2760.43800 => 8 33 21 55 51 48 6 20 52 63
2766.50111 => 59 55 4 88 74 63 20 33 28 34 3 93 9 19 10 22 42 44
3587.61500 => 13 69 53 24 61 90 56 28 61 82 17 85 12 59 14 55
3714.33857 => 27 32 54 19 46 20 38 93 61 19 9 53 25 1
4359.73000 => 91 84 9 40 13 98 88 60 17 83
4400.39667 => 13 42 79 34 5 47 25 20 78 35 59 75 89 42 0 26 48 36
4420.68800 => 43 83 41 83 16 69 99 49 22 60
4437.52375 => 33 44 1 71 35 71 97 26 39 78 31 3 32 65 87 61
4642.57000 => 70 98 20 25 79 19 18 49 48 78 50 77 40 53
4680.39600 => 55 90 88 6 9 1 56 45 26 56
4737.51125 => 98 33 3 22 75 40 64 18 91 67 8 65 29 68 11 96
4820.32000 => 46 57 45 2 64 46 46 1 40 54
4844.49444 => 20 43 25 36 33 84 63 11 15 2 70 69 47 77 67 91 96 32
4849.23333 => 26 21 25 46 46 14 79 11 85 39 30 9
4885.40571 => 37 18 90 23 38 13 97 63 17 26 41 56 22 85
4900.49444 => 67 66 7 45 77 19 4 84 74 53 0 65 37 12 91 65 84 36
5080.38000 => 51 38 31 65 62 4 37 35 73 48
5266.59167 => 84 26 93 43 11 80 16 50 66 80 46 76
5350.28000 => 67 0 57 24 46 50 44 38
5511.37333 => 72 27 30 52 37 35 7 76 23 45 71 25 75 17 86 29 95 30
5912.56625 => 53 23 72 95 27 29 94 59 18 22 89 33 57 97 63 95
5977.42111 => 82 24 88 16 49 9 63 19 84 77 25 90 48 11 69 45 30 88
6599.53250 => 92 44 27 30 94 43 51 96
6899.52714 => 45 32 65 80 58 22 95 44 51 36 93 61 76 94
7100.49500 => 76 20 41 22 93 64 74 92
7250.45167 => 70 26 38 71 78 36 84 58 84 5 81 75
7599.52250 => 60 73 51 45 95 63 98 28
7950.34500 => 92 32 91 28 80 76 55 2
8100.23000 => 94 40 90 13 57 36 83 3
8660.23400 => 98 42 79 0 72 26 95 11 89 38

 ------

2760.43800 => 8 33 21 55 51 48 6 20 52 63
2766.50111 => 59 55 4 88 74 63 20 33 28 34 3 93 9 19 10 22 42 44
3000.54000 => 59 55 4 88 74 63 20 33 28 34 3 93 10 22 42 44
3300.49750 => 8 33 21 55 51 48 52 63
3512.61375 => 15 76 53 28 52 90 49 19 69 79 13 85 16 59 14 55
3587.61500 => 15 76 53 28 52 90 49 19 69 79 13 85 16 59 14 55
3714.33857 => 21 32 62 19 51 20 30 92 69 9 13 53 25 8
3871.33286 => 21 32 62 19 51 20 30 92 69 9 13 53 25 8
4224.53625 => 25 41 1 69 40 77 97 26 38 78 26 3 32 74 79 61
4239.70000 => 91 77 9 32 13 98 88 63 11 80
4250.50167 => 20 25 79 19 18 49 48 78 50 77 40 53
4359.73000 => 91 77 9 32 13 98 88 63 11 80
4400.39667 => 13 42 79 34 5 47 25 20 78 35 59 75 89 42 0 26 48 36
4420.68800 => 43 83 41 83 16 69 99 49 22 60
4437.52375 => 25 41 1 69 40 77 97 26 38 78 26 3 32 74 79 61
4600.23333 => 26 21 25 46 37 14 79 11 85 39 24 9
4642.57000 => 70 98 20 25 79 19 18 49 48 78 50 77 40 53
4657.39286 => 37 18 90 14 31 13 91 63 14 26 41 56 22 85
4680.39600 => 55 90 88 6 9 1 56 45 26 56
4700.52875 => 98 32 -6 22 75 48 64 18 91 67 8 70 29 77 17 89
4737.51125 => 98 32 -6 22 75 48 64 18 91 67 8 70 29 77 17 89
4740.30600 => 46 50 41 2 64 46 46 1 40 54
4820.32000 => 46 50 41 2 64 46 46 1 40 54
4844.49444 => 20 43 25 36 33 84 63 11 15 2 70 69 47 77 67 91 96 32
4849.23333 => 26 21 25 46 37 14 79 11 85 39 24 9
4880.39200 => 41 38 31 65 62 -5 37 41 73 57
4885.40571 => 37 18 90 14 31 13 91 63 14 26 41 56 22 85
4887.38750 => 13 42 79 34 25 20 78 35 59 75 89 42 0 26 48 36
4900.37333 => 57 24 46 50 44 38
4900.49444 => 67 74 7 38 77 19 4 91 74 53 0 65 42 18 100 57 84 30
5055.49444 => 67 74 7 38 77 19 4 91 74 53 0 65 42 18 100 57 84 30
5080.38000 => 41 38 31 65 62 -5 37 41 73 57
5125.38375 => 72 27 30 52 37 35 7 76 23 45 71 25 75 17 95 30
5125.68750 => 43 83 41 83 99 49 22 60
5137.51125 => 20 43 33 84 63 11 15 2 70 69 47 77 67 91 96 32
5200.35500 => 55 90 88 6 9 1 56 45
5266.59167 => 84 26 93 43 11 80 16 50 66 80 46 76
5350.28000 => 67 0 57 24 46 50 44 38
5511.37333 => 72 27 30 52 37 35 7 76 23 45 71 25 75 17 86 29 95 30
5912.56625 => 53 23 72 95 27 29 94 59 18 22 89 33 57 97 63 95
5977.42111 => 82 24 88 16 49 9 63 19 84 77 25 90 48 11 69 45 30 88
6000.61000 => 84 26 93 43 11 80 66 80 46 76
6124.46000 => 82 24 88 16 49 9 63 19 84 77 25 90 69 45 30 88
6500.61571 => 53 23 72 95 27 29 94 59 89 33 57 97 63 95
6599.53250 => 92 44 27 30 94 43 51 96
6899.52714 => 45 32 74 80 58 22 95 50 55 36 93 58 74 94
7000.35333 => 76 20 41 22 93 64
7057.53143 => 45 32 74 80 58 22 95 50 55 36 93 58 74 94
7100.39000 => 92 44 27 30 94 43
7100.49500 => 76 20 41 22 93 64 74 92
7139.47000 => 70 26 38 71 84 58 84 5 81 75
7250.45167 => 70 26 38 71 78 36 84 58 84 5 81 75
7599.52250 => 52 73 58 37 95 54 103 28
7700.48000 => 52 73 58 37 95 54 103 28
7849.35000 => 88 39 91 29 80 70 55 2
7950.34500 => 88 39 91 29 80 70 55 2
8100.23000 => 94 40 90 13 57 36 83 3
8660.23400 => 98 47 88 0 72 16 103 11 89 38
8900.18667 => 94 40 90 13 83 3
9000.22400 => 98 47 88 0 72 16 103 11 89 38

##</code><code>##

#! perl -slw
use strict;
use Data::Dumper;
use List::Util qw[ reduce sum ];
use constant {
	MAXX => 100,
	MAXY => 100,
};

sub calcSig {
	my $sum = reduce { 
		$a->[ 0 ] += $b->[ 0 ] / MAXX;
		$a->[ 1 ] += $b->[ 1 ] / MAXY;
		$a;
	} [], @_;
	$sum->[ 0 ] /= @_; 
	$sum->[ 1 ] /= @_;
	return int( $sum->[ 0 ] * MAXX * MAXY ) + $sum->[ 1 ]	
}

my( @sigs, %sigs );
while( <DATA> ) {
	chomp;
	my @points;
	push @points, [ $1, $2 ] while m[\((\d+?),(\d+?)\)(?:,\s|$)]g;
#	print Dumper \@points;
	push @sigs, my $sig = calcSig @points;
	$sigs{ $sig } = \@points;
}

@sigs = sort{ $a <=> $b } @sigs;
printf "%9.5f => %s\n", $_, join ' ', map{ @$_ } @{ $sigs{ $_ } } for @sigs;
print "\n ------ \n";

my @adjusted = map{ [ @$_ ] } values %sigs;
for my $aref ( @adjusted ) {
	if( rand > .3 ) { ## delete a pair
		splice @$aref, rand( @$aref ), 1;
	}
	else { ## Adjust a few values;
		@$aref = map{
			rand > .5 and $_->[ 0 ] += -10+int( rand 20 );
			rand > .5 and $_->[ 1 ] += -10+int( rand 20 );
			$_;
		} @$aref;
	}
	push @sigs, my $sig = calcSig @$aref;
	$sigs{ $sig } = $aref;
}
@sigs = sort{ $a <=> $b } @sigs;
printf "%9.5f => %s\n", $_, join ' ', map{ @$_ } @{ $sigs{ $_ } } for @sigs;

__DATA__
(67,66), (7,45), (77,19), (4,84), (74,53), (0,65), (37,12), (91,65), (84,36)
(92,44), (27,30), (94,43), (51,96)
(46,57), (45,2), (64,46), (46,1), (40,54)
(84,26), (93,43), (11,80), (16,50), (66,80), (46,76)
(92,32), (91,28), (80,76), (55,2)
(94,40), (90,13), (57,36), (83,3)
(13,69), (53,24), (61,90), (56,28), (61,82), (17,85), (12,59), (14,55)
(33,44), (1,71), (35,71), (97,26), (39,78), (31,3), (32,65), (87,61)
(70,26), (38,71), (78,36), (84,58), (84,5), (81,75)
(70,98), (20,25), (79,19), (18,49), (48,78), (50,77), (40,53)
(27,32), (54,19), (46,20), (38,93), (61,19), (9,53), (25,1)
(43,83), (41,83), (16,69), (99,49), (22,60)
(98,42), (79,0), (72,26), (95,11), (89,38)
(67,0), (57,24), (46,50), (44,38)
(76,20), (41,22), (93,64), (74,92)
(82,24), (88,16), (49,9), (63,19), (84,77), (25,90), (48,11), (69,45), (30,88)
(53,23), (72,95), (27,29), (94,59), (18,22), (89,33), (57,97), (63,95)
(20,43), (25,36), (33,84), (63,11), (15,2), (70,69), (47,77), (67,91), (96,32)
(59,55), (4,88), (74,63), (20,33), (28,34), (3,93), (9,19), (10,22), (42,44)
(8,33), (21,55), (51,48), (6,20), (52,63)
(72,27), (30,52), (37,35), (7,76), (23,45), (71,25), (75,17), (86,29), (95,30)
(51,38), (31,65), (62,4), (37,35), (73,48)
(98,33), (3,22), (75,40), (64,18), (91,67), (8,65), (29,68), (11,96)
(45,32), (65,80), (58,22), (95,44), (51,36), (93,61), (76,94)
(55,90), (88,6), (9,1), (56,45), (26,56)
(26,21), (25,46), (46,14), (79,11), (85,39), (30,9)
(37,18), (90,23), (38,13), (97,63), (17,26), (41,56), (22,85)
(13,42), (79,34), (5,47), (25,20), (78,35), (59,75), (89,42), (0,26), (48,36)
(60,73), (51,45), (95,63), (98,28)
(91,84), (9,40), (13,98), (88,60), (17,83)