Exploring through the paths of subgroups, collecting indexes on the way…
June 6, 2011 Posted by Emre S. Tasci
Having a personal wiki has its pros and cons with the pros being obvious but, on the other hand, one doesn’t feel like reposting what he has already committed into the corresponding wikipedia entry (and since reposting means filtering out the sensitive information and generalizing it, it is double the effort). So this fact, more or less, explains my absence of activity in this blog for the last 1.5 years. But then, there is one negative aspect of personal wikipedia “blogging” – it’s like putting everything under the rug : you classify the data/information and then you forget that it is there. That’s when “actual” blogging (like this one) comes handy. So, sorry & welcome back..
Today, I’ll present a code that I’ve just written to parse out the compatible paths from a tree. In my case, the three is the list of subgroups with indexes that one can acquire using Bilbao Crystallographic Server’s marvelous SUBGROUPGRAPH tool. For low indexes, you can already have SUBGROUPGRAPH do this for you by specifying your supergroup G, subgroup H and the index [G:H]. For example, for G=136, H=14 and [G:H] = 8, you can have the following paths drawn:
But as I said, things can get rough when you have a high index. In that case, we can (and we will) try to parse and analyze the paths tree which is outputted by SUBGROUPGRAPH when no index is designated, e.g., for G=136, H=14:
Where you see the maximal subgroups for the involved groups and their corresponding indexes. So, to go from P4_2/mnm (#136) to P2_1/c (#14) with index 8, we can follow the path:
P4_2/mnm (#136) –[2]–> Cmmm (#65) –[2]–> Pmna (#53) –[2]–> P2_1/c (#14)
with the related indexes given in the brackets totaling to 2x2x2 = 8.
The problem I had today was to find possible paths going from G=Fd-3m (#227) to H=Cc (#9) with index [G:H] = 192.
I first parsed the subgroup list into an array with their indexes, then followed the possible paths.
<?PHP
/* Emre S. Tasci <exxx.txxxx@ehu.es> *
* By parsing the possible subgroup paths obtained from
* SUBGROUPGRAPH, finds the paths that are compatible
* with the given terminal super & sub groups and the
* designated index.
*
* 06/06/11 */
# Input Data === 0 ====================================================
$start_sup = 227;
$crit_index = 192;
$end_sub = 9;
$arr = file("data.txt"); # A sample of data.txt for the case of #227->#9
# is included at the end of the code.
# Input Data === 1 ====================================================
$arr_subs = Array();
$arr_labels = Array();
foreach($arr as $line)
{
$auxarr = preg_split("/[ \t]+/",trim($line));
#echo $auxarr[2]."\n";
$sup = $auxarr[1];
$suplabel = $auxarr[2];
$arrsubs = split(";",$auxarr[3]);
$arr_labels[$sup] = $suplabel;
foreach($arrsubs as $subind)
{
$auxarr2 = Array();
preg_match("/([0-9]+)\[([0-9]+)\]/",$subind,$auxarr2);
#print_r($auxarr2);
$sub = $auxarr2[1];
$index = $auxarr2[2];
$arr_subs[$sup][$index][] = $sub;
}
}
#print_r($arr_subs);
# Start exploring
$start_sup = sprintf("%03d",$start_sup);
$end_sub = sprintf("%03d",$end_sub);
$arr_paths = Array();
$arr_paths[$start_sup] = 1;
findpath($start_sup);
function findpath($current_sup)
{
global $arr_paths,$arr_subs,$crit_index,$end_sub;
#echo "*".$current_sup."*\n";
if(strrpos($current_sup,"-") !== FALSE)
{
$current_sup_last_sup = substr($current_sup,strrpos($current_sup,"-")+1);
$current_sup_last_sup = substr($current_sup_last_sup,0,strpos($current_sup_last_sup,"["));
}
else
$current_sup_last_sup = $current_sup;
#echo "*".$current_sup_last_sup."*\n";
$subindexes = array_keys($arr_subs[$current_sup_last_sup]);
foreach($subindexes as $subindex)
{
$subs = $arr_subs[$current_sup_last_sup][$subindex];
echo $subindex.": ".join(",",$subs)."\n";
foreach($subs as $sub)
{
echo $current_sup."-".$sub."[".$subindex."]"."\n";
$arr_paths[$current_sup."-".$sub."[".$subindex."]"] = $arr_paths[$current_sup] * $subindex;
if($arr_paths[$current_sup."-".$sub."[".$subindex."]"]<$crit_index)
findpath($current_sup."-".$sub."[".$subindex."]");
elseif($arr_paths[$current_sup."-".$sub."[".$subindex."]"] == $crit_index && $sub == $end_sub)
echo "\nPath Found: ".$current_sup."-".$sub."[".$subindex."]"."\n\n";
}
}
#print_r($subindexes);
}
print_r($arr_paths);
/*
data.txt:
1 227 Fd-3m 141[3];166[4];203[2];216[2]
2 220 I-43d 122[3];161[4]
3 219 F-43c 120[3];161[4];218[4]
4 218 P-43n 112[3];161[4];220[4]
5 217 I-43m 121[3];160[4];215[2];218[2]
6 216 F-43m 119[3];160[4];215[4]
7 215 P-43m 111[3];160[4];216[2];217[4];219[2]
8 203 Fd-3 070[3]
9 167 R-3c 015[3];161[2];165[3];167[4];167[5];167[7]
10 166 R-3m 012[3];160[2];164[3];166[2];166[4];166[5];166[7];167[2]
11 165 P-3c1 015[3];158[2];163[3];165[3];165[4];165[5];165[7]
12 164 P-3m1 012[3];156[2];162[3];164[2];164[3];164[4];164[5];164[7];165[2]
13 163 P-31c 015[3];159[2];163[3];163[4];163[5];163[7];165[3];167[3]
14 162 P-31m 012[3];157[2];162[2];162[3];162[4];162[5];162[7];163[2];164[3];166[3]
15 161 R3c 009[3];158[3];161[4];161[5];161[7]
16 160 R3m 008[3];156[3];160[2];160[4];160[5];160[7];161[2]
17 159 P31c 009[3];158[3];159[3];159[4];159[5];159[7];161[3]
18 158 P3c1 009[3];158[3];158[4];158[5];158[7];159[3]
19 157 P31m 008[3];156[3];157[2];157[3];157[4];157[5];157[7];159[2];160[3]
20 156 P3m1 008[3];156[2];156[3];156[4];156[5];156[7];157[3];158[2]
21 141 I41/amd 070[2];074[2];088[2];109[2];119[2];122[2];141[3];141[5];141[7];141[9]
22 122 I-42d 043[2];122[3];122[5];122[7];122[9]
23 121 I-42m 042[2];111[2];112[2];113[2];114[2];121[3];121[5];121[7];121[9]
24 120 I-4c2 045[2];116[2];117[2];120[3];120[5];120[7];120[9]
25 119 I-4m2 044[2];115[2];118[2];119[3];119[5];119[7];119[9]
26 118 P-4n2 034[2];118[3];118[5];118[7];118[9];122[2]
27 117 P-4b2 032[2];117[2];117[3];117[5];117[7];117[9];118[2]
28 116 P-4c2 027[2];112[2];114[2];116[3];116[5];116[7];116[9]
29 115 P-4m2 025[2];111[2];113[2];115[2];115[3];115[5];115[7];115[9];116[2];121[2]
30 114 P-421c 037[2];114[3];114[5];114[7];114[9]
31 113 P-421m 035[2];113[2];113[3];113[5];113[7];113[9];114[2]
32 112 P-42c 037[2];112[3];112[5];112[7];112[9];116[2];118[2]
33 111 P-42m 035[2];111[2];111[3];111[5];111[7];111[9];112[2];115[2];117[2];119[2];120[2]
34 109 I41md 043[2];044[2];109[3];109[5];109[7];109[9]
35 088 I41/a 015[2];088[3];088[5];088[7];088[9]
36 074 Imma 012[2];015[2];044[2];046[2];051[2];052[2];053[2];062[2];074[3];074[5];074[7]
37 070 Fddd 015[2];043[2];070[3];070[5];070[7]
38 064 Cmce 012[2];014[2];015[2];036[2];039[2];041[2];053[2];054[2];055[2];056[2];057[2];060[2];061[2];062[2];064[3];064[5];064[7]
39 063 Cmcm 011[2];012[2];015[2];036[2];038[2];040[2];051[2];052[2];057[2];058[2];059[2];060[2];062[2];063[3];063[5];063[7]
40 062 Pnma 011[2];014[2];026[2];031[2];033[2];062[3];062[5];062[7]
41 061 Pbca 014[2];029[2];061[3];061[5];061[7]
42 060 Pbcn 013[2];014[2];029[2];030[2];033[2];060[3];060[5];060[7]
43 059 Pmmn 011[2];013[2];025[2];031[2];056[2];059[2];059[3];059[5];059[7];062[2]
44 058 Pnnm 010[2];014[2];031[2];034[2];058[3];058[5];058[7]
45 057 Pbcm 011[2];013[2];014[2];026[2];028[2];029[2];057[2];057[3];057[5];057[7];060[2];061[2];062[2]
46 056 Pccn 013[2];014[2];027[2];033[2];056[3];056[5];056[7]
47 055 Pbam 010[2];014[2];026[2];032[2];055[2];055[3];055[5];055[7];058[2];062[2]
48 054 Pcca 013[2];014[2];027[2];029[2];032[2];052[2];054[2];054[3];054[5];054[7];056[2];060[2]
49 053 Pmna 010[2];013[2];014[2];028[2];030[2];031[2];052[2];053[2];053[3];053[5];053[7];058[2];060[2]
50 052 Pnna 013[2];014[2];030[2];033[2];034[2];052[3];052[5];052[7]
51 051 Pmma 010[2];011[2];013[2];025[2];026[2];028[2];051[2];051[3];051[5];051[7];053[2];054[2];055[2];057[2];059[2];063[2];064[2]
52 046 Ima2 008[2];009[2];026[2];028[2];030[2];033[2];046[3];046[5];046[7]
53 045 Iba2 009[2];027[2];029[2];032[2];045[3];045[5];045[7]
54 044 Imm2 008[2];025[2];031[2];034[2];044[3];044[5];044[7]
55 043 Fdd2 009[2];043[3];043[5];043[7]
56 042 Fmm2 008[2];035[2];036[2];037[2];038[2];039[2];040[2];041[2];042[3];042[5];042[7]
57 041 Aea2 007[2];009[2];029[2];030[2];032[2];033[2];041[3];041[5];041[7]
58 040 Ama2 006[2];009[2];028[2];031[2];033[2];034[2];040[3];040[5];040[7]
59 039 Aem2 007[2];008[2];026[2];027[2];028[2];029[2];039[2];039[3];039[5];039[7];041[2];045[2];046[2]
60 038 Amm2 006[2];008[2];025[2];026[2];030[2];031[2];038[2];038[3];038[5];038[7];040[2];044[2];046[2]
61 037 Ccc2 009[2];027[2];030[2];034[2];037[3];037[5];037[7]
62 036 Cmc21 008[2];009[2];026[2];029[2];031[2];033[2];036[3];036[5];036[7]
63 035 Cmm2 008[2];025[2];028[2];032[2];035[2];035[3];035[5];035[7];036[2];037[2];044[2];045[2];046[2]
64 034 Pnn2 007[2];034[3];034[5];034[7];043[2]
65 033 Pna21 007[2];033[3];033[5];033[7]
66 032 Pba2 007[2];032[2];032[3];032[5];032[7];033[2];034[2]
67 031 Pmn21 006[2];007[2];031[2];031[3];031[5];031[7];033[2]
68 030 Pnc2 007[2];030[2];030[3];030[5];030[7];034[2]
69 029 Pca21 007[2];029[2];029[3];029[5];029[7];033[2]
70 028 Pma2 006[2];007[2];028[2];028[3];028[5];028[7];029[2];030[2];031[2];032[2];040[2];041[2]
71 027 Pcc2 007[2];027[2];027[3];027[5];027[7];030[2];037[2]
72 026 Pmc21 006[2];007[2];026[2];026[3];026[5];026[7];029[2];031[2];036[2]
73 025 Pmm2 006[2];025[2];025[3];025[5];025[7];026[2];027[2];028[2];035[2];038[2];039[2];042[2]
74 015 C2/c 009[2];013[2];014[2];015[3];015[5];015[7]
75 014 P21/c 007[2];014[2];014[3];014[5];014[7]
76 013 P2/c 007[2];013[2];013[3];013[5];013[7];014[2];015[2]
77 012 C2/m 008[2];010[2];011[2];012[2];012[3];012[5];012[7];013[2];014[2];015[2]
78 011 P21/m 006[2];011[2];011[3];011[5];011[7];014[2]
79 010 P2/m 006[2];010[2];010[3];010[5];010[7];011[2];012[2];013[2]
80 008 Cm 006[2];007[2];008[2];008[3];008[5];008[7];009[2]
81 007 Pc 007[2];007[3];007[5];007[7];009[2]
82 006 Pm 006[2];006[3];006[5];006[7];007[2];008[2]
83 009 Cc 007[2];009[3];009[5];009[7]
*/
When run, the code lists all the paths with the matching ones preceded by “Path Found”, so if you grep wrt it, you’ll have, for this example:
sururi@husniya:/xxx$ php find_trpath_for_index.php |grep Path|sed "s:Path Found\: ::"
227-141[3]-070[2]-015[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-007[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-013[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-013[2]-015[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-014[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-014[2]-007[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-014[2]-014[2]-007[2]-009[2]
227-141[3]-070[2]-043[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-012[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-012[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-011[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-011[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-011[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-012[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-012[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-014[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-014[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-014[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-014[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-026[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-026[2]-036[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-027[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-027[2]-037[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-028[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-028[2]-040[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-028[2]-041[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-036[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-037[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-045[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-046[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-038[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-038[2]-040[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-038[2]-046[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-041[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-045[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-046[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-036[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-037[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-040[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-041[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-031[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-033[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-034[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-026[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-026[2]-036[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-029[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-031[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-036[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-006[2]-007[2]-009[2]
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227-216[2]-119[3]-115[2]-111[2]-035[2]-046[2]-009[2]
227-216[2]-119[3]-115[2]-111[2]-112[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-111[2]-120[2]-045[2]-009[2]
227-216[2]-119[3]-115[2]-113[2]-035[2]-008[2]-009[2]
227-216[2]-119[3]-115[2]-113[2]-035[2]-036[2]-009[2]
227-216[2]-119[3]-115[2]-113[2]-035[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-113[2]-035[2]-045[2]-009[2]
227-216[2]-119[3]-115[2]-113[2]-035[2]-046[2]-009[2]
227-216[2]-119[3]-115[2]-113[2]-114[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-116[2]-027[2]-007[2]-009[2]
227-216[2]-119[3]-115[2]-116[2]-027[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-116[2]-112[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-116[2]-114[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-121[2]-042[2]-008[2]-009[2]
227-216[2]-119[3]-115[2]-121[2]-042[2]-036[2]-009[2]
227-216[2]-119[3]-115[2]-121[2]-042[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-121[2]-042[2]-040[2]-009[2]
227-216[2]-119[3]-115[2]-121[2]-042[2]-041[2]-009[2]
227-216[2]-119[3]-115[2]-121[2]-112[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-121[2]-114[2]-037[2]-009[2]
227-216[2]-119[3]-118[2]-034[2]-007[2]-007[2]-009[2]
227-216[2]-160[4]-008[3]-006[2]-007[2]-009[2]
227-216[2]-160[4]-008[3]-006[2]-008[2]-009[2]
227-216[2]-160[4]-008[3]-007[2]-007[2]-009[2]
227-216[2]-160[4]-008[3]-008[2]-007[2]-009[2]
227-216[2]-160[4]-008[3]-008[2]-008[2]-009[2]
227-216[2]-160[4]-008[3]-009[2]-007[2]-009[2]
227-216[2]-160[4]-160[2]-008[3]-007[2]-009[2]
227-216[2]-160[4]-160[2]-008[3]-008[2]-009[2]
227-216[2]-160[4]-160[2]-160[2]-008[3]-009[2]
227-216[2]-160[4]-160[2]-160[2]-161[2]-009[3]
227-216[2]-160[4]-161[2]-009[3]-007[2]-009[2]
227-216[2]-160[4]-161[2]-161[4]-009[3]
227-216[2]-160[4]-160[4]-008[3]-009[2]
227-216[2]-160[4]-160[4]-161[2]-009[3]
227-216[2]-215[4]-111[3]-035[2]-008[2]-009[2]
227-216[2]-215[4]-111[3]-035[2]-036[2]-009[2]
227-216[2]-215[4]-111[3]-035[2]-037[2]-009[2]
227-216[2]-215[4]-111[3]-035[2]-045[2]-009[2]
227-216[2]-215[4]-111[3]-035[2]-046[2]-009[2]
227-216[2]-215[4]-111[3]-112[2]-037[2]-009[2]
227-216[2]-215[4]-111[3]-120[2]-045[2]-009[2]
227-216[2]-215[4]-160[4]-008[3]-009[2]
227-216[2]-215[4]-160[4]-161[2]-009[3]
227-216[2]-215[4]-219[2]-120[3]-045[2]-009[2]
227-216[2]-215[4]-219[2]-161[4]-009[3]
