BeeGass commited on
Commit
1f5ecc5
·
verified ·
1 Parent(s): edb5c72

Upload folder using huggingface_hub

Browse files
data/s6_data/README.md ADDED
@@ -0,0 +1,122 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ ---
2
+ pretty_name: Permutation Composition Dataset (S6)
3
+ size_categories:
4
+ - small
5
+ - medium
6
+ - large
7
+ - xlarge
8
+ - xxlarge
9
+ tags:
10
+ - mathematics
11
+ - group-theory
12
+ - permutations
13
+ - sequence-to-sequence
14
+ - benchmark
15
+ - generated
16
+ task_categories:
17
+ - text-generation
18
+ - sequence-modeling
19
+ annotations_creators:
20
+ - no-annotations
21
+ language_creators:
22
+ - other
23
+ language:
24
+ - en
25
+ licenses:
26
+ - mit
27
+ ---
28
+
29
+ # Permutation Composition Dataset for S6
30
+
31
+ This dataset contains sequences of permutation IDs and their compositions, designed for benchmarking sequence-to-sequence models on group theory tasks.
32
+
33
+ ## Dataset Structure
34
+
35
+ The dataset is split into `train` and `test` sets. Each sample in the dataset has the following features:
36
+
37
+ - `input_sequence`: A space-separated string of integer IDs representing the sequence of permutations to be composed.
38
+ - `target`: An integer ID representing the composition of the `input_sequence` permutations.
39
+
40
+ ## Group Details
41
+
42
+ - **Group Name**: S6
43
+ - **Group Type**: Symmetric Group
44
+ - **Degree**: 6 (permutations act on 6 elements)
45
+ - **Order**: 720 (total number of elements in the group)
46
+
47
+ ## Data Generation
48
+
49
+ This dataset was generated using the `s5-data-gen` script. The generation process involves:
50
+
51
+ 1. Generating all unique permutations for the specified group.
52
+ 2. Mapping each unique permutation to a unique integer ID.
53
+ 3. Randomly sampling sequences of these permutation IDs.
54
+ 4. Composing the permutations in the sequence (from right to left: `p_n o ... o p_2 o p_1`).
55
+ 5. Mapping the resulting composed permutation to its integer ID as the target.
56
+
57
+ ### Generation Parameters:
58
+
59
+ - **Total Samples**: 100000
60
+ - **Minimum Sequence Length**: 3
61
+ - **Maximum Sequence Length**: 512
62
+ - **Test Split Size**: 0.2
63
+
64
+ ## Dataset Statistics
65
+
66
+ - **Train Samples**: 80000
67
+ - **Test Samples**: 20000
68
+
69
+ ## Permutation Mapping
70
+
71
+ The mapping from integer IDs to their corresponding permutation array forms is provided in the `metadata.json` file alongside the dataset. This file is crucial for interpreting the `input_sequence` and `target` IDs.
72
+
73
+ Example of `metadata.json` content:
74
+
75
+ ```json
76
+ {
77
+ "0": "[0, 1, 2, 3, 4]",
78
+ "1": "[0, 1, 3, 2, 4]",
79
+ "2": "[0, 1, 4, 3, 2]",
80
+ "3": "[0, 2, 1, 3, 4]",
81
+ "4": "[0, 2, 3, 1, 4]"
82
+ // ... and so on for all 720 permutations
83
+ }
84
+ ```
85
+
86
+ ## Usage
87
+
88
+ You can load this dataset using the Hugging Face `datasets` library:
89
+
90
+ ```python
91
+ from datasets import load_dataset
92
+ import json
93
+ from huggingface_hub import hf_hub_download
94
+
95
+ # Load the dataset
96
+ dataset = load_dataset("BeeGass/permutation-groups")
97
+
98
+ # Load the permutation mapping
99
+ metadata_path = hf_hub_download(repo_id="BeeGass/permutation-groups", filename="metadata.json")
100
+ with open(metadata_path, "r") as f:
101
+ id_to_perm_map = json.load(f)
102
+
103
+ # Example: Decode a sample
104
+ first_train_sample = dataset["train"][0]
105
+ input_ids = [int(x) for x in first_train_sample["input_sequence"].split(" ")]
106
+ target_id = int(first_train_sample["target"])
107
+
108
+ print(f"Input sequence IDs: {input_ids}")
109
+ print(f"Target ID: {target_id}")
110
+
111
+ # Convert IDs back to permutations (example for the first input permutation)
112
+ # Note: SymPy Permutation expects a list of integers, not a string representation
113
+ # You would need to parse the string representation from id_to_perm_map
114
+ # For example: eval(id_to_perm_map[str(input_ids[0])])
115
+
116
+ print(f"First input permutation (array form): {id_to_perm_map[str(input_ids[0])]}")
117
+ print(f"Target permutation (array form): {id_to_perm_map[str(target_id)]}")
118
+ ```
119
+
120
+ ## License
121
+
122
+ This dataset is licensed under the MIT License.
data/s6_data/dataset_dict.json ADDED
@@ -0,0 +1 @@
 
 
1
+ {"splits": ["train", "test"]}
data/s6_data/metadata.json ADDED
@@ -0,0 +1,722 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "0": "[0, 1, 3, 5, 2, 4]",
3
+ "1": "[1, 2, 4, 0, 3, 5]",
4
+ "2": "[2, 3, 5, 1, 4, 0]",
5
+ "3": "[3, 4, 0, 2, 5, 1]",
6
+ "4": "[4, 5, 2, 0, 1, 3]",
7
+ "5": "[5, 1, 3, 0, 2, 4]",
8
+ "6": "[0, 2, 3, 4, 1, 5]",
9
+ "7": "[1, 3, 4, 5, 2, 0]",
10
+ "8": "[2, 4, 5, 0, 3, 1]",
11
+ "9": "[3, 5, 0, 1, 4, 2]",
12
+ "10": "[4, 1, 2, 3, 5, 0]",
13
+ "11": "[5, 2, 3, 4, 1, 0]",
14
+ "12": "[0, 3, 2, 4, 1, 5]",
15
+ "13": "[1, 4, 3, 5, 2, 0]",
16
+ "14": "[2, 5, 4, 0, 3, 1]",
17
+ "15": "[3, 0, 5, 1, 4, 2]",
18
+ "16": "[4, 2, 1, 3, 5, 0]",
19
+ "17": "[5, 3, 2, 4, 1, 0]",
20
+ "18": "[0, 4, 1, 3, 5, 2]",
21
+ "19": "[1, 5, 2, 4, 0, 3]",
22
+ "20": "[2, 0, 3, 5, 1, 4]",
23
+ "21": "[3, 1, 4, 0, 2, 5]",
24
+ "22": "[4, 3, 5, 2, 0, 1]",
25
+ "23": "[5, 4, 1, 3, 0, 2]",
26
+ "24": "[0, 5, 2, 4, 1, 3]",
27
+ "25": "[1, 0, 3, 5, 2, 4]",
28
+ "26": "[2, 1, 4, 0, 3, 5]",
29
+ "27": "[3, 2, 5, 1, 4, 0]",
30
+ "28": "[4, 0, 1, 3, 5, 2]",
31
+ "29": "[5, 0, 2, 4, 1, 3]",
32
+ "30": "[0, 1, 2, 5, 3, 4]",
33
+ "31": "[1, 2, 3, 0, 4, 5]",
34
+ "32": "[2, 3, 4, 1, 5, 0]",
35
+ "33": "[3, 4, 5, 2, 0, 1]",
36
+ "34": "[4, 5, 1, 0, 2, 3]",
37
+ "35": "[5, 1, 2, 0, 3, 4]",
38
+ "36": "[0, 2, 1, 4, 3, 5]",
39
+ "37": "[1, 3, 2, 5, 4, 0]",
40
+ "38": "[2, 4, 3, 0, 5, 1]",
41
+ "39": "[3, 5, 4, 1, 0, 2]",
42
+ "40": "[4, 1, 5, 3, 2, 0]",
43
+ "41": "[5, 2, 1, 4, 3, 0]",
44
+ "42": "[0, 3, 1, 4, 2, 5]",
45
+ "43": "[1, 4, 2, 5, 3, 0]",
46
+ "44": "[2, 5, 3, 0, 4, 1]",
47
+ "45": "[3, 0, 4, 1, 5, 2]",
48
+ "46": "[4, 2, 5, 3, 1, 0]",
49
+ "47": "[5, 3, 1, 4, 2, 0]",
50
+ "48": "[0, 4, 5, 3, 1, 2]",
51
+ "49": "[1, 5, 0, 4, 2, 3]",
52
+ "50": "[2, 0, 1, 5, 3, 4]",
53
+ "51": "[3, 1, 2, 0, 4, 5]",
54
+ "52": "[4, 3, 0, 2, 5, 1]",
55
+ "53": "[5, 4, 0, 3, 1, 2]",
56
+ "54": "[0, 5, 1, 4, 2, 3]",
57
+ "55": "[1, 0, 2, 5, 3, 4]",
58
+ "56": "[2, 1, 3, 0, 4, 5]",
59
+ "57": "[3, 2, 4, 1, 5, 0]",
60
+ "58": "[4, 0, 5, 3, 1, 2]",
61
+ "59": "[5, 0, 1, 4, 2, 3]",
62
+ "60": "[0, 1, 2, 3, 4, 5]",
63
+ "61": "[1, 2, 3, 4, 5, 0]",
64
+ "62": "[2, 3, 4, 5, 0, 1]",
65
+ "63": "[3, 4, 5, 0, 1, 2]",
66
+ "64": "[4, 5, 1, 2, 3, 0]",
67
+ "65": "[5, 1, 2, 3, 4, 0]",
68
+ "66": "[0, 2, 1, 3, 5, 4]",
69
+ "67": "[1, 3, 2, 4, 0, 5]",
70
+ "68": "[2, 4, 3, 5, 1, 0]",
71
+ "69": "[3, 5, 4, 0, 2, 1]",
72
+ "70": "[4, 1, 5, 2, 0, 3]",
73
+ "71": "[5, 2, 1, 3, 0, 4]",
74
+ "72": "[0, 3, 1, 2, 5, 4]",
75
+ "73": "[1, 4, 2, 3, 0, 5]",
76
+ "74": "[2, 5, 3, 4, 1, 0]",
77
+ "75": "[3, 0, 4, 5, 2, 1]",
78
+ "76": "[4, 2, 5, 1, 0, 3]",
79
+ "77": "[5, 3, 1, 2, 0, 4]",
80
+ "78": "[0, 4, 5, 1, 2, 3]",
81
+ "79": "[1, 5, 0, 2, 3, 4]",
82
+ "80": "[2, 0, 1, 3, 4, 5]",
83
+ "81": "[3, 1, 2, 4, 5, 0]",
84
+ "82": "[4, 3, 0, 5, 1, 2]",
85
+ "83": "[5, 4, 0, 1, 2, 3]",
86
+ "84": "[0, 5, 1, 2, 3, 4]",
87
+ "85": "[1, 0, 2, 3, 4, 5]",
88
+ "86": "[2, 1, 3, 4, 5, 0]",
89
+ "87": "[3, 2, 4, 5, 0, 1]",
90
+ "88": "[4, 0, 5, 1, 2, 3]",
91
+ "89": "[5, 0, 1, 2, 3, 4]",
92
+ "90": "[0, 1, 2, 3, 5, 4]",
93
+ "91": "[1, 2, 3, 4, 0, 5]",
94
+ "92": "[2, 3, 4, 5, 1, 0]",
95
+ "93": "[3, 4, 5, 0, 2, 1]",
96
+ "94": "[4, 5, 1, 2, 0, 3]",
97
+ "95": "[5, 1, 2, 3, 0, 4]",
98
+ "96": "[0, 2, 1, 3, 4, 5]",
99
+ "97": "[1, 3, 2, 4, 5, 0]",
100
+ "98": "[2, 4, 3, 5, 0, 1]",
101
+ "99": "[3, 5, 4, 0, 1, 2]",
102
+ "100": "[4, 1, 5, 2, 3, 0]",
103
+ "101": "[5, 2, 1, 3, 4, 0]",
104
+ "102": "[0, 3, 1, 2, 4, 5]",
105
+ "103": "[1, 4, 2, 3, 5, 0]",
106
+ "104": "[2, 5, 3, 4, 0, 1]",
107
+ "105": "[3, 0, 4, 5, 1, 2]",
108
+ "106": "[4, 2, 5, 1, 3, 0]",
109
+ "107": "[5, 3, 1, 2, 4, 0]",
110
+ "108": "[0, 4, 5, 1, 3, 2]",
111
+ "109": "[1, 5, 0, 2, 4, 3]",
112
+ "110": "[2, 0, 1, 3, 5, 4]",
113
+ "111": "[3, 1, 2, 4, 0, 5]",
114
+ "112": "[4, 3, 0, 5, 2, 1]",
115
+ "113": "[5, 4, 0, 1, 3, 2]",
116
+ "114": "[0, 5, 1, 2, 4, 3]",
117
+ "115": "[1, 0, 2, 3, 5, 4]",
118
+ "116": "[2, 1, 3, 4, 0, 5]",
119
+ "117": "[3, 2, 4, 5, 1, 0]",
120
+ "118": "[4, 0, 5, 1, 3, 2]",
121
+ "119": "[5, 0, 1, 2, 4, 3]",
122
+ "120": "[0, 1, 5, 4, 2, 3]",
123
+ "121": "[1, 2, 0, 5, 3, 4]",
124
+ "122": "[2, 3, 1, 0, 4, 5]",
125
+ "123": "[3, 4, 2, 1, 5, 0]",
126
+ "124": "[4, 5, 0, 3, 1, 2]",
127
+ "125": "[5, 1, 0, 4, 2, 3]",
128
+ "126": "[0, 2, 4, 5, 1, 3]",
129
+ "127": "[1, 3, 5, 0, 2, 4]",
130
+ "128": "[2, 4, 0, 1, 3, 5]",
131
+ "129": "[3, 5, 1, 2, 4, 0]",
132
+ "130": "[4, 1, 3, 0, 5, 2]",
133
+ "131": "[5, 2, 4, 0, 1, 3]",
134
+ "132": "[0, 3, 4, 5, 1, 2]",
135
+ "133": "[1, 4, 5, 0, 2, 3]",
136
+ "134": "[2, 5, 0, 1, 3, 4]",
137
+ "135": "[3, 0, 1, 2, 4, 5]",
138
+ "136": "[4, 2, 3, 0, 5, 1]",
139
+ "137": "[5, 3, 4, 0, 1, 2]",
140
+ "138": "[0, 4, 3, 2, 5, 1]",
141
+ "139": "[1, 5, 4, 3, 0, 2]",
142
+ "140": "[2, 0, 5, 4, 1, 3]",
143
+ "141": "[3, 1, 0, 5, 2, 4]",
144
+ "142": "[4, 3, 2, 1, 0, 5]",
145
+ "143": "[5, 4, 3, 2, 0, 1]",
146
+ "144": "[0, 5, 4, 3, 1, 2]",
147
+ "145": "[1, 0, 5, 4, 2, 3]",
148
+ "146": "[2, 1, 0, 5, 3, 4]",
149
+ "147": "[3, 2, 1, 0, 4, 5]",
150
+ "148": "[4, 0, 3, 2, 5, 1]",
151
+ "149": "[5, 0, 4, 3, 1, 2]",
152
+ "150": "[0, 1, 5, 4, 3, 2]",
153
+ "151": "[1, 2, 0, 5, 4, 3]",
154
+ "152": "[2, 3, 1, 0, 5, 4]",
155
+ "153": "[3, 4, 2, 1, 0, 5]",
156
+ "154": "[4, 5, 0, 3, 2, 1]",
157
+ "155": "[5, 1, 0, 4, 3, 2]",
158
+ "156": "[0, 2, 4, 5, 3, 1]",
159
+ "157": "[1, 3, 5, 0, 4, 2]",
160
+ "158": "[2, 4, 0, 1, 5, 3]",
161
+ "159": "[3, 5, 1, 2, 0, 4]",
162
+ "160": "[4, 1, 3, 0, 2, 5]",
163
+ "161": "[5, 2, 4, 0, 3, 1]",
164
+ "162": "[0, 3, 4, 5, 2, 1]",
165
+ "163": "[1, 4, 5, 0, 3, 2]",
166
+ "164": "[2, 5, 0, 1, 4, 3]",
167
+ "165": "[3, 0, 1, 2, 5, 4]",
168
+ "166": "[4, 2, 3, 0, 1, 5]",
169
+ "167": "[5, 3, 4, 0, 2, 1]",
170
+ "168": "[0, 4, 3, 2, 1, 5]",
171
+ "169": "[1, 5, 4, 3, 2, 0]",
172
+ "170": "[2, 0, 5, 4, 3, 1]",
173
+ "171": "[3, 1, 0, 5, 4, 2]",
174
+ "172": "[4, 3, 2, 1, 5, 0]",
175
+ "173": "[5, 4, 3, 2, 1, 0]",
176
+ "174": "[0, 5, 4, 3, 2, 1]",
177
+ "175": "[1, 0, 5, 4, 3, 2]",
178
+ "176": "[2, 1, 0, 5, 4, 3]",
179
+ "177": "[3, 2, 1, 0, 5, 4]",
180
+ "178": "[4, 0, 3, 2, 1, 5]",
181
+ "179": "[5, 0, 4, 3, 2, 1]",
182
+ "180": "[0, 1, 3, 5, 4, 2]",
183
+ "181": "[1, 2, 4, 0, 5, 3]",
184
+ "182": "[2, 3, 5, 1, 0, 4]",
185
+ "183": "[3, 4, 0, 2, 1, 5]",
186
+ "184": "[4, 5, 2, 0, 3, 1]",
187
+ "185": "[5, 1, 3, 0, 4, 2]",
188
+ "186": "[0, 2, 3, 4, 5, 1]",
189
+ "187": "[1, 3, 4, 5, 0, 2]",
190
+ "188": "[2, 4, 5, 0, 1, 3]",
191
+ "189": "[3, 5, 0, 1, 2, 4]",
192
+ "190": "[4, 1, 2, 3, 0, 5]",
193
+ "191": "[5, 2, 3, 4, 0, 1]",
194
+ "192": "[0, 3, 2, 4, 5, 1]",
195
+ "193": "[1, 4, 3, 5, 0, 2]",
196
+ "194": "[2, 5, 4, 0, 1, 3]",
197
+ "195": "[3, 0, 5, 1, 2, 4]",
198
+ "196": "[4, 2, 1, 3, 0, 5]",
199
+ "197": "[5, 3, 2, 4, 0, 1]",
200
+ "198": "[0, 4, 1, 3, 2, 5]",
201
+ "199": "[1, 5, 2, 4, 3, 0]",
202
+ "200": "[2, 0, 3, 5, 4, 1]",
203
+ "201": "[3, 1, 4, 0, 5, 2]",
204
+ "202": "[4, 3, 5, 2, 1, 0]",
205
+ "203": "[5, 4, 1, 3, 2, 0]",
206
+ "204": "[0, 5, 2, 4, 3, 1]",
207
+ "205": "[1, 0, 3, 5, 4, 2]",
208
+ "206": "[2, 1, 4, 0, 5, 3]",
209
+ "207": "[3, 2, 5, 1, 0, 4]",
210
+ "208": "[4, 0, 1, 3, 2, 5]",
211
+ "209": "[5, 0, 2, 4, 3, 1]",
212
+ "210": "[0, 1, 3, 4, 5, 2]",
213
+ "211": "[1, 2, 4, 5, 0, 3]",
214
+ "212": "[2, 3, 5, 0, 1, 4]",
215
+ "213": "[3, 4, 0, 1, 2, 5]",
216
+ "214": "[4, 5, 2, 3, 0, 1]",
217
+ "215": "[5, 1, 3, 4, 0, 2]",
218
+ "216": "[0, 2, 3, 5, 4, 1]",
219
+ "217": "[1, 3, 4, 0, 5, 2]",
220
+ "218": "[2, 4, 5, 1, 0, 3]",
221
+ "219": "[3, 5, 0, 2, 1, 4]",
222
+ "220": "[4, 1, 2, 0, 3, 5]",
223
+ "221": "[5, 2, 3, 0, 4, 1]",
224
+ "222": "[0, 3, 2, 5, 4, 1]",
225
+ "223": "[1, 4, 3, 0, 5, 2]",
226
+ "224": "[2, 5, 4, 1, 0, 3]",
227
+ "225": "[3, 0, 5, 2, 1, 4]",
228
+ "226": "[4, 2, 1, 0, 3, 5]",
229
+ "227": "[5, 3, 2, 0, 4, 1]",
230
+ "228": "[0, 4, 1, 2, 3, 5]",
231
+ "229": "[1, 5, 2, 3, 4, 0]",
232
+ "230": "[2, 0, 3, 4, 5, 1]",
233
+ "231": "[3, 1, 4, 5, 0, 2]",
234
+ "232": "[4, 3, 5, 1, 2, 0]",
235
+ "233": "[5, 4, 1, 2, 3, 0]",
236
+ "234": "[0, 5, 2, 3, 4, 1]",
237
+ "235": "[1, 0, 3, 4, 5, 2]",
238
+ "236": "[2, 1, 4, 5, 0, 3]",
239
+ "237": "[3, 2, 5, 0, 1, 4]",
240
+ "238": "[4, 0, 1, 2, 3, 5]",
241
+ "239": "[5, 0, 2, 3, 4, 1]",
242
+ "240": "[0, 1, 4, 3, 2, 5]",
243
+ "241": "[1, 2, 5, 4, 3, 0]",
244
+ "242": "[2, 3, 0, 5, 4, 1]",
245
+ "243": "[3, 4, 1, 0, 5, 2]",
246
+ "244": "[4, 5, 3, 2, 1, 0]",
247
+ "245": "[5, 1, 4, 3, 2, 0]",
248
+ "246": "[0, 2, 5, 3, 1, 4]",
249
+ "247": "[1, 3, 0, 4, 2, 5]",
250
+ "248": "[2, 4, 1, 5, 3, 0]",
251
+ "249": "[3, 5, 2, 0, 4, 1]",
252
+ "250": "[4, 1, 0, 2, 5, 3]",
253
+ "251": "[5, 2, 0, 3, 1, 4]",
254
+ "252": "[0, 3, 5, 2, 1, 4]",
255
+ "253": "[1, 4, 0, 3, 2, 5]",
256
+ "254": "[2, 5, 1, 4, 3, 0]",
257
+ "255": "[3, 0, 2, 5, 4, 1]",
258
+ "256": "[4, 2, 0, 1, 5, 3]",
259
+ "257": "[5, 3, 0, 2, 1, 4]",
260
+ "258": "[0, 4, 2, 1, 5, 3]",
261
+ "259": "[1, 5, 3, 2, 0, 4]",
262
+ "260": "[2, 0, 4, 3, 1, 5]",
263
+ "261": "[3, 1, 5, 4, 2, 0]",
264
+ "262": "[4, 3, 1, 5, 0, 2]",
265
+ "263": "[5, 4, 2, 1, 0, 3]",
266
+ "264": "[0, 5, 3, 2, 1, 4]",
267
+ "265": "[1, 0, 4, 3, 2, 5]",
268
+ "266": "[2, 1, 5, 4, 3, 0]",
269
+ "267": "[3, 2, 0, 5, 4, 1]",
270
+ "268": "[4, 0, 2, 1, 5, 3]",
271
+ "269": "[5, 0, 3, 2, 1, 4]",
272
+ "270": "[0, 1, 4, 2, 3, 5]",
273
+ "271": "[1, 2, 5, 3, 4, 0]",
274
+ "272": "[2, 3, 0, 4, 5, 1]",
275
+ "273": "[3, 4, 1, 5, 0, 2]",
276
+ "274": "[4, 5, 3, 1, 2, 0]",
277
+ "275": "[5, 1, 4, 2, 3, 0]",
278
+ "276": "[0, 2, 5, 1, 3, 4]",
279
+ "277": "[1, 3, 0, 2, 4, 5]",
280
+ "278": "[2, 4, 1, 3, 5, 0]",
281
+ "279": "[3, 5, 2, 4, 0, 1]",
282
+ "280": "[4, 1, 0, 5, 2, 3]",
283
+ "281": "[5, 2, 0, 1, 3, 4]",
284
+ "282": "[0, 3, 5, 1, 2, 4]",
285
+ "283": "[1, 4, 0, 2, 3, 5]",
286
+ "284": "[2, 5, 1, 3, 4, 0]",
287
+ "285": "[3, 0, 2, 4, 5, 1]",
288
+ "286": "[4, 2, 0, 5, 1, 3]",
289
+ "287": "[5, 3, 0, 1, 2, 4]",
290
+ "288": "[0, 4, 2, 5, 1, 3]",
291
+ "289": "[1, 5, 3, 0, 2, 4]",
292
+ "290": "[2, 0, 4, 1, 3, 5]",
293
+ "291": "[3, 1, 5, 2, 4, 0]",
294
+ "292": "[4, 3, 1, 0, 5, 2]",
295
+ "293": "[5, 4, 2, 0, 1, 3]",
296
+ "294": "[0, 5, 3, 1, 2, 4]",
297
+ "295": "[1, 0, 4, 2, 3, 5]",
298
+ "296": "[2, 1, 5, 3, 4, 0]",
299
+ "297": "[3, 2, 0, 4, 5, 1]",
300
+ "298": "[4, 0, 2, 5, 1, 3]",
301
+ "299": "[5, 0, 3, 1, 2, 4]",
302
+ "300": "[0, 1, 5, 2, 4, 3]",
303
+ "301": "[1, 2, 0, 3, 5, 4]",
304
+ "302": "[2, 3, 1, 4, 0, 5]",
305
+ "303": "[3, 4, 2, 5, 1, 0]",
306
+ "304": "[4, 5, 0, 1, 3, 2]",
307
+ "305": "[5, 1, 0, 2, 4, 3]",
308
+ "306": "[0, 2, 4, 1, 5, 3]",
309
+ "307": "[1, 3, 5, 2, 0, 4]",
310
+ "308": "[2, 4, 0, 3, 1, 5]",
311
+ "309": "[3, 5, 1, 4, 2, 0]",
312
+ "310": "[4, 1, 3, 5, 0, 2]",
313
+ "311": "[5, 2, 4, 1, 0, 3]",
314
+ "312": "[0, 3, 4, 1, 5, 2]",
315
+ "313": "[1, 4, 5, 2, 0, 3]",
316
+ "314": "[2, 5, 0, 3, 1, 4]",
317
+ "315": "[3, 0, 1, 4, 2, 5]",
318
+ "316": "[4, 2, 3, 5, 0, 1]",
319
+ "317": "[5, 3, 4, 1, 0, 2]",
320
+ "318": "[0, 4, 3, 5, 2, 1]",
321
+ "319": "[1, 5, 4, 0, 3, 2]",
322
+ "320": "[2, 0, 5, 1, 4, 3]",
323
+ "321": "[3, 1, 0, 2, 5, 4]",
324
+ "322": "[4, 3, 2, 0, 1, 5]",
325
+ "323": "[5, 4, 3, 0, 2, 1]",
326
+ "324": "[0, 5, 4, 1, 3, 2]",
327
+ "325": "[1, 0, 5, 2, 4, 3]",
328
+ "326": "[2, 1, 0, 3, 5, 4]",
329
+ "327": "[3, 2, 1, 4, 0, 5]",
330
+ "328": "[4, 0, 3, 5, 2, 1]",
331
+ "329": "[5, 0, 4, 1, 3, 2]",
332
+ "330": "[0, 1, 4, 2, 5, 3]",
333
+ "331": "[1, 2, 5, 3, 0, 4]",
334
+ "332": "[2, 3, 0, 4, 1, 5]",
335
+ "333": "[3, 4, 1, 5, 2, 0]",
336
+ "334": "[4, 5, 3, 1, 0, 2]",
337
+ "335": "[5, 1, 4, 2, 0, 3]",
338
+ "336": "[0, 2, 5, 1, 4, 3]",
339
+ "337": "[1, 3, 0, 2, 5, 4]",
340
+ "338": "[2, 4, 1, 3, 0, 5]",
341
+ "339": "[3, 5, 2, 4, 1, 0]",
342
+ "340": "[4, 1, 0, 5, 3, 2]",
343
+ "341": "[5, 2, 0, 1, 4, 3]",
344
+ "342": "[0, 3, 5, 1, 4, 2]",
345
+ "343": "[1, 4, 0, 2, 5, 3]",
346
+ "344": "[2, 5, 1, 3, 0, 4]",
347
+ "345": "[3, 0, 2, 4, 1, 5]",
348
+ "346": "[4, 2, 0, 5, 3, 1]",
349
+ "347": "[5, 3, 0, 1, 4, 2]",
350
+ "348": "[0, 4, 2, 5, 3, 1]",
351
+ "349": "[1, 5, 3, 0, 4, 2]",
352
+ "350": "[2, 0, 4, 1, 5, 3]",
353
+ "351": "[3, 1, 5, 2, 0, 4]",
354
+ "352": "[4, 3, 1, 0, 2, 5]",
355
+ "353": "[5, 4, 2, 0, 3, 1]",
356
+ "354": "[0, 5, 3, 1, 4, 2]",
357
+ "355": "[1, 0, 4, 2, 5, 3]",
358
+ "356": "[2, 1, 5, 3, 0, 4]",
359
+ "357": "[3, 2, 0, 4, 1, 5]",
360
+ "358": "[4, 0, 2, 5, 3, 1]",
361
+ "359": "[5, 0, 3, 1, 4, 2]",
362
+ "360": "[0, 1, 3, 4, 2, 5]",
363
+ "361": "[1, 2, 4, 5, 3, 0]",
364
+ "362": "[2, 3, 5, 0, 4, 1]",
365
+ "363": "[3, 4, 0, 1, 5, 2]",
366
+ "364": "[4, 5, 2, 3, 1, 0]",
367
+ "365": "[5, 1, 3, 4, 2, 0]",
368
+ "366": "[0, 2, 3, 5, 1, 4]",
369
+ "367": "[1, 3, 4, 0, 2, 5]",
370
+ "368": "[2, 4, 5, 1, 3, 0]",
371
+ "369": "[3, 5, 0, 2, 4, 1]",
372
+ "370": "[4, 1, 2, 0, 5, 3]",
373
+ "371": "[5, 2, 3, 0, 1, 4]",
374
+ "372": "[0, 3, 2, 5, 1, 4]",
375
+ "373": "[1, 4, 3, 0, 2, 5]",
376
+ "374": "[2, 5, 4, 1, 3, 0]",
377
+ "375": "[3, 0, 5, 2, 4, 1]",
378
+ "376": "[4, 2, 1, 0, 5, 3]",
379
+ "377": "[5, 3, 2, 0, 1, 4]",
380
+ "378": "[0, 4, 1, 2, 5, 3]",
381
+ "379": "[1, 5, 2, 3, 0, 4]",
382
+ "380": "[2, 0, 3, 4, 1, 5]",
383
+ "381": "[3, 1, 4, 5, 2, 0]",
384
+ "382": "[4, 3, 5, 1, 0, 2]",
385
+ "383": "[5, 4, 1, 2, 0, 3]",
386
+ "384": "[0, 5, 2, 3, 1, 4]",
387
+ "385": "[1, 0, 3, 4, 2, 5]",
388
+ "386": "[2, 1, 4, 5, 3, 0]",
389
+ "387": "[3, 2, 5, 0, 4, 1]",
390
+ "388": "[4, 0, 1, 2, 5, 3]",
391
+ "389": "[5, 0, 2, 3, 1, 4]",
392
+ "390": "[0, 1, 2, 4, 3, 5]",
393
+ "391": "[1, 2, 3, 5, 4, 0]",
394
+ "392": "[2, 3, 4, 0, 5, 1]",
395
+ "393": "[3, 4, 5, 1, 0, 2]",
396
+ "394": "[4, 5, 1, 3, 2, 0]",
397
+ "395": "[5, 1, 2, 4, 3, 0]",
398
+ "396": "[0, 2, 1, 5, 3, 4]",
399
+ "397": "[1, 3, 2, 0, 4, 5]",
400
+ "398": "[2, 4, 3, 1, 5, 0]",
401
+ "399": "[3, 5, 4, 2, 0, 1]",
402
+ "400": "[4, 1, 5, 0, 2, 3]",
403
+ "401": "[5, 2, 1, 0, 3, 4]",
404
+ "402": "[0, 3, 1, 5, 2, 4]",
405
+ "403": "[1, 4, 2, 0, 3, 5]",
406
+ "404": "[2, 5, 3, 1, 4, 0]",
407
+ "405": "[3, 0, 4, 2, 5, 1]",
408
+ "406": "[4, 2, 5, 0, 1, 3]",
409
+ "407": "[5, 3, 1, 0, 2, 4]",
410
+ "408": "[0, 4, 5, 2, 1, 3]",
411
+ "409": "[1, 5, 0, 3, 2, 4]",
412
+ "410": "[2, 0, 1, 4, 3, 5]",
413
+ "411": "[3, 1, 2, 5, 4, 0]",
414
+ "412": "[4, 3, 0, 1, 5, 2]",
415
+ "413": "[5, 4, 0, 2, 1, 3]",
416
+ "414": "[0, 5, 1, 3, 2, 4]",
417
+ "415": "[1, 0, 2, 4, 3, 5]",
418
+ "416": "[2, 1, 3, 5, 4, 0]",
419
+ "417": "[3, 2, 4, 0, 5, 1]",
420
+ "418": "[4, 0, 5, 2, 1, 3]",
421
+ "419": "[5, 0, 1, 3, 2, 4]",
422
+ "420": "[0, 1, 2, 5, 4, 3]",
423
+ "421": "[1, 2, 3, 0, 5, 4]",
424
+ "422": "[2, 3, 4, 1, 0, 5]",
425
+ "423": "[3, 4, 5, 2, 1, 0]",
426
+ "424": "[4, 5, 1, 0, 3, 2]",
427
+ "425": "[5, 1, 2, 0, 4, 3]",
428
+ "426": "[0, 2, 1, 4, 5, 3]",
429
+ "427": "[1, 3, 2, 5, 0, 4]",
430
+ "428": "[2, 4, 3, 0, 1, 5]",
431
+ "429": "[3, 5, 4, 1, 2, 0]",
432
+ "430": "[4, 1, 5, 3, 0, 2]",
433
+ "431": "[5, 2, 1, 4, 0, 3]",
434
+ "432": "[0, 3, 1, 4, 5, 2]",
435
+ "433": "[1, 4, 2, 5, 0, 3]",
436
+ "434": "[2, 5, 3, 0, 1, 4]",
437
+ "435": "[3, 0, 4, 1, 2, 5]",
438
+ "436": "[4, 2, 5, 3, 0, 1]",
439
+ "437": "[5, 3, 1, 4, 0, 2]",
440
+ "438": "[0, 4, 5, 3, 2, 1]",
441
+ "439": "[1, 5, 0, 4, 3, 2]",
442
+ "440": "[2, 0, 1, 5, 4, 3]",
443
+ "441": "[3, 1, 2, 0, 5, 4]",
444
+ "442": "[4, 3, 0, 2, 1, 5]",
445
+ "443": "[5, 4, 0, 3, 2, 1]",
446
+ "444": "[0, 5, 1, 4, 3, 2]",
447
+ "445": "[1, 0, 2, 5, 4, 3]",
448
+ "446": "[2, 1, 3, 0, 5, 4]",
449
+ "447": "[3, 2, 4, 1, 0, 5]",
450
+ "448": "[4, 0, 5, 3, 2, 1]",
451
+ "449": "[5, 0, 1, 4, 3, 2]",
452
+ "450": "[0, 1, 2, 4, 5, 3]",
453
+ "451": "[1, 2, 3, 5, 0, 4]",
454
+ "452": "[2, 3, 4, 0, 1, 5]",
455
+ "453": "[3, 4, 5, 1, 2, 0]",
456
+ "454": "[4, 5, 1, 3, 0, 2]",
457
+ "455": "[5, 1, 2, 4, 0, 3]",
458
+ "456": "[0, 2, 1, 5, 4, 3]",
459
+ "457": "[1, 3, 2, 0, 5, 4]",
460
+ "458": "[2, 4, 3, 1, 0, 5]",
461
+ "459": "[3, 5, 4, 2, 1, 0]",
462
+ "460": "[4, 1, 5, 0, 3, 2]",
463
+ "461": "[5, 2, 1, 0, 4, 3]",
464
+ "462": "[0, 3, 1, 5, 4, 2]",
465
+ "463": "[1, 4, 2, 0, 5, 3]",
466
+ "464": "[2, 5, 3, 1, 0, 4]",
467
+ "465": "[3, 0, 4, 2, 1, 5]",
468
+ "466": "[4, 2, 5, 0, 3, 1]",
469
+ "467": "[5, 3, 1, 0, 4, 2]",
470
+ "468": "[0, 4, 5, 2, 3, 1]",
471
+ "469": "[1, 5, 0, 3, 4, 2]",
472
+ "470": "[2, 0, 1, 4, 5, 3]",
473
+ "471": "[3, 1, 2, 5, 0, 4]",
474
+ "472": "[4, 3, 0, 1, 2, 5]",
475
+ "473": "[5, 4, 0, 2, 3, 1]",
476
+ "474": "[0, 5, 1, 3, 4, 2]",
477
+ "475": "[1, 0, 2, 4, 5, 3]",
478
+ "476": "[2, 1, 3, 5, 0, 4]",
479
+ "477": "[3, 2, 4, 0, 1, 5]",
480
+ "478": "[4, 0, 5, 2, 3, 1]",
481
+ "479": "[5, 0, 1, 3, 4, 2]",
482
+ "480": "[0, 1, 5, 3, 2, 4]",
483
+ "481": "[1, 2, 0, 4, 3, 5]",
484
+ "482": "[2, 3, 1, 5, 4, 0]",
485
+ "483": "[3, 4, 2, 0, 5, 1]",
486
+ "484": "[4, 5, 0, 2, 1, 3]",
487
+ "485": "[5, 1, 0, 3, 2, 4]",
488
+ "486": "[0, 2, 4, 3, 1, 5]",
489
+ "487": "[1, 3, 5, 4, 2, 0]",
490
+ "488": "[2, 4, 0, 5, 3, 1]",
491
+ "489": "[3, 5, 1, 0, 4, 2]",
492
+ "490": "[4, 1, 3, 2, 5, 0]",
493
+ "491": "[5, 2, 4, 3, 1, 0]",
494
+ "492": "[0, 3, 4, 2, 1, 5]",
495
+ "493": "[1, 4, 5, 3, 2, 0]",
496
+ "494": "[2, 5, 0, 4, 3, 1]",
497
+ "495": "[3, 0, 1, 5, 4, 2]",
498
+ "496": "[4, 2, 3, 1, 5, 0]",
499
+ "497": "[5, 3, 4, 2, 1, 0]",
500
+ "498": "[0, 4, 3, 1, 5, 2]",
501
+ "499": "[1, 5, 4, 2, 0, 3]",
502
+ "500": "[2, 0, 5, 3, 1, 4]",
503
+ "501": "[3, 1, 0, 4, 2, 5]",
504
+ "502": "[4, 3, 2, 5, 0, 1]",
505
+ "503": "[5, 4, 3, 1, 0, 2]",
506
+ "504": "[0, 5, 4, 2, 1, 3]",
507
+ "505": "[1, 0, 5, 3, 2, 4]",
508
+ "506": "[2, 1, 0, 4, 3, 5]",
509
+ "507": "[3, 2, 1, 5, 4, 0]",
510
+ "508": "[4, 0, 3, 1, 5, 2]",
511
+ "509": "[5, 0, 4, 2, 1, 3]",
512
+ "510": "[0, 1, 5, 2, 3, 4]",
513
+ "511": "[1, 2, 0, 3, 4, 5]",
514
+ "512": "[2, 3, 1, 4, 5, 0]",
515
+ "513": "[3, 4, 2, 5, 0, 1]",
516
+ "514": "[4, 5, 0, 1, 2, 3]",
517
+ "515": "[5, 1, 0, 2, 3, 4]",
518
+ "516": "[0, 2, 4, 1, 3, 5]",
519
+ "517": "[1, 3, 5, 2, 4, 0]",
520
+ "518": "[2, 4, 0, 3, 5, 1]",
521
+ "519": "[3, 5, 1, 4, 0, 2]",
522
+ "520": "[4, 1, 3, 5, 2, 0]",
523
+ "521": "[5, 2, 4, 1, 3, 0]",
524
+ "522": "[0, 3, 4, 1, 2, 5]",
525
+ "523": "[1, 4, 5, 2, 3, 0]",
526
+ "524": "[2, 5, 0, 3, 4, 1]",
527
+ "525": "[3, 0, 1, 4, 5, 2]",
528
+ "526": "[4, 2, 3, 5, 1, 0]",
529
+ "527": "[5, 3, 4, 1, 2, 0]",
530
+ "528": "[0, 4, 3, 5, 1, 2]",
531
+ "529": "[1, 5, 4, 0, 2, 3]",
532
+ "530": "[2, 0, 5, 1, 3, 4]",
533
+ "531": "[3, 1, 0, 2, 4, 5]",
534
+ "532": "[4, 3, 2, 0, 5, 1]",
535
+ "533": "[5, 4, 3, 0, 1, 2]",
536
+ "534": "[0, 5, 4, 1, 2, 3]",
537
+ "535": "[1, 0, 5, 2, 3, 4]",
538
+ "536": "[2, 1, 0, 3, 4, 5]",
539
+ "537": "[3, 2, 1, 4, 5, 0]",
540
+ "538": "[4, 0, 3, 5, 1, 2]",
541
+ "539": "[5, 0, 4, 1, 2, 3]",
542
+ "540": "[0, 1, 3, 2, 4, 5]",
543
+ "541": "[1, 2, 4, 3, 5, 0]",
544
+ "542": "[2, 3, 5, 4, 0, 1]",
545
+ "543": "[3, 4, 0, 5, 1, 2]",
546
+ "544": "[4, 5, 2, 1, 3, 0]",
547
+ "545": "[5, 1, 3, 2, 4, 0]",
548
+ "546": "[0, 2, 3, 1, 5, 4]",
549
+ "547": "[1, 3, 4, 2, 0, 5]",
550
+ "548": "[2, 4, 5, 3, 1, 0]",
551
+ "549": "[3, 5, 0, 4, 2, 1]",
552
+ "550": "[4, 1, 2, 5, 0, 3]",
553
+ "551": "[5, 2, 3, 1, 0, 4]",
554
+ "552": "[0, 3, 2, 1, 5, 4]",
555
+ "553": "[1, 4, 3, 2, 0, 5]",
556
+ "554": "[2, 5, 4, 3, 1, 0]",
557
+ "555": "[3, 0, 5, 4, 2, 1]",
558
+ "556": "[4, 2, 1, 5, 0, 3]",
559
+ "557": "[5, 3, 2, 1, 0, 4]",
560
+ "558": "[0, 4, 1, 5, 2, 3]",
561
+ "559": "[1, 5, 2, 0, 3, 4]",
562
+ "560": "[2, 0, 3, 1, 4, 5]",
563
+ "561": "[3, 1, 4, 2, 5, 0]",
564
+ "562": "[4, 3, 5, 0, 1, 2]",
565
+ "563": "[5, 4, 1, 0, 2, 3]",
566
+ "564": "[0, 5, 2, 1, 3, 4]",
567
+ "565": "[1, 0, 3, 2, 4, 5]",
568
+ "566": "[2, 1, 4, 3, 5, 0]",
569
+ "567": "[3, 2, 5, 4, 0, 1]",
570
+ "568": "[4, 0, 1, 5, 2, 3]",
571
+ "569": "[5, 0, 2, 1, 3, 4]",
572
+ "570": "[0, 1, 3, 2, 5, 4]",
573
+ "571": "[1, 2, 4, 3, 0, 5]",
574
+ "572": "[2, 3, 5, 4, 1, 0]",
575
+ "573": "[3, 4, 0, 5, 2, 1]",
576
+ "574": "[4, 5, 2, 1, 0, 3]",
577
+ "575": "[5, 1, 3, 2, 0, 4]",
578
+ "576": "[0, 2, 3, 1, 4, 5]",
579
+ "577": "[1, 3, 4, 2, 5, 0]",
580
+ "578": "[2, 4, 5, 3, 0, 1]",
581
+ "579": "[3, 5, 0, 4, 1, 2]",
582
+ "580": "[4, 1, 2, 5, 3, 0]",
583
+ "581": "[5, 2, 3, 1, 4, 0]",
584
+ "582": "[0, 3, 2, 1, 4, 5]",
585
+ "583": "[1, 4, 3, 2, 5, 0]",
586
+ "584": "[2, 5, 4, 3, 0, 1]",
587
+ "585": "[3, 0, 5, 4, 1, 2]",
588
+ "586": "[4, 2, 1, 5, 3, 0]",
589
+ "587": "[5, 3, 2, 1, 4, 0]",
590
+ "588": "[0, 4, 1, 5, 3, 2]",
591
+ "589": "[1, 5, 2, 0, 4, 3]",
592
+ "590": "[2, 0, 3, 1, 5, 4]",
593
+ "591": "[3, 1, 4, 2, 0, 5]",
594
+ "592": "[4, 3, 5, 0, 2, 1]",
595
+ "593": "[5, 4, 1, 0, 3, 2]",
596
+ "594": "[0, 5, 2, 1, 4, 3]",
597
+ "595": "[1, 0, 3, 2, 5, 4]",
598
+ "596": "[2, 1, 4, 3, 0, 5]",
599
+ "597": "[3, 2, 5, 4, 1, 0]",
600
+ "598": "[4, 0, 1, 5, 3, 2]",
601
+ "599": "[5, 0, 2, 1, 4, 3]",
602
+ "600": "[0, 1, 4, 5, 2, 3]",
603
+ "601": "[1, 2, 5, 0, 3, 4]",
604
+ "602": "[2, 3, 0, 1, 4, 5]",
605
+ "603": "[3, 4, 1, 2, 5, 0]",
606
+ "604": "[4, 5, 3, 0, 1, 2]",
607
+ "605": "[5, 1, 4, 0, 2, 3]",
608
+ "606": "[0, 2, 5, 4, 1, 3]",
609
+ "607": "[1, 3, 0, 5, 2, 4]",
610
+ "608": "[2, 4, 1, 0, 3, 5]",
611
+ "609": "[3, 5, 2, 1, 4, 0]",
612
+ "610": "[4, 1, 0, 3, 5, 2]",
613
+ "611": "[5, 2, 0, 4, 1, 3]",
614
+ "612": "[0, 3, 5, 4, 1, 2]",
615
+ "613": "[1, 4, 0, 5, 2, 3]",
616
+ "614": "[2, 5, 1, 0, 3, 4]",
617
+ "615": "[3, 0, 2, 1, 4, 5]",
618
+ "616": "[4, 2, 0, 3, 5, 1]",
619
+ "617": "[5, 3, 0, 4, 1, 2]",
620
+ "618": "[0, 4, 2, 3, 5, 1]",
621
+ "619": "[1, 5, 3, 4, 0, 2]",
622
+ "620": "[2, 0, 4, 5, 1, 3]",
623
+ "621": "[3, 1, 5, 0, 2, 4]",
624
+ "622": "[4, 3, 1, 2, 0, 5]",
625
+ "623": "[5, 4, 2, 3, 0, 1]",
626
+ "624": "[0, 5, 3, 4, 1, 2]",
627
+ "625": "[1, 0, 4, 5, 2, 3]",
628
+ "626": "[2, 1, 5, 0, 3, 4]",
629
+ "627": "[3, 2, 0, 1, 4, 5]",
630
+ "628": "[4, 0, 2, 3, 5, 1]",
631
+ "629": "[5, 0, 3, 4, 1, 2]",
632
+ "630": "[0, 1, 4, 5, 3, 2]",
633
+ "631": "[1, 2, 5, 0, 4, 3]",
634
+ "632": "[2, 3, 0, 1, 5, 4]",
635
+ "633": "[3, 4, 1, 2, 0, 5]",
636
+ "634": "[4, 5, 3, 0, 2, 1]",
637
+ "635": "[5, 1, 4, 0, 3, 2]",
638
+ "636": "[0, 2, 5, 4, 3, 1]",
639
+ "637": "[1, 3, 0, 5, 4, 2]",
640
+ "638": "[2, 4, 1, 0, 5, 3]",
641
+ "639": "[3, 5, 2, 1, 0, 4]",
642
+ "640": "[4, 1, 0, 3, 2, 5]",
643
+ "641": "[5, 2, 0, 4, 3, 1]",
644
+ "642": "[0, 3, 5, 4, 2, 1]",
645
+ "643": "[1, 4, 0, 5, 3, 2]",
646
+ "644": "[2, 5, 1, 0, 4, 3]",
647
+ "645": "[3, 0, 2, 1, 5, 4]",
648
+ "646": "[4, 2, 0, 3, 1, 5]",
649
+ "647": "[5, 3, 0, 4, 2, 1]",
650
+ "648": "[0, 4, 2, 3, 1, 5]",
651
+ "649": "[1, 5, 3, 4, 2, 0]",
652
+ "650": "[2, 0, 4, 5, 3, 1]",
653
+ "651": "[3, 1, 5, 0, 4, 2]",
654
+ "652": "[4, 3, 1, 2, 5, 0]",
655
+ "653": "[5, 4, 2, 3, 1, 0]",
656
+ "654": "[0, 5, 3, 4, 2, 1]",
657
+ "655": "[1, 0, 4, 5, 3, 2]",
658
+ "656": "[2, 1, 5, 0, 4, 3]",
659
+ "657": "[3, 2, 0, 1, 5, 4]",
660
+ "658": "[4, 0, 2, 3, 1, 5]",
661
+ "659": "[5, 0, 3, 4, 2, 1]",
662
+ "660": "[0, 1, 5, 3, 4, 2]",
663
+ "661": "[1, 2, 0, 4, 5, 3]",
664
+ "662": "[2, 3, 1, 5, 0, 4]",
665
+ "663": "[3, 4, 2, 0, 1, 5]",
666
+ "664": "[4, 5, 0, 2, 3, 1]",
667
+ "665": "[5, 1, 0, 3, 4, 2]",
668
+ "666": "[0, 2, 4, 3, 5, 1]",
669
+ "667": "[1, 3, 5, 4, 0, 2]",
670
+ "668": "[2, 4, 0, 5, 1, 3]",
671
+ "669": "[3, 5, 1, 0, 2, 4]",
672
+ "670": "[4, 1, 3, 2, 0, 5]",
673
+ "671": "[5, 2, 4, 3, 0, 1]",
674
+ "672": "[0, 3, 4, 2, 5, 1]",
675
+ "673": "[1, 4, 5, 3, 0, 2]",
676
+ "674": "[2, 5, 0, 4, 1, 3]",
677
+ "675": "[3, 0, 1, 5, 2, 4]",
678
+ "676": "[4, 2, 3, 1, 0, 5]",
679
+ "677": "[5, 3, 4, 2, 0, 1]",
680
+ "678": "[0, 4, 3, 1, 2, 5]",
681
+ "679": "[1, 5, 4, 2, 3, 0]",
682
+ "680": "[2, 0, 5, 3, 4, 1]",
683
+ "681": "[3, 1, 0, 4, 5, 2]",
684
+ "682": "[4, 3, 2, 5, 1, 0]",
685
+ "683": "[5, 4, 3, 1, 2, 0]",
686
+ "684": "[0, 5, 4, 2, 3, 1]",
687
+ "685": "[1, 0, 5, 3, 4, 2]",
688
+ "686": "[2, 1, 0, 4, 5, 3]",
689
+ "687": "[3, 2, 1, 5, 0, 4]",
690
+ "688": "[4, 0, 3, 1, 2, 5]",
691
+ "689": "[5, 0, 4, 2, 3, 1]",
692
+ "690": "[0, 1, 4, 3, 5, 2]",
693
+ "691": "[1, 2, 5, 4, 0, 3]",
694
+ "692": "[2, 3, 0, 5, 1, 4]",
695
+ "693": "[3, 4, 1, 0, 2, 5]",
696
+ "694": "[4, 5, 3, 2, 0, 1]",
697
+ "695": "[5, 1, 4, 3, 0, 2]",
698
+ "696": "[0, 2, 5, 3, 4, 1]",
699
+ "697": "[1, 3, 0, 4, 5, 2]",
700
+ "698": "[2, 4, 1, 5, 0, 3]",
701
+ "699": "[3, 5, 2, 0, 1, 4]",
702
+ "700": "[4, 1, 0, 2, 3, 5]",
703
+ "701": "[5, 2, 0, 3, 4, 1]",
704
+ "702": "[0, 3, 5, 2, 4, 1]",
705
+ "703": "[1, 4, 0, 3, 5, 2]",
706
+ "704": "[2, 5, 1, 4, 0, 3]",
707
+ "705": "[3, 0, 2, 5, 1, 4]",
708
+ "706": "[4, 2, 0, 1, 3, 5]",
709
+ "707": "[5, 3, 0, 2, 4, 1]",
710
+ "708": "[0, 4, 2, 1, 3, 5]",
711
+ "709": "[1, 5, 3, 2, 4, 0]",
712
+ "710": "[2, 0, 4, 3, 5, 1]",
713
+ "711": "[3, 1, 5, 4, 0, 2]",
714
+ "712": "[4, 3, 1, 5, 2, 0]",
715
+ "713": "[5, 4, 2, 1, 3, 0]",
716
+ "714": "[0, 5, 3, 2, 4, 1]",
717
+ "715": "[1, 0, 4, 3, 5, 2]",
718
+ "716": "[2, 1, 5, 4, 0, 3]",
719
+ "717": "[3, 2, 0, 5, 1, 4]",
720
+ "718": "[4, 0, 2, 1, 3, 5]",
721
+ "719": "[5, 0, 3, 2, 4, 1]"
722
+ }
data/s6_data/test/data-00000-of-00001.arrow ADDED
@@ -0,0 +1,3 @@
 
 
 
 
1
+ version https://git-lfs.github.com/spec/v1
2
+ oid sha256:6034c12b12ce336b08e222c397fe0c78b6420e9350921bd08de330a915c2b16f
3
+ size 20004864
data/s6_data/test/dataset_info.json ADDED
@@ -0,0 +1,16 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "citation": "",
3
+ "description": "Permutation composition benchmark for the S6 group.",
4
+ "features": {
5
+ "input_sequence": {
6
+ "dtype": "string",
7
+ "_type": "Value"
8
+ },
9
+ "target": {
10
+ "dtype": "string",
11
+ "_type": "Value"
12
+ }
13
+ },
14
+ "homepage": "https://github.com/your-repo",
15
+ "license": "mit"
16
+ }
data/s6_data/test/state.json ADDED
@@ -0,0 +1,13 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "_data_files": [
3
+ {
4
+ "filename": "data-00000-of-00001.arrow"
5
+ }
6
+ ],
7
+ "_fingerprint": "acac120478c20fdf",
8
+ "_format_columns": null,
9
+ "_format_kwargs": {},
10
+ "_format_type": null,
11
+ "_output_all_columns": false,
12
+ "_split": null
13
+ }
data/s6_data/train/data-00000-of-00001.arrow ADDED
@@ -0,0 +1,3 @@
 
 
 
 
1
+ version https://git-lfs.github.com/spec/v1
2
+ oid sha256:104bc39eaba74649900d2f29161dfa4353e5ebb67a01f135ad0d40bab6851513
3
+ size 80106792
data/s6_data/train/dataset_info.json ADDED
@@ -0,0 +1,16 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "citation": "",
3
+ "description": "Permutation composition benchmark for the S6 group.",
4
+ "features": {
5
+ "input_sequence": {
6
+ "dtype": "string",
7
+ "_type": "Value"
8
+ },
9
+ "target": {
10
+ "dtype": "string",
11
+ "_type": "Value"
12
+ }
13
+ },
14
+ "homepage": "https://github.com/your-repo",
15
+ "license": "mit"
16
+ }
data/s6_data/train/state.json ADDED
@@ -0,0 +1,13 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "_data_files": [
3
+ {
4
+ "filename": "data-00000-of-00001.arrow"
5
+ }
6
+ ],
7
+ "_fingerprint": "15ef5aa63e0908c4",
8
+ "_format_columns": null,
9
+ "_format_kwargs": {},
10
+ "_format_type": null,
11
+ "_output_all_columns": false,
12
+ "_split": null
13
+ }