data Distance = Conditional | Distributional
measure :: Distance -> Matrix Int -> Matrix Double
measure Conditional = measureConditional
-measure Distributional = distributional
-------------------------------------------------------------------------
+measure Distributional = logDistributional
+------------------------------------------------------------------------
withMetric :: GraphMetric -> Matrix Int -> Matrix Double
withMetric Order1 = measureConditional
-withMetric Order2 = distributional
+withMetric Order2 = logDistributional
------------------------------------------------------------------------
data GraphMetric = Order1 | Order2
diff --git a/src/Gargantext/Core/Methods/Distances/Accelerate/Distributional.hs b/src/Gargantext/Core/Methods/Distances/Accelerate/Distributional.hs
index 324cecde..1c6f5fe8 100644
--- a/src/Gargantext/Core/Methods/Distances/Accelerate/Distributional.hs
+++ b/src/Gargantext/Core/Methods/Distances/Accelerate/Distributional.hs
@@ -116,10 +116,14 @@ distributional m' = run result
result = termDivNan z_1 z_2
logDistributional :: Matrix Int -> Matrix Double
-logDistributional m' = run result
+logDistributional m = run $ diagNull n $ matMiniMax $ logDistributional' n m
+ where
+ n = dim m
+
+logDistributional' :: Int -> Matrix Int -> Acc (Matrix Double)
+logDistributional' n m' = result
where
m = map fromIntegral $ use m'
- n = dim m'
-- Scalar. Sum of all elements of m.
to = the $ sum (flatten m)
@@ -234,6 +238,6 @@ rIJ n m = matMiniMax $ divide a b
-- | Test perfermance with this matrix
-- TODO : add this in a benchmark folder
distriTest :: Int -> Matrix Double
-distriTest n = distributional (theMatrixInt n)
+distriTest n = logDistributional (theMatrixInt n)
diff --git a/src/Gargantext/Core/Methods/Distances/Conditional.hs b/src/Gargantext/Core/Methods/Distances/Conditional.hs
index e528cac3..2f084c53 100644
--- a/src/Gargantext/Core/Methods/Distances/Conditional.hs
+++ b/src/Gargantext/Core/Methods/Distances/Conditional.hs
@@ -15,24 +15,17 @@ Motivation and definition of the @Conditional@ distance.
module Gargantext.Core.Methods.Distances.Conditional
where
-import Data.Matrix hiding (identity)
-
import Data.List (sortOn)
-
import Data.Map (Map)
+import Data.Matrix hiding (identity)
+import Gargantext.Core.Viz.Graph.Utils
+import Gargantext.Prelude
import qualified Data.Map as M
-
import qualified Data.Set as S
-
import qualified Data.Vector as V
-import Gargantext.Prelude
-import Gargantext.Core.Viz.Graph.Utils
-
-------------------------------------------------------------------------
------------------------------------------------------------------------
-- | Optimisation issue
-
toBeOptimized :: (Num a, Fractional a, Ord a) => Matrix a -> Matrix a
toBeOptimized m = proba Col m
@@ -56,7 +49,6 @@ mapOnly Row = mapRow
mapAll :: (a -> a) -> Matrix a -> Matrix a
mapAll f m = mapOn Col (\_ -> f) m
-
---------------------------------------------------------------
-- | Compute a distance from axis
-- xs = (sum Col x') - x'
diff --git a/src/Gargantext/Core/Methods/Matrix/Accelerate/Utils.hs b/src/Gargantext/Core/Methods/Matrix/Accelerate/Utils.hs
index 4cb7ee49..873382e2 100644
--- a/src/Gargantext/Core/Methods/Matrix/Accelerate/Utils.hs
+++ b/src/Gargantext/Core/Methods/Matrix/Accelerate/Utils.hs
@@ -242,7 +242,7 @@ matMiniMax :: (Elt a, Ord a, P.Num a)
-> Acc (Matrix a)
matMiniMax m = filterWith' miniMax' (constant 0) m
where
- miniMax' = the $ minimum $ maximum m
+ miniMax' = the $ maximum $ minimum m
-- | Filters the matrix with a constant
diff --git a/src/Gargantext/Core/Text/Examples.hs b/src/Gargantext/Core/Text/Examples.hs
index 36408e02..27ec21f8 100644
--- a/src/Gargantext/Core/Text/Examples.hs
+++ b/src/Gargantext/Core/Text/Examples.hs
@@ -112,7 +112,7 @@ ex_cooc_mat :: IO (Map Label Index, Matrix Int, Matrix Double, (DAA.Vector Gener
ex_cooc_mat = do
m <- ex_cooc
let (ti,_) = createIndices m
- let mat_cooc = cooc2mat ti m
+ let mat_cooc = cooc2mat Triangular ti m
pure ( ti
, mat_cooc
, incExcSpeGen_proba mat_cooc
@@ -123,7 +123,7 @@ ex_incExcSpeGen :: IO ([(Label, Double)], [(Label, Double)])
ex_incExcSpeGen = incExcSpeGen_sorted <$> ex_cooc
incExcSpeGen_sorted :: Ord t => Map (t,t) Int -> ([(t,Double)],[(t,Double)])
-incExcSpeGen_sorted m = both ordonne (incExcSpeGen $ cooc2mat ti m)
+incExcSpeGen_sorted m = both ordonne (incExcSpeGen $ cooc2mat Triangular ti m)
where
(ti,fi) = createIndices m
ordonne x = sortWith (Down . snd)
diff --git a/src/Gargantext/Core/Text/Metrics.hs b/src/Gargantext/Core/Text/Metrics.hs
index 6a096c70..287e75e1 100644
--- a/src/Gargantext/Core/Text/Metrics.hs
+++ b/src/Gargantext/Core/Text/Metrics.hs
@@ -70,7 +70,7 @@ localMetrics' m = Map.fromList $ zipWith (\(_,t) (inc,spe) -> (t, Vec.fromList [
scores
where
(ti, fi) = createIndices m
- (is, ss) = incExcSpeGen $ cooc2mat ti m
+ (is, ss) = incExcSpeGen $ cooc2mat Triangular ti m
scores = DAA.toList
$ DAA.run
$ DAA.zip (DAA.use is) (DAA.use ss)
@@ -82,7 +82,7 @@ scored' :: Ord t => Map (t,t) Int -> [Scored t]
scored' m = zipWith (\(_,t) (inc,spe) -> Scored t inc spe) (Map.toList fi) scores
where
(ti, fi) = createIndices m
- (is, ss) = incExcSpeGen $ cooc2mat ti m
+ (is, ss) = incExcSpeGen $ cooc2mat Triangular ti m
scores = DAA.toList
$ DAA.run
$ DAA.zip (DAA.use is) (DAA.use ss)
diff --git a/src/Gargantext/Core/Viz/Graph/API.hs b/src/Gargantext/Core/Viz/Graph/API.hs
index ed73201e..e54bbd10 100644
--- a/src/Gargantext/Core/Viz/Graph/API.hs
+++ b/src/Gargantext/Core/Viz/Graph/API.hs
@@ -79,12 +79,12 @@ graphAPI u n = getGraph u n
getGraph :: UserId -> NodeId -> GargNoServer HyperdataGraphAPI
getGraph _uId nId = do
nodeGraph <- getNodeWith nId (Proxy :: Proxy HyperdataGraph)
- let graph = nodeGraph ^. node_hyperdata . hyperdataGraph
- let camera = nodeGraph ^. node_hyperdata . hyperdataCamera
-
repo <- getRepo
- let cId = maybe (panic "[G.V.G.API] Node has no parent")
+ let
+ graph = nodeGraph ^. node_hyperdata . hyperdataGraph
+ camera = nodeGraph ^. node_hyperdata . hyperdataCamera
+ cId = maybe (panic "[G.V.G.API] Node has no parent")
identity
$ nodeGraph ^. node_parentId
@@ -94,8 +94,9 @@ getGraph _uId nId = do
-- graph' <- computeGraph cId Distributional NgramsTerms repo
graph' <- computeGraph cId Conditional NgramsTerms repo
mt <- defaultGraphMetadata cId "Title" repo
- let graph'' = set graph_metadata (Just mt) graph'
- let hg = HyperdataGraphAPI graph'' camera
+ let
+ graph'' = set graph_metadata (Just mt) graph'
+ hg = HyperdataGraphAPI graph'' camera
-- _ <- updateHyperdata nId hg
_ <- updateHyperdata nId (HyperdataGraph (Just graph'') camera)
pure $ trace "[G.V.G.API] Graph empty, computing" hg
@@ -107,14 +108,16 @@ getGraph _uId nId = do
recomputeGraph :: UserId -> NodeId -> Distance -> GargNoServer Graph
recomputeGraph _uId nId d = do
nodeGraph <- getNodeWith nId (Proxy :: Proxy HyperdataGraph)
- let graph = nodeGraph ^. node_hyperdata . hyperdataGraph
- let camera = nodeGraph ^. node_hyperdata . hyperdataCamera
- let graphMetadata = graph ^? _Just . graph_metadata . _Just
- let listVersion = graph ^? _Just . graph_metadata . _Just . gm_list . lfg_version
+ let
+ graph = nodeGraph ^. node_hyperdata . hyperdataGraph
+ camera = nodeGraph ^. node_hyperdata . hyperdataCamera
+ graphMetadata = graph ^? _Just . graph_metadata . _Just
+ listVersion = graph ^? _Just . graph_metadata . _Just . gm_list . lfg_version
repo <- getRepo
- let v = repo ^. r_version
- let cId = maybe (panic "[G.V.G.API.recomputeGraph] Node has no parent")
+ let
+ v = repo ^. r_version
+ cId = maybe (panic "[G.V.G.API.recomputeGraph] Node has no parent")
identity
$ nodeGraph ^. node_parentId
@@ -144,18 +147,19 @@ computeGraph :: HasNodeError err
-> Cmd err Graph
computeGraph cId d nt repo = do
lId <- defaultList cId
-
lIds <- selectNodesWithUsername NodeList userMaster
- let ngs = filterListWithRoot MapTerm $ mapTermListRoot [lId] nt repo
- -- TODO split diagonal
- myCooc <- HashMap.filter (>1)
+ let ngs = filterListWithRoot MapTerm
+ $ mapTermListRoot [lId] nt repo
+
+ myCooc <- HashMap.filter (>1) -- Removing the hapax (ngrams with 1 cooc)
<$> getCoocByNgrams (Diagonal True)
<$> groupNodesByNgrams ngs
<$> getNodesByNgramsOnlyUser cId (lIds <> [lId]) nt (HashMap.keys ngs)
- graph <- liftBase $ cooc2graphWith Spinglass d 0 myCooc
+ printDebug "myCooc" myCooc
+ graph <- liftBase $ cooc2graphWith Spinglass d 0 myCooc
pure graph
@@ -205,7 +209,7 @@ graphRecompute u n logStatus = do
, _scst_remaining = Just 1
, _scst_events = Just []
}
- _g <- trace (show u) $ recomputeGraph u n Conditional -- Distributional
+ _g <- trace (show u) $ recomputeGraph u n Distributional
pure JobLog { _scst_succeeded = Just 1
, _scst_failed = Just 0
, _scst_remaining = Just 0
@@ -226,12 +230,17 @@ graphVersionsAPI u n =
graphVersions :: NodeId -> GargNoServer GraphVersions
graphVersions nId = do
nodeGraph <- getNodeWith nId (Proxy :: Proxy HyperdataGraph)
- let graph = nodeGraph ^. node_hyperdata . hyperdataGraph
- let listVersion = graph ^? _Just
- . graph_metadata
- . _Just
- . gm_list
- . lfg_version
+ let
+ graph = nodeGraph
+ ^. node_hyperdata
+ . hyperdataGraph
+
+ listVersion = graph
+ ^? _Just
+ . graph_metadata
+ . _Just
+ . gm_list
+ . lfg_version
repo <- getRepo
let v = repo ^. r_version
@@ -240,7 +249,7 @@ graphVersions nId = do
, gv_repo = v }
recomputeVersions :: UserId -> NodeId -> GargNoServer Graph
-recomputeVersions uId nId = recomputeGraph uId nId Conditional -- Distributional
+recomputeVersions uId nId = recomputeGraph uId nId Distributional
------------------------------------------------------------
graphClone :: UserId
diff --git a/src/Gargantext/Core/Viz/Graph/Index.hs b/src/Gargantext/Core/Viz/Graph/Index.hs
index 13be4c15..26dde256 100644
--- a/src/Gargantext/Core/Viz/Graph/Index.hs
+++ b/src/Gargantext/Core/Viz/Graph/Index.hs
@@ -44,25 +44,34 @@ type Index = Int
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
-score :: (Ord t) => (A.Matrix Int -> A.Matrix Double)
- -> Map (t, t) Int
- -> Map (t, t) Double
-score f m = fromIndex fromI . mat2map . f $ cooc2mat toI m
+score :: (Ord t) => MatrixShape
+ -> (A.Matrix Int -> A.Matrix Double)
+ -> Map (t, t) Int
+ -> Map (t, t) Double
+score s f m = fromIndex fromI . mat2map . f $ cooc2mat s toI m
where
(toI, fromI) = createIndices m
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
-cooc2mat :: Ord t => Map t Index -> Map (t, t) Int -> Matrix Int
-cooc2mat ti m = map2mat 0 n idx
+cooc2mat :: Ord t => MatrixShape -> Map t Index -> Map (t, t) Int -> Matrix Int
+cooc2mat sym ti m = map2mat sym 0 n idx
where
n = M.size ti
idx = toIndex ti m -- it is important to make sure that toIndex is ran only once.
-map2mat :: Elt a => a -> Int -> Map (Index, Index) a -> Matrix a
-map2mat def n m = A.fromFunction shape (\(Z :. x :. y) -> fromMaybe def $ M.lookup (x, y) m)
+data MatrixShape = Triangular | Square
+
+map2mat :: Elt a => MatrixShape -> a -> Int -> Map (Index, Index) a -> Matrix a
+map2mat sym def n m = A.fromFunction shape getData
where
- shape = (Z :. n :. n)
+ getData = (\(Z :. x :. y) ->
+ case sym of
+ Triangular -> fromMaybe def (M.lookup (x,y) m)
+ Square -> fromMaybe (fromMaybe def $ M.lookup (y,x) m)
+ $ M.lookup (x, y) m
+ )
+ shape = (Z :. n :. n)
mat2map :: (Elt a, Shape (Z :. Index)) =>
A.Array (Z :. Index :. Index) a -> Map (Index, Index) a
@@ -73,15 +82,19 @@ mat2map m = M.fromList . map f . A.toList . A.run . A.indexed $ A.use m
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
-toIndex :: Ord t => Map t Index -> Map (t,t) a -> Map (Index,Index) a
-toIndex ni ns = indexConversion ni ns
+toIndex :: Ord t
+ => Map t Index
+ -> Map (t,t) a
+ -> Map (Index,Index) a
+toIndex = indexConversion
fromIndex :: Ord t => Map Index t -> Map (Index, Index) a -> Map (t,t) a
fromIndex ni ns = indexConversion ni ns
indexConversion :: (Ord b, Ord k) => Map k b -> Map (k,k) a -> Map (b, b) a
indexConversion index ms = M.fromList
- $ map (\((k1,k2),c) -> ( ((M.!) index k1, (M.!) index k2), c)) (M.toList ms)
+ $ map (\((k1,k2),c) -> ( ((M.!) index k1, (M.!) index k2), c))
+ (M.toList ms)
---------------------------------------------------------------------------------
-------------------------------------------------------------------------------
diff --git a/src/Gargantext/Core/Viz/Graph/Tools.hs b/src/Gargantext/Core/Viz/Graph/Tools.hs
index a8d3550f..77892160 100644
--- a/src/Gargantext/Core/Viz/Graph/Tools.hs
+++ b/src/Gargantext/Core/Viz/Graph/Tools.hs
@@ -14,8 +14,8 @@ module Gargantext.Core.Viz.Graph.Tools
-- import Data.Graph.Clustering.Louvain (hLouvain, {-iLouvainMap-})
import Data.Graph.Clustering.Louvain.CplusPlus (cLouvain)
-import Data.Map (Map)
import Data.HashMap.Strict (HashMap)
+import Data.Map (Map)
import Data.Text (Text)
import Debug.Trace (trace)
import GHC.Float (sin, cos)
@@ -25,17 +25,17 @@ import Gargantext.Core.Methods.Graph.BAC.Proxemy (confluence)
import Gargantext.Core.Statistics
import Gargantext.Core.Viz.Graph
import Gargantext.Core.Viz.Graph.Bridgeness (bridgeness, Partitions, ToComId(..))
+import Gargantext.Core.Viz.Graph.Index (createIndices, toIndex, map2mat, mat2map, Index, MatrixShape(..))
import Gargantext.Core.Viz.Graph.Tools.IGraph (mkGraphUfromEdges, spinglass)
-import Gargantext.Core.Viz.Graph.Index (createIndices, toIndex, map2mat, mat2map, Index)
import Gargantext.Prelude
import IGraph.Random -- (Gen(..))
+import qualified Data.HashMap.Strict as HashMap
import qualified Data.List as List
import qualified Data.Map as Map
import qualified Data.Set as Set
import qualified Data.Vector.Storable as Vec
import qualified IGraph as Igraph
import qualified IGraph.Algorithms.Layout as Layout
-import qualified Data.HashMap.Strict as HashMap
type Threshold = Double
@@ -44,13 +44,19 @@ cooc2graph' :: Ord t => Distance
-> Double
-> Map (t, t) Int
-> Map (Index, Index) Double
-cooc2graph' distance threshold myCooc = distanceMap
- where
- (ti, _) = createIndices myCooc
- myCooc' = toIndex ti myCooc
- matCooc = map2mat 0 (Map.size ti) $ Map.filter (> 1) myCooc'
- distanceMat = measure distance matCooc
- distanceMap = Map.filter (> threshold) $ mat2map distanceMat
+cooc2graph' distance threshold myCooc
+ = Map.filter (> threshold)
+ $ mat2map
+ $ measure distance
+ $ case distance of
+ Conditional -> map2mat Triangular 0 (Map.size ti)
+ Distributional -> map2mat Square 0 (Map.size ti)
+ $ Map.filter (> 1) myCooc'
+
+ where
+ (ti, _) = createIndices myCooc
+ myCooc' = toIndex ti myCooc
+
data PartitionMethod = Louvain | Spinglass
@@ -70,17 +76,33 @@ cooc2graphWith' :: ToComId a
-> HashMap (NgramsTerm, NgramsTerm) Int
-> IO Graph
cooc2graphWith' doPartitions distance threshold myCooc = do
- printDebug "cooc2graph" distance
let
-- TODO remove below
theMatrix = Map.fromList $ HashMap.toList myCooc
+
(ti, _) = createIndices theMatrix
myCooc' = toIndex ti theMatrix
- matCooc = map2mat 0 (Map.size ti)
- $ Map.filterWithKey (\(a,b) _ -> a /= b)
- $ Map.filter (> 1) myCooc'
- distanceMat = measure distance matCooc
- distanceMap = Map.filter (> threshold) $ mat2map distanceMat
+ matCooc = case distance of -- Shape of the Matrix
+ Conditional -> map2mat Triangular 0 (Map.size ti)
+ Distributional -> map2mat Square 0 (Map.size ti)
+ $ case distance of -- Removing the Diagonal ?
+ Conditional -> Map.filterWithKey (\(a,b) _ -> a /= b)
+ Distributional -> identity
+ $ Map.filter (>1) myCooc'
+
+ printDebug "myCooc'" myCooc'
+ printDebug "ti" (Map.size ti)
+
+ let
+ similarities = measure distance matCooc
+
+ printDebug "Similarities" similarities
+
+ let
+ distanceMap = case distance of
+ Conditional -> Map.filter (> threshold)
+ Distributional -> Map.filter (> 0)
+ $ mat2map similarities
nodesApprox :: Int
nodesApprox = n'
@@ -89,18 +111,15 @@ cooc2graphWith' doPartitions distance threshold myCooc = do
n' = Set.size $ Set.fromList $ as <> bs
ClustersParams rivers _level = clustersParams nodesApprox
- printDebug "Start" ("partitions" :: Text)
partitions <- if (Map.size distanceMap > 0)
- -- then iLouvainMap 100 10 distanceMap
- -- then hLouvain distanceMap
then doPartitions distanceMap
else panic "Text.Flow: DistanceMap is empty"
- printDebug "End" ("partitions" :: Text)
let
-- bridgeness' = distanceMap
bridgeness' = trace ("Rivers: " <> show rivers)
$ bridgeness rivers partitions distanceMap
+
confluence' = confluence (Map.keys bridgeness') 3 True False
pure $ data2graph (Map.toList $ Map.mapKeys unNgramsTerm ti)
@@ -230,4 +249,14 @@ layout m n gen = maybe (panic "") identity $ Map.lookup n $ coord
--p = Layout.defaultLGL
p = Layout.kamadaKawai
g = mkGraphUfromEdges $ map fst $ List.filter (\e -> snd e > 0) $ Map.toList m
-
+-----------------------------------------------------------------------------
+-----------------------------------------------------------------------------
+-----------------------------------------------------------------------------
+-- Debug
+{-
+-- measure logDistributional
+dataDebug = map2mat Square (0::Int) 19 dataBug'
+
+dataBug' :: Map (Int, Int) Int
+dataBug' = Map.fromList [((0,0),28),((0,1),8),((0,2),6),((0,3),2),((0,5),4),((0,6),4),((0,7),2),((0,9),7),((0,10),4),((0,13),4),((0,14),2),((0,15),5),((0,16),8),((0,17),3),((1,1),28),((1,2),6),((1,3),7),((1,4),5),((1,5),7),((1,6),5),((1,7),2),((1,9),6),((1,10),7),((1,11),5),((1,13),6),((1,15),6),((1,16),14),((1,18),4),((2,2),39),((2,3),5),((2,4),4),((2,5),3),((2,6),4),((2,7),4),((2,8),3),((2,9),17),((2,10),4),((2,11),8),((2,12),2),((2,13),15),((2,14),4),((2,15),5),((2,16),21),((2,18),4),((3,3),48),((3,4),10),((3,5),7),((3,6),3),((3,7),7),((3,8),6),((3,9),12),((3,10),9),((3,11),8),((3,12),5),((3,13),15),((3,14),5),((3,15),9),((3,16),17),((3,18),4),((4,4),33),((4,5),2),((4,6),5),((4,7),7),((4,8),4),((4,9),6),((4,10),12),((4,11),8),((4,12),3),((4,13),16),((4,14),4),((4,15),4),((4,16),5),((4,17),2),((4,18),12),((5,5),27),((5,6),2),((5,8),3),((5,9),12),((5,10),6),((5,11),9),((5,13),4),((5,14),2),((5,15),7),((5,16),11),((5,18),4),((6,6),34),((6,7),4),((6,8),3),((6,9),12),((6,10),8),((6,11),2),((6,12),5),((6,13),6),((6,14),6),((6,15),5),((6,16),22),((6,17),8),((6,18),4),((7,7),27),((7,8),2),((7,9),6),((7,10),2),((7,11),4),((7,13),13),((7,15),2),((7,16),8),((7,17),6),((7,18),4),((8,8),30),((8,9),9),((8,10),6),((8,11),9),((8,12),6),((8,13),3),((8,14),3),((8,15),4),((8,16),15),((8,17),3),((8,18),5),((9,9),69),((9,10),9),((9,11),22),((9,12),15),((9,13),18),((9,14),10),((9,15),14),((9,16),48),((9,17),6),((9,18),9),((10,10),39),((10,11),15),((10,12),5),((10,13),11),((10,14),2),((10,15),4),((10,16),19),((10,17),3),((10,18),11),((11,11),48),((11,12),9),((11,13),20),((11,14),2),((11,15),13),((11,16),29),((11,18),13),((12,12),30),((12,13),4),((12,15),5),((12,16),16),((12,17),6),((12,18),2),((13,13),65),((13,14),10),((13,15),14),((13,16),23),((13,17),6),((13,18),10),((14,14),25),((14,16),9),((14,17),3),((14,18),3),((15,15),38),((15,16),17),((15,18),4),((16,16),99),((16,17),11),((16,18),14),((17,17),29),((18,18),23)]
+-}
--
2.21.0