# Hex, Bugs and More Physics | Emre S. Tasci

a blog about physics, computation, computational physics and materials…

## 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]
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227-216[2]-119[3]-115[2]-025[2]-039[2]-045[2]-009[2]
227-216[2]-119[3]-115[2]-025[2]-039[2]-046[2]-009[2]
227-216[2]-119[3]-115[2]-025[2]-042[2]-008[2]-009[2]
227-216[2]-119[3]-115[2]-025[2]-042[2]-036[2]-009[2]
227-216[2]-119[3]-115[2]-025[2]-042[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-025[2]-042[2]-040[2]-009[2]
227-216[2]-119[3]-115[2]-025[2]-042[2]-041[2]-009[2]
227-216[2]-119[3]-115[2]-111[2]-035[2]-008[2]-009[2]
227-216[2]-119[3]-115[2]-111[2]-035[2]-036[2]-009[2]
227-216[2]-119[3]-115[2]-111[2]-035[2]-037[2]-009[2]
227-216[2]-119[3]-115[2]-111[2]-035[2]-045[2]-009[2]
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]
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