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The TREE Procedure

Example 66.2: Iris Data

Fisher's (1936) iris data gives sepal and petal dimensions for three different species of iris. The data are clustered by kth-nearest-neighbor density linkage using the CLUSTER procedure with K=8. Observations are identified by species (Setosa, Versicolor or Virginica) in the tree diagram, which is oriented with the height axis horizontal. The following statements produce Output 66.2.1 and Output 66.2.2.

   proc format;
      value specname
         1='Setosa    '
         2='Versicolor'
         3='Virginica ';
   run;

   data iris;
      title 'Fisher (1936) Iris Data';
      input SepalLength SepalWidth PetalLength PetalWidth 
            Species @@;
      format Species specname.;
      label SepalLength='Sepal Length in mm.'
            SepalWidth ='Sepal Width in mm.'
            PetalLength='Petal Length in mm.'
            PetalWidth ='Petal Width in mm.';
      symbol = put(species, specname10.);
      datalines;
   50 33 14 02 1 64 28 56 22 3 65 28 46 15 2 67 31 56 24 3
   63 28 51 15 3 46 34 14 03 1 69 31 51 23 3 62 22 45 15 2
   59 32 48 18 2 46 36 10 02 1 61 30 46 14 2 60 27 51 16 2
   65 30 52 20 3 56 25 39 11 2 65 30 55 18 3 58 27 51 19 3
   68 32 59 23 3 51 33 17 05 1 57 28 45 13 2 62 34 54 23 3
   77 38 67 22 3 63 33 47 16 2 67 33 57 25 3 76 30 66 21 3
   49 25 45 17 3 55 35 13 02 1 67 30 52 23 3 70 32 47 14 2
   64 32 45 15 2 61 28 40 13 2 48 31 16 02 1 59 30 51 18 3
   55 24 38 11 2 63 25 50 19 3 64 32 53 23 3 52 34 14 02 1
   49 36 14 01 1 54 30 45 15 2 79 38 64 20 3 44 32 13 02 1
   67 33 57 21 3 50 35 16 06 1 58 26 40 12 2 44 30 13 02 1
   77 28 67 20 3 63 27 49 18 3 47 32 16 02 1 55 26 44 12 2
   50 23 33 10 2 72 32 60 18 3 48 30 14 03 1 51 38 16 02 1
   61 30 49 18 3 48 34 19 02 1 50 30 16 02 1 50 32 12 02 1
   61 26 56 14 3 64 28 56 21 3 43 30 11 01 1 58 40 12 02 1
   51 38 19 04 1 67 31 44 14 2 62 28 48 18 3 49 30 14 02 1
   51 35 14 02 1 56 30 45 15 2 58 27 41 10 2 50 34 16 04 1
   46 32 14 02 1 60 29 45 15 2 57 26 35 10 2 57 44 15 04 1
   50 36 14 02 1 77 30 61 23 3 63 34 56 24 3 58 27 51 19 3
   57 29 42 13 2 72 30 58 16 3 54 34 15 04 1 52 41 15 01 1
   71 30 59 21 3 64 31 55 18 3 60 30 48 18 3 63 29 56 18 3
   49 24 33 10 2 56 27 42 13 2 57 30 42 12 2 55 42 14 02 1
   49 31 15 02 1 77 26 69 23 3 60 22 50 15 3 54 39 17 04 1
   66 29 46 13 2 52 27 39 14 2 60 34 45 16 2 50 34 15 02 1
   44 29 14 02 1 50 20 35 10 2 55 24 37 10 2 58 27 39 12 2
   47 32 13 02 1 46 31 15 02 1 69 32 57 23 3 62 29 43 13 2
   74 28 61 19 3 59 30 42 15 2 51 34 15 02 1 50 35 13 03 1
   56 28 49 20 3 60 22 40 10 2 73 29 63 18 3 67 25 58 18 3
   49 31 15 01 1 67 31 47 15 2 63 23 44 13 2 54 37 15 02 1
   56 30 41 13 2 63 25 49 15 2 61 28 47 12 2 64 29 43 13 2
   51 25 30 11 2 57 28 41 13 2 65 30 58 22 3 69 31 54 21 3
   54 39 13 04 1 51 35 14 03 1 72 36 61 25 3 65 32 51 20 3
   61 29 47 14 2 56 29 36 13 2 69 31 49 15 2 64 27 53 19 3
   68 30 55 21 3 55 25 40 13 2 48 34 16 02 1 48 30 14 01 1
   45 23 13 03 1 57 25 50 20 3 57 38 17 03 1 51 38 15 03 1
   55 23 40 13 2 66 30 44 14 2 68 28 48 14 2 54 34 17 02 1
   51 37 15 04 1 52 35 15 02 1 58 28 51 24 3 67 30 50 17 2
   63 33 60 25 3 53 37 15 02 1
   ;
   proc cluster data=iris method=twostage print=10 
                outtree=tree k=8 noeigen;
      var SepalLength SepalWidth PetalLength PetalWidth;
      copy Species;
      id Species;
   run;

   options pagesize=60 linesize=110;

   proc tree data=tree horizontal lineprinter pages=1 maxh=10;
      id species;
   run;

The PAGES=1 option specifies that the tree diagram extends over one page from tree to root. Since the HORIZONTAL option is also specified, the horizontal extent of the diagram is one page. The number of vertical pages required for the diagram is dictated by the number of leaves in the tree.

The MAXH=10 limits the values displayed on the height axis to a maximum of 10. This prunes the tree diagram so that only the portion from the leaves to level 10 is displayed. You can see this pruning effect in Output 66.2.2.

Output 66.2.1: Clustering of Fisher's Iris Data

Fisher (1936) Iris Data

The CLUSTER Procedure
Two-Stage Density Linkage Clustering

K = 8

Root-Mean-Square Total-Sample Standard Deviation = 10.69224

Cluster History
NCL   FREQ Normalized
Fusion Density
Maximum Density
in Each Cluster
T
i
e
Clusters Joined Lesser Greater
10 CL11 Versicolor 48 0.2879 0.1479 8.3678  
9 CL13 Virginica 46 0.2802 0.2005 3.5156  
8 CL10 Virginica 49 0.2699 0.1372 8.3678  
7 CL8 Versicolor 50 0.2586 0.1372 8.3678  
6 CL9 Virginica 47 0.1412 0.0832 3.5156  
5 CL6 Virginica 48 0.107 0.0605 3.5156  
4 CL5 Virginica 49 0.0969 0.0541 3.5156  
3 CL4 Virginica 50 0.0715 0.0370 3.5156  
2 CL3 CL7 100 2.6277 3.5156 8.3678  

3 modal clusters have been formed.

Output 66.2.2: Horizontal Tree for Fisher's Iris Data

                                                                                                              
                                                                                                              
                                     Two-Stage Density Linkage Clustering                                     
                                                                                                              
                                                  Cluster Fusion Density                                      
                                                                                                              
                0        1        2        3        4        5        6        7        8        9       10   
                +--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+   
  S   Virginica XX.........................................................................................   
  p             XX                                                                                            
  e   Virginica XX.........................................................................................   
  c             XX                                                                                            
  i   Virginica XXXX.......................................................................................   
  e             XXXX                                                                                          
  s   Virginica XXXX.......................................................................................   
                XXXX                                                                                          
      Virginica XXXXXX.....................................................................................   
                XXXXXX                                                                                        
     Versicolor XXXXXXX....................................................................................   
                XXXXXXX                                                                                       
      Virginica XXXXXXXX...................................................................................   
                XXXXXXXX                                                                                      
      Virginica XXXXXXXXX..................................................................................   
                XXXXXXXXX                                                                                     
      Virginica XXXXXXXXXXXXXXX............................................................................   
                XXXXXXXXXXXXXXX                                                                               
      Virginica XXXXXXXXXXXXXXXX...........................................................................   
                XXXXXXXXXXXXXXXX                                                                              
      Virginica XXXXXXXXXXXXXXXXXX.........................................................................   
                XXXXXXXXXXXXXXXXXX                                                                            
      Virginica XXXXXXXXXXXXXXXXXXXX.......................................................................   
                XXXXXXXXXXXXXXXXXXXX                                                                          
      Virginica XXXXXXXXXXXXXXXXXXXXX......................................................................   
                XXXXXXXXXXXXXXXXXXXXX                                                                         
      Virginica XXXXXXXXXXXXXXXXXXXXXX.....................................................................   
                XXXXXXXXXXXXXXXXXXXXXX                                                                        
      Virginica XXXXXXXXXXXXXXXXXXXXXX.....................................................................   
                XXXXXXXXXXXXXXXXXXXXXX                                                                        
      Virginica XXXXXXXXXXXXXXXXXXXXXX.....................................................................   
                XXXXXXXXXXXXXXXXXXXXXX                                                                        
      Virginica XXXXXXXXXXXXXXXXXXXXXXX....................................................................   
                XXXXXXXXXXXXXXXXXXXXXXX                                                                       
      Virginica XXXXXXXXXXXXXXXXXXXXXXX....................................................................   
                XXXXXXXXXXXXXXXXXXXXXXX                                                                       
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXX................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXX                                                                   
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXXX................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXX                                                                    
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXX.................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXX                                                                    
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXX.................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXX                                                                     
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                                  
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                               
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                               
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                                 
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXX                                                                   
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXXX................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXX                                                                    
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXX.................................................................   
                XXXXXXXXXXXXXXXXXXXXXXX                                                                       
      Virginica XXXXXXXXXXXXXXXXXXXXXXX....................................................................   
                XXXXXXXXXXXXXXXXXXXXXX                                                                        
                                                                                                              
                                                                                                              
     Versicolor XXXXXXXXXXXXXXXXXXXXXX.....................................................................   
                XXXXXXXXXXXXXXXXXXXXXX                                                                        
      Virginica XXXXXXXXXXXXXXXXXXXXXX.....................................................................   
                XXXXXXXXXXXXXXXXXXXXX                                                                         
      Virginica XXXXXXXXXXXXXXXXXXXXX......................................................................   
                XXXXXXXXXXXXXXXXXXXXX                                                                         
      Virginica XXXXXXXXXXXXXXXXXXXXX......................................................................   
                XXXXXXXXXXXXXXXXXXX                                                                           
      Virginica XXXXXXXXXXXXXXXXXXX........................................................................   
                XXXXXXXXXXXXXXXXXXX                                                                           
      Virginica XXXXXXXXXXXXXXXXXXX........................................................................   
                XXXXXXXXXXXXXXXXXX                                                                            
      Virginica XXXXXXXXXXXXXXXXXX.........................................................................   
                XXXXXXXXXXXXXXXX                                                                              
      Virginica XXXXXXXXXXXXXXXX...........................................................................   
                XXXXXXXXXXXXXXXX                                                                              
      Virginica XXXXXXXXXXXXXXXX...........................................................................   
                XXXXXXXXXXX                                                                                   
      Virginica XXXXXXXXXXX................................................................................   
                XXXXXXXXXXX                                                                                   
      Virginica XXXXXXXXXXX................................................................................   
                XXXXXXXXX                                                                                     
      Virginica XXXXXXXXX..................................................................................   
                XXXXXXXX                                                                                      
      Virginica XXXXXXXX...................................................................................   
                XXXXXX                                                                                        
      Virginica XXXXXX.....................................................................................   
                XXXXXX                                                                                        
      Virginica XXXXXX.....................................................................................   
                XXXXXX                                                                                        
      Virginica XXXXXX.....................................................................................   
                XXXXXX                                                                                        
      Virginica XXXXXX.....................................................................................   
                XXXXX                                                                                         
      Virginica XXXXX......................................................................................   
                XX                                                                                            
      Virginica XX.........................................................................................   
                XX                                                                                            
      Virginica XX.........................................................................................   
                X                                                                                             
      Virginica XXX........................................................................................   
                XXX                                                                                           
     Versicolor XXXX.......................................................................................   
                XXXX                                                                                          
     Versicolor XXXXXXXXXXX................................................................................   
                XXXXXXXXXXX                                                                                   
     Versicolor XXXXXXXXXXXXX..............................................................................   
                XXXXXXXXXXXXX                                                                                 
     Versicolor XXXXXXXXXXXXXXX............................................................................   
                XXXXXXXXXXXXXXX                                                                               
     Versicolor XXXXXXXXXXXXXXXX...........................................................................   
                XXXXXXXXXXXXXXXX                                                                              
     Versicolor XXXXXXXXXXXXXXXXX..........................................................................   
                XXXXXXXXXXXXXXXXX                                                                             
     Versicolor XXXXXXXXXXXXXXXXXX.........................................................................   
                XXXXXXXXXXXXXXXXXX                                                                            
     Versicolor XXXXXXXXXXXXXXXXXXXX.......................................................................   
                XXXXXXXXXXXXXXXXXXXX                                                                          
     Versicolor XXXXXXXXXXXXXXXXXXXXXX.....................................................................   
                XXXXXXXXXXXXXXXXXXXXXX                                                                        
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXX..................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXX                                                                     
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXX..................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXX                                                                     
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXX..................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXX                                                                     
                                                                                                              
                                                                                                              
      Virginica XXXXXXXXXXXXXXXXXXXXXXXXXX.................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXX                                                                    
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                                 
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                                
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...........................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                              
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                 
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.............................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.........................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                            
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.....................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                        
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.....................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                        
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                 
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                      
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                        
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.....................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                            
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.........................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                  
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                             
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..........................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                               
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                                 
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXX..............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXX                                                                    
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXX.................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXX                                                                     
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXX.................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXX                                                                    
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...........................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                              
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX........................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                           
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX......................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                         
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX......................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                           
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX........................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                              
     Versicolor XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...........................................................   
                XXXXXXXXXXXXXXXXXXXXXXX                                                                       
     Versicolor XXXXXXXXXXXXXXXXXXXXXXX....................................................................   
                XXXXXXXXXXXXXXXXXXXX                                                                          
     Versicolor XXXXXXXXXXXXXXXXXXXX.......................................................................   
                XXXXXXXXXXXXXXXXXXX                                                                           
     Versicolor XXXXXXXXXXXXXXXXXXX........................................................................   
                XXXXXXXXXXXXXXXXX                                                                             
     Versicolor XXXXXXXXXXXXXXXXX..........................................................................   
                XXXXXXXXXXXXXXXXX                                                                             
     Versicolor XXXXXXXXXXXXXXXXX..........................................................................   
                XXXXXXXXXXXXXX                                                                                
      Virginica XXXXXXXXXXXXXX.............................................................................   
                XXXXXXXXXXXXX                                                                                 
     Versicolor XXXXXXXXXXXXX..............................................................................   
                XXXXXXXXXX                                                                                    
                                                                                                              
                                                                                                              
     Versicolor XXXXXXXXXX.................................................................................   
                XXXX                                                                                          
     Versicolor XXXX.......................................................................................   
                XXXX                                                                                          
     Versicolor XXXX.......................................................................................   
                XXX                                                                                           
     Versicolor XXX........................................................................................   
                                                                                                              
         Setosa XXXXXXXXXXXXXXXX...........................................................................   
                XXXXXXXXXXXXXXXX                                                                              
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXX.................................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXX                                                                    
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                               
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                  
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...............................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                  
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...........................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                              
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..........................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                             
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                      
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX    
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                                                                                                              
                                                                                                              
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX     
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                             
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..........................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                               
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                               
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX............................................   
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                                                           
         Setosa XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX........................................................   
                XXXXXXXXXXXXXXXXXXXXXX                                                                        
         Setosa XXXXXXXXXXXXXXXXXXXXXX.....................................................................   
                XXXXXXXXXXXXXXXXXXX                                                                           
         Setosa XXXXXXXXXXXXXXXXXXX........................................................................   
                XXXXXXXXXXXXXXXXXXX                                                                           
         Setosa XXXXXXXXXXXXXXXXXXX........................................................................   
                XXXXXXXXXXXXXX                                                                                
         Setosa XXXXXXXXXXXXXX.............................................................................   
                XXXXXXXXX                                                                                     
         Setosa XXXXXXXXX..................................................................................   
                XXXXX                                                                                         
         Setosa XXXXX......................................................................................   
                XXXX                                                                                          
         Setosa XXXX.......................................................................................   

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