File size distribution

File size distribution is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Beginning from the current directory, or optionally from a directory specified as a command-line argument, determine how many files there are of various sizes in a directory hierarchy.

My suggestion is to sort by logarithmn of file size, since a few bytes here or there, or even a factor of two or three, may not be that significant.

Don't forget that empty files may exist, to serve as a marker.

Is your file system predominantly devoted to a large number of smaller files, or a smaller number of huge files?

C

The platform independent way to get the file size in C involves opening every file and reading the size. The implementation below works for Windows and utilizes command scripts to get size information quickly even for a large number of files, recursively traversing a large number of directories. Both textual and graphical ( ASCII ) outputs are shown. The same can be done for Linux by a combination of the find, ls and stat commands and my plan was to make it work on both OS types, but I don't have access to a Linux system right now. This would also mean either abandoning scaling the graphical output in order to fit the console buffer or porting that as well, thus including windows.h selectively.

Windows

<lang C>

1. include<windows.h>
2. include<string.h>
3. include<stdio.h>

1. define MAXORDER 25

int main(int argC, char* argV[]) { char str[MAXORDER],commandString[1000],*startPath; long int* fileSizeLog = (long int*)calloc(sizeof(long int),MAXORDER),max; int i,j,len; double scale; FILE* fp;

if(argC==1) printf("Usage : %s <followed by directory to start search from(. for current dir), followed by \n optional parameters (T or G) to show text or graph output>",argV[0]); else{ if(strchr(argV[1],' ')!=NULL){ len = strlen(argV[1]); startPath = (char*)malloc((len+2)*sizeof(char)); startPath[0] = '\"'; startPath[len+1]='\"'; strncpy(startPath+1,argV[1],len); startPath[len+2] = argV[1][len]; sprintf(commandString,"forfiles /p %s /s /c \"cmd /c echo @fsize\" 2>&1",startPath); }

else if(strlen(argV[1])==1 && argV[1][0]=='.') strcpy(commandString,"forfiles /s /c \"cmd /c echo @fsize\" 2>&1");

else sprintf(commandString,"forfiles /p %s /s /c \"cmd /c echo @fsize\" 2>&1",argV[1]);

fp = popen(commandString,"r");

while(fgets(str,100,fp)!=NULL){ if(str[0]=='0') fileSizeLog[0]++; else fileSizeLog[strlen(str)]++; }

if(argC==2 || (argC==3 && (argV[2][0]=='t'||argV[2][0]=='T'))){ for(i=0;i<MAXORDER;i++){ printf("\nSize Order < 10^%2d bytes : %Ld",i,fileSizeLog[i]); } }

else if(argC==3 && (argV[2][0]=='g'||argV[2][0]=='G')){ CONSOLE_SCREEN_BUFFER_INFO csbi; int val = GetConsoleScreenBufferInfo(GetStdHandle( STD_OUTPUT_HANDLE ),&csbi); if(val) {

max = fileSizeLog[0];

for(i=1;i<MAXORDER;i++) (fileSizeLog[i]>max)?max=fileSizeLog[i]:max;

(max < csbi.dwSize.X)?(scale=1):(scale=(1.0*(csbi.dwSize.X-50))/max);

for(i=0;i<MAXORDER;i++){ printf("\nSize Order < 10^%2d bytes |",i); for(j=0;j<(int)(scale*fileSizeLog[i]);j++) printf("%c",219); printf("%Ld",fileSizeLog[i]); } }

} return 0; } } </lang> Invocation and textual output :

C:\My Projects\threeJS>fileSize.exe "C:\My Projects" t

Size Order < 10^ 0 bytes : 1770
Size Order < 10^ 1 bytes : 1
Size Order < 10^ 2 bytes : 20
Size Order < 10^ 3 bytes : 219
Size Order < 10^ 4 bytes : 1793
Size Order < 10^ 5 bytes : 1832
Size Order < 10^ 6 bytes : 631
Size Order < 10^ 7 bytes : 124
Size Order < 10^ 8 bytes : 26
Size Order < 10^ 9 bytes : 0
Size Order < 10^10 bytes : 0
Size Order < 10^11 bytes : 0
Size Order < 10^12 bytes : 0
Size Order < 10^13 bytes : 0
Size Order < 10^14 bytes : 0
Size Order < 10^15 bytes : 0
Size Order < 10^16 bytes : 0
Size Order < 10^17 bytes : 0
Size Order < 10^18 bytes : 0
Size Order < 10^19 bytes : 0
Size Order < 10^20 bytes : 0
Size Order < 10^21 bytes : 0
Size Order < 10^22 bytes : 0
Size Order < 10^23 bytes : 0
Size Order < 10^24 bytes : 0

Invocation and graphical output :

C:\My Projects\threeJS>fileSize.exe "C:\My Projects" g

Size Order < 10^ 0 bytes |█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████1770
Size Order < 10^ 1 bytes |1
Size Order < 10^ 2 bytes |██20
Size Order < 10^ 3 bytes |█████████████████████████████219
Size Order < 10^ 4 bytes |████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████1793
Size Order < 10^ 5 bytes |██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████1832
Size Order < 10^ 6 bytes |██████████████████████████████████████████████████████████████████████████████████████631
Size Order < 10^ 7 bytes |████████████████124
Size Order < 10^ 8 bytes |███26
Size Order < 10^ 9 bytes |0
Size Order < 10^10 bytes |0
Size Order < 10^11 bytes |0
Size Order < 10^12 bytes |0
Size Order < 10^13 bytes |0
Size Order < 10^14 bytes |0
Size Order < 10^15 bytes |0
Size Order < 10^16 bytes |0
Size Order < 10^17 bytes |0
Size Order < 10^18 bytes |0
Size Order < 10^19 bytes |0
Size Order < 10^20 bytes |0
Size Order < 10^21 bytes |0
Size Order < 10^22 bytes |0
Size Order < 10^23 bytes |0
Size Order < 10^24 bytes |0

Note that it is possible to track files up to 10^24 (Yottabyte) in size with this implementation, but if you have a file that large, you shouldn't be needing such programs. :)

Julia

Works with: Julia version 0.6

<lang julia>using Humanize

function sizelist(path::AbstractString)

   rst = Vector{Int}(0)
   for (root, dirs, files) in walkdir(path)
       files = joinpath.(root, files)
       tmp = collect(filesize(f) for f in files if !islink(f))
       append!(rst, tmp)
   end
   return rst

end

byclass(y, classes) = Dict{eltype(classes),Int}(c => count(c[1] .≤ y .< c[2]) for c in classes)

function main(path::AbstractString)

   s = sizelist(path)
   cls = append!([(0, 1)], collect((10 ^ (i-1), 10 ^ i) for i in 1:9))
   f = byclass(s, cls)

   println("filesizes: ")
   for c in cls
       @printf(" - between %8s and %8s bytes: %3i\n", datasize(c[1]), datasize(c[2]), f[c])
   end
   println("\n-> total: $(datasize(sum(s))) bytes and $(length(s)) files")

end

main(".")</lang>

Output:

filesizes: 
 - between    0.0 B and    1.0 B bytes:   0
 - between    1.0 B and   10.0 B bytes:   1
 - between   10.0 B and  100.0 B bytes:  44
 - between  100.0 B and   1.0 kB bytes: 1068
 - between   1.0 kB and  10.0 kB bytes: 250
 - between  10.0 kB and 100.0 kB bytes:   7
 - between 100.0 kB and   1.0 MB bytes:   4
 - between   1.0 MB and  10.0 MB bytes:   2
 - between  10.0 MB and 100.0 MB bytes:   0
 - between 100.0 MB and   1.0 GB bytes:   0

-> total: 7.3 MB bytes and 1376 files

Kotlin

<lang scala>// version 1.2.10

import java.io.File import kotlin.math.log10 import kotlin.math.floor

fun fileSizeDistribution(path: String) {

   val sizes = IntArray(12)
   val p = File(path)
   val files = p.walk()
   var accessible = 0
   var notAccessible = 0
   var totalSize = 0L
   for (file in files) {
       try {
           if (file.isFile()) {
               val len = file.length()
               accessible++
               if (len == 0L) {
                   sizes[0]++
                   continue
               }
               totalSize += len
               val logLen = log10(len.toDouble())
               val index = floor(logLen).toInt()
               sizes[index + 1]++
           }
       }
       catch (se: SecurityException) {
           notAccessible++
       }
   }

   println("File size distribution for '$path' :-\n")
   for (i in 0 until sizes.size) {
       print(if (i == 0) "  " else "+ ")
       print("Files less than 10 ^ ${"%-2d".format(i)} bytes : ")
       println("%5d".format(sizes[i]))
   }
   println("                                  -----")
   println("= Number of accessible files    : ${"%5d".format(accessible)}")
   println("\n  Total size in bytes           : $totalSize")
   println("\n  Number of inaccessible files  : ${"%5d".format(notAccessible)}")

}

fun main(args: Array<String>) {

   fileSizeDistribution("./")  // current directory

}</lang>

Output:

File size distribution for './' :-

  Files less than 10 ^ 0  bytes :     2
+ Files less than 10 ^ 1  bytes :     0
+ Files less than 10 ^ 2  bytes :    46
+ Files less than 10 ^ 3  bytes :   380
+ Files less than 10 ^ 4  bytes :   558
+ Files less than 10 ^ 5  bytes :    19
+ Files less than 10 ^ 6  bytes :     6
+ Files less than 10 ^ 7  bytes :     5
+ Files less than 10 ^ 8  bytes :     0
+ Files less than 10 ^ 9  bytes :     0
+ Files less than 10 ^ 10 bytes :     0
+ Files less than 10 ^ 11 bytes :     0
                                  -----
= Number of accessible files    :  1016

  Total size in bytes           : 14459732

  Number of inaccessible files  :     0

Perl

Translation of: Perl 6

<lang perl>use File::Find; use List::Util qw(max);

my %fsize; $dir = shift || '.'; find(\&fsize, $dir);

$max = max($max,$fsize{$_}) for keys %fsize; $total += $size while (undef,$size) = each %fsize;

push @res, "File size distribution in bytes for directory: $dir\n"; for (0 .. max(keys %fsize)) {

   printf "# files @ %4sb %8s: %s\n", $_ ? '10e'.($_-1) : 0, $fsize{$_} // 0,
      histogram( $max, $fsize{$_} // 0, 80);

} print "$total total files.\n";

sub histogram {

   my($max, $value, $width) = @_;
   my @blocks = qw<| ▏ ▎ ▍ ▌ ▋ ▊ ▉ █>;
   my $scaled = int $value * $width / $max;
   my $end =     $scaled % 8;
   my $bar = int $scaled / 8;
   my $B = $blocks[8] x ($bar * 8) . ($end ? $blocks[$end] : );

}

sub fsize { $fsize{ log10( (lstat($_))[7] ) }++ } sub log10 { my($s) = @_; $s ? int log($s)/log(10) : 0 }</lang>

Output:

# files @    0b        5:
# files @ 10e0b    46455: ████████████████████████████████████████████████████████████████████████████████
# files @ 10e1b    26146: ████████████████████████████████████████▋
# files @ 10e2b     3993: ▊
# files @ 10e3b     1222: ▎
# files @ 10e4b       19:
# files @ 10e5b        3:
77843 total files.

Perl 6

Works with: Rakudo version 2017.05

By default, process the current and all readable sub-directories, or, pass in a directory path at the command line.

<lang perl6>sub MAIN($dir = '.') {

   sub log10 (Int $s) { $s ?? $s.log(10).Int !! 0 }
   my %fsize;
   my @dirs = $dir.IO;
   while @dirs {
       for @dirs.pop.dir -> $path {
           %fsize{$path.s.&log10}++ if $path.f;
           @dirs.push: $path if $path.d and $path.r
       }
   }
   my $max = %fsize.values.max;
   my $bar-size = 80;
   say "File size distribution in bytes for directory: $dir\n";
   say sprintf( "# Files @     0b %8s: ", %fsize{0} // 0 ),
       histogram( $max, %fsize{0} // 0, $bar-size );
   for 1 .. %fsize.keys.max {
         say sprintf( "# Files @ %5sb %8s: ", "10e{$_-1}", %fsize{$_} // 0 ),
             histogram( $max, %fsize{$_} // 0, $bar-size )
   }
   say %fsize.values.sum, ' total files.';

}

sub histogram ($max, $value, $width = 60) {

   my @blocks = <| ▏ ▎ ▍ ▌ ▋ ▊ ▉ █>;
   my $scaled = ($value * $width / $max).Int;
   my ($end, $bar) = $scaled.polymod(8);
   (@blocks[8] x $bar * 8) ~ (@blocks[$end] if $end) ~ "\n"

}</lang>

Output:

File size distribution in bytes for directory: /home

# Files @     0b      989: ▏

# Files @  10e0b     6655: ████████

# Files @  10e1b    31776: ████████████████████████████████████████

# Files @  10e2b    63165: ████████████████████████████████████████████████████████████████████████████████

# Files @  10e3b    19874: ████████████████████████▏

# Files @  10e4b     7730: ████████▏

# Files @  10e5b     3418: ▌

# Files @  10e6b     1378: ▏

# Files @  10e7b      199:

# Files @  10e8b       45:

135229 total files.

Python

The distribution is stored in a collections.Counter object (like a dictionary with automatic 0 value when a key is not found, useful when incrementing). Anything could be done with this object, here the number of files is printed for increasing sizes. No check is made during the directory walk: usually, safeguards would be needed or the program will fail on any unreadable file or directory (depending on rights, or too deep paths, for instance). Here links are skipped, so it should avoid cycles.

<lang python>import sys, os from collections import Counter

def dodir(path):

   global h

   for name in os.listdir(path):
       p = os.path.join(path, name)

       if os.path.islink(p):
           pass
       elif os.path.isfile(p):
           h[os.stat(p).st_size] += 1
       elif os.path.isdir(p):
           dodir(p)
       else:
           pass

def main(arg):

   global h
   h = Counter()
   for dir in arg:
       dodir(dir)
   
   s = n = 0
   for k, v in sorted(h.items()):
       print("Size %d -> %d file(s)" % (k, v))
       n += v
       s += k * v
   print("Total %d bytes for %d files" % (s, n))

main(sys.argv[1:])</lang>

Racket

<lang racket>#lang racket

(define (file-size-distribution (d (current-directory)) #:size-group-function (sgf values))

 (for/fold ((rv (hash)) (Σ 0) (n 0)) ((f (in-directory d)) #:when (file-exists? f))
   (define sz (file-size f))
   (values (hash-update rv (sgf sz) add1 0) (+ Σ sz) (add1 n))))

(define (log10-or-so x) (if (zero? x) #f (round (/ (log x) (log 10)))))

(define number-maybe-<

 (match-lambda** [(#f #f) #f]
                 [(#f _) #t]
                 [(_ #f) #f]
                 [(a b) (< a b)]))

(define ...s? (match-lambda** [(one 1) one] [(one n) (string-append one "s")]))

(define ((report-fsd f) fsd Σ n)

 (for/list ((k (in-list (sort (hash-keys fsd) number-maybe-<))))
   (printf "~a(size): ~a -> ~a ~a~%"
           (object-name f)
           k
           (hash-ref fsd k) (...s? "file" (hash-ref fsd k))))
 (printf "Total: ~a ~a in ~a ~a~%" Σ (...s? "byte" Σ) n (...s? "file" n)))

(module+ test

 (call-with-values (λ () (file-size-distribution #:size-group-function log10-or-so))
                   (report-fsd log10-or-so)))</lang>

Output:

log10-or-so(size): #f -> 3 files
log10-or-so(size): 0 -> 4 files
log10-or-so(size): 1.0 -> 39 files
log10-or-so(size): 2.0 -> 57 files
log10-or-so(size): 3.0 -> 406 files
log10-or-so(size): 4.0 -> 198 files
log10-or-so(size): 5.0 -> 20 files
log10-or-so(size): 6.0 -> 6 files
Total: 10210127 bytes in 733 files

REXX

This REXX version works for Microsoft Windows using the   dir   subcommand;   extra code was added for
older versions of Windows that used suffixes to express big numbers   (the size of a file),   and also versions
that used a mixed case for showing the output text. <lang rexx>/*REXX program displays a histogram of filesize distribution of a directory structure(s)*/ numeric digits 30 /*ensure enough decimal digits for a #.*/ parse arg ds . /*obtain optional argument from the CL.*/ parse source . . path . /* " the path of this REXX program.*/ fID= substr(path, 1 + lastpos('\', path) ) /* " the filename and the filetype.*/ parse var fID fn '.' /* " just the pure filename of pgm.*/ sw=max(79, linesize() - 1) /* " terminal width (linesize) - 1.*/

                               work= fn".OUT"   /*filename for workfile output of  DIR.*/

'DIR' ds '/s /-c /a-d >' work /*do (DOS) DIR cmd for a data structure*/ call linein 0, 1 /*open output file, point to 1st record*/ maxL= 0; @.= 00; g= 0 /*max len size; log array; # good recs.*/ $=0 /*$: total bytes used by files found. */

    do while lines(work)\==0;  _= linein(work)  /*process the data in the DIR work file*/
    if left(_, 1)==' '    then iterate          /*Is the record not legitimate?  Skip. */
    parse upper  var   _    .  .  sz  .                              /*uppercase suffix*/
    if \datatype(sz,'W')  then do; #= left(sz, length(sz) - 1)       /*SZ has a suffix?*/
                                   if \datatype(#,'N')  then iterate /*Meat ¬ numeric? */
                                   sz= # * 1024 ** pos( right(sz, 1), 'KMGTPEZYXWVU') / 1
                               end                                   /* [↑]  use suffix*/
    $= $ + sz                                   /*keep a running total for the filesize*/
    if sz==0  then L= 0                         /*handle special case for an empty file*/
              else L= length(sz)                /*obtain the length of filesize number.*/
    g= g + 1                                    /*bump the counter of # of good records*/
    maxL= max(L, maxL)                          /*get max length filesize for alignment*/
    @.L= @.L + 1                                /*bump counter of record size category.*/
    end   /*j*/                                 /* [↑]   categories:  split by log ten.*/

if g==0 then do; say 'file not found: ' ds; exit 13; end /*no good records*/ say ' record size range count ' hdr= '══════════════════ ══════════ '; say hdr; Lhdr=length(hdr) mC=0 /*mC: the maximum count for any range.*/

    do   t=1  to 2                              /*T==1   is used to find the max count.*/
      do k=0  to maxL;  mC= max(mC, @.k);  if t==1  then iterate           /*1st pass? */
                            if k==0  then y= center('zero',  length( word(hdr, 1)  ) )
                                     else y= '10^'left(k-1,2)  "──► 10^"left(k,2)  '-1'
      say y || right( commas(@.k), 11)   copies('─', max(1, (@.k / mC * sw % 1) - LHdr) )
      end   /*k*/
    end     /*y*/

say trace off; 'ERASE' work /*perform clean─up (erase a work file).*/ say commas(g) ' files detected, ' commas($) " total bytes." exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg _; do j#=length(_)-3 to 1 by -3; _=insert(',', _, j#); end; return _</lang> This REXX program makes use of   LINESIZE   REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console) so as to maximize the width of the histogram.

The   LINESIZE.REX   REXX program is included here   ──►   LINESIZE.REX.

output   when using the default input:   (which in this case was the   C:   homedrive, a Windows/XP system.)

 record size range   count
══════════════════ ═════════
     zero              1,591 ─
    1 ──►     9          207 ─
   10 ──►    99        2,024 ─
  100 ──►   999        5,472 ─
 1000 ──►  9999       25,215 ──────────────────────────────────────────────────────────────────
10^4  ──► 10^5  -1    14,624 ──────────────────────────
10^5  ──► 10^6  -1     5,234 ─
10^6  ──► 10^7  -1     1,017 ─
10^7  ──► 10^8  -1       151 ─
10^8  ──► 10^9  -1         3 ─
10^9  ──► 10^10 -1         1 ─

55,539  files detected,  12,656,593,862  total bytes.

output   when using the default input:   (which in this case was the   C:   homedrive, a Windows 7 system.)

 record size range   count
══════════════════ ═════════
     zero                162 ─
    1 ──►     9          129 ─
   10 ──►    99        2,292 ─
  100 ──►   999       23,212 ─────────
 1000 ──►  9999       54,814 ───────────────────────────────────────────────────
10^4  ──► 10^5  ─1    37,335 ────────────────────────
10^5  ──► 10^6  ─1    17,523 ─
10^6  ──► 10^7  ─1     9,732 ─
10^7  ──► 10^8  ─1       549 ─
10^8  ──► 10^9  ─1       144 ─
10^9  ──► 10^10 ─1         8 ─
10^10 ──► 10^11 ─1         1 ─

145,901  files detected, 118,717,664,126  total bytes.

output   when using the (my)   K:   drive:

 record size range   count
══════════════════ ═════════
     zero                 30 ─
    1 ──►     9          131 ─
   10 ──►    99          821 ─
  100 ──►   999        3,866 ────────────────────────
 1000 ──►  9999        5,962 ─────────────────────────────────────────────────────
10^4  ──► 10^5  -1     6,876 ──────────────────────────────────────────────────────────────────
10^5  ──► 10^6  -1     2,454 ────
10^6  ──► 10^7  -1       239 ─
10^7  ──► 10^8  -1         6 ─

20,385  files detected,  1,625,509,222  total bytes.

Sidef

<lang ruby>func traverse(Block callback, Dir dir) {

   dir.open(\var dir_h) || return nil

 

   for entry in (dir_h.entries) {
       if (entry.kind_of(Dir)) {
           traverse(callback, entry)
       } else {
           callback(entry)
       }
   }

}   var dir = (ARGV ? Dir(ARGV[0]) : Dir.cwd)

var group = Hash() var files_num = 0 var total_size = 0

traverse({ |file|

   group{file.size+1 -> log10.round} := 0 += 1
   total_size += file.size
   files_num += 1

}, dir)

for k,v in (group.sort_by { |k,_| Num(k) }) {

   say "log10(size) ~~ #{k} -> #{v} files"

}

say "Total: #{total_size} bytes in #{files_num} files"</lang>

Output:

$ sidef script.sf /usr/bin
log10(size) ~~ 1 -> 4 files
log10(size) ~~ 2 -> 70 files
log10(size) ~~ 3 -> 246 files
log10(size) ~~ 4 -> 1337 files
log10(size) ~~ 5 -> 815 files
log10(size) ~~ 6 -> 167 files
log10(size) ~~ 7 -> 9 files
log10(size) ~~ 8 -> 2 files
Total: 370026462 bytes in 2650 files

zkl

<lang zkl>pipe:=Thread.Pipe();

   // hoover all files in tree, don't return directories

fcn(pipe,dir){ File.globular(dir,"*",True,8,pipe); } .launch(pipe,vm.arglist[0]); // thread

dist,N,SZ,maxd:=List.createLong(50,0),0,0,0; foreach fnm in (pipe){

  sz,szd:=File.len(fnm), sz.numDigits;
  dist[szd]+=1;
  N+=1; SZ+=sz; maxd=maxd.max(szd);

} println("Found %d files, %,d bytes, %,d mean.".fmt(N,SZ,SZ/N)); scale:=50.0/(0.0).max(dist); szchrs,idx,comma:=",nnn"*20, -1, Walker.cycle(0,0,1).next; println("%15s %s (* = %.2f)".fmt("File size","Number of files",1.0/scale)); foreach sz,cnt in ([0..].zip(dist[0,maxd])){

  println("%15s : %s".fmt(szchrs[idx,*], "*"*(scale*cnt).round().toInt()));
  idx-=1 + comma();

}</lang>

Output:

$ zkl flSzDist.zkl ..
Found 1832 files, 108,667,806 bytes, 59,316 mean.
      File size   Number of files (* = 13.44)
              n : *
             nn : ***
            nnn : ********
          n,nnn : **********************************
         nn,nnn : **************************************************
        nnn,nnn : ********************************
      n,nnn,nnn : *******

$ zkl flSzDist.zkl /media/Tunes/
Found 4320 files, 67,627,849,052 bytes, 15,654,594 mean.
      File size   Number of files (* = 69.84)
              n : 
             nn : 
            nnn : 
          n,nnn : *
         nn,nnn : 
        nnn,nnn : 
      n,nnn,nnn : *
     nn,nnn,nnn : **************************************************
    nnn,nnn,nnn : ********
  n,nnn,nnn,nnn : *