You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer must be formatted exactly as follows:
<think>
[your reasoning process here]
</think>
<answer>
[your answer here]
</answer>
You can choose to imitate the reasoning process of relevant algorithms or explore an appropriate solution on your own. DO NOT use code, and remember to focus on the logical flow.
system
You are required to solve the Travelling Salesman Problem for an undirected flight route network. Your objective is to determine the shortest possible route that visits each of the listed airports exactly once and returns to the starting point.

**Problem to Solve**

- Airports to visit: LOE, YAK, UTN, RGK, HOR, TKU, HRG, KGT, WAT, AUH, AOK, HVG, SAV, ASR, IAN, IRC
- Travel distances (in kilometers) between each pair of airports:
LOE to TKU: 8702
LOE to HRG: 7552
LOE to IRC: 15070
LOE to IAN: 15699
LOE to AUH: 5473
LOE to AOK: 8729
LOE to SAV: 15506
LOE to YAK: 14179
LOE to WAT: 10493
LOE to KGT: 2486
LOE to ASR: 8447
LOE to HOR: 12708
LOE to RGK: 10753
LOE to UTN: 10764
LOE to HVG: 9991
YAK to TKU: 9990
YAK to HRG: 13294
YAK to IRC: 1223
YAK to IAN: 1570
YAK to AUH: 14145
YAK to AOK: 12186
YAK to SAV: 5626
YAK to WAT: 9590
YAK to KGT: 12206
YAK to ASR: 12346
YAK to HOR: 9873
YAK to RGK: 14085
YAK to UTN: 19228
YAK to HVG: 10298
UTN to TKU: 10409
UTN to HRG: 7134
UTN to IRC: 19883
UTN to IAN: 20230
UTN to AUH: 7032
UTN to AOK: 8505
UTN to SAV: 14659
UTN to WAT: 10321
UTN to KGT: 11262
UTN to ASR: 8873
UTN to HOR: 10586
UTN to RGK: 12964
UTN to HVG: 11815
RGK to TKU: 4201
RGK to HRG: 6271
RGK to IRC: 14976
RGK to IAN: 15605
RGK to AUH: 6821
RGK to AOK: 5493
RGK to SAV: 11812
RGK to WAT: 6038
RGK to KGT: 9300
RGK to ASR: 5424
RGK to HOR: 8428
RGK to HVG: 5486
HOR to TKU: 4446
HOR to HRG: 5904
HOR to IRC: 10545
HOR to IAN: 10892
HOR to AUH: 7796
HOR to AOK: 4934
HOR to SAV: 5571
HOR to WAT: 3448
HOR to KGT: 11269
HOR to ASR: 5474
HOR to HVG: 5361
TKU to HRG: 3822
TKU to IRC: 10881
TKU to IAN: 11510
TKU to AUH: 4784
TKU to AOK: 2922
TKU to SAV: 7705
TKU to WAT: 2022
TKU to KGT: 7014
TKU to ASR: 2811
TKU to HVG: 1677
HRG to IRC: 14185
HRG to IAN: 14814
HRG to AUH: 2180
HRG to AOK: 1908
HRG to SAV: 10570
HRG to WAT: 4428
HRG to KGT: 7105
HRG to ASR: 2286
HRG to HVG: 5228
KGT to IRC: 13097
KGT to IAN: 13726
KGT to AUH: 5064
KGT to AOK: 7932
KGT to SAV: 13533
KGT to WAT: 8873
KGT to ASR: 7574
KGT to HVG: 8290
WAT to IRC: 10481
WAT to IAN: 11110
WAT to AUH: 5987
WAT to AOK: 3320
WAT to SAV: 6865
WAT to ASR: 3587
WAT to HVG: 2764
AUH to IRC: 15036
AUH to IAN: 15665
AUH to AOK: 3502
AUH to SAV: 12185
AUH to ASR: 3557
AUH to HVG: 6075
AOK to IRC: 13077
AOK to IAN: 13706
AOK to SAV: 9487
AOK to ASR: 1410
AOK to HVG: 4270
HVG to IRC: 11189
HVG to IAN: 11818
HVG to SAV: 8025
HVG to ASR: 4225
SAV to IRC: 6439
SAV to IAN: 6786
SAV to ASR: 9792
ASR to IRC: 13237
ASR to IAN: 13866
IAN to IRC: 1599
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
user
{"directed": false, "multigraph": false, "graph": {}, "nodes": [{"name": "LOE", "id": 0}, {"name": "YAK", "id": 1}, {"name": "UTN", "id": 2}, {"name": "RGK", "id": 3}, {"name": "HOR", "id": 4}, {"name": "TKU", "id": 5}, {"name": "HRG", "id": 6}, {"name": "KGT", "id": 7}, {"name": "WAT", "id": 8}, {"name": "AUH", "id": 9}, {"name": "AOK", "id": 10}, {"name": "HVG", "id": 11}, {"name": "SAV", "id": 12}, {"name": "ASR", "id": 13}, {"name": "IAN", "id": 14}, {"name": "IRC", "id": 15}], "links": [{"weight": 8702, "source": 0, "target": 5}, {"weight": 7552, "source": 0, "target": 6}, {"weight": 15070, "source": 0, "target": 15}, {"weight": 15699, "source": 0, "target": 14}, {"weight": 5473, "source": 0, "target": 9}, {"weight": 8729, "source": 0, "target": 10}, {"weight": 15506, "source": 0, "target": 12}, {"weight": 14179, "source": 0, "target": 1}, {"weight": 10493, "source": 0, "target": 8}, {"weight": 2486, "source": 0, "target": 7}, {"weight": 8447, "source": 0, "target": 13}, {"weight": 12708, "source": 0, "target": 4}, {"weight": 10753, "source": 0, "target": 3}, {"weight": 10764, "source": 0, "target": 2}, {"weight": 9991, "source": 0, "target": 11}, {"weight": 9990, "source": 1, "target": 5}, {"weight": 13294, "source": 1, "target": 6}, {"weight": 1223, "source": 1, "target": 15}, {"weight": 1570, "source": 1, "target": 14}, {"weight": 14145, "source": 1, "target": 9}, {"weight": 12186, "source": 1, "target": 10}, {"weight": 5626, "source": 1, "target": 12}, {"weight": 9590, "source": 1, "target": 8}, {"weight": 12206, "source": 1, "target": 7}, {"weight": 12346, "source": 1, "target": 13}, {"weight": 9873, "source": 1, "target": 4}, {"weight": 14085, "source": 1, "target": 3}, {"weight": 19228, "source": 1, "target": 2}, {"weight": 10298, "source": 1, "target": 11}, {"weight": 10409, "source": 2, "target": 5}, {"weight": 7134, "source": 2, "target": 6}, {"weight": 19883, "source": 2, "target": 15}, {"weight": 20230, "source": 2, "target": 14}, {"weight": 7032, "source": 2, "target": 9}, {"weight": 8505, "source": 2, "target": 10}, {"weight": 14659, "source": 2, "target": 12}, {"weight": 10321, "source": 2, "target": 8}, {"weight": 11262, "source": 2, "target": 7}, {"weight": 8873, "source": 2, "target": 13}, {"weight": 10586, "source": 2, "target": 4}, {"weight": 12964, "source": 2, "target": 3}, {"weight": 11815, "source": 2, "target": 11}, {"weight": 4201, "source": 3, "target": 5}, {"weight": 6271, "source": 3, "target": 6}, {"weight": 14976, "source": 3, "target": 15}, {"weight": 15605, "source": 3, "target": 14}, {"weight": 6821, "source": 3, "target": 9}, {"weight": 5493, "source": 3, "target": 10}, {"weight": 11812, "source": 3, "target": 12}, {"weight": 6038, "source": 3, "target": 8}, {"weight": 9300, "source": 3, "target": 7}, {"weight": 5424, "source": 3, "target": 13}, {"weight": 8428, "source": 3, "target": 4}, {"weight": 5486, "source": 3, "target": 11}, {"weight": 4446, "source": 4, "target": 5}, {"weight": 5904, "source": 4, "target": 6}, {"weight": 10545, "source": 4, "target": 15}, {"weight": 10892, "source": 4, "target": 14}, {"weight": 7796, "source": 4, "target": 9}, {"weight": 4934, "source": 4, "target": 10}, {"weight": 5571, "source": 4, "target": 12}, {"weight": 3448, "source": 4, "target": 8}, {"weight": 11269, "source": 4, "target": 7}, {"weight": 5474, "source": 4, "target": 13}, {"weight": 5361, "source": 4, "target": 11}, {"weight": 3822, "source": 5, "target": 6}, {"weight": 10881, "source": 5, "target": 15}, {"weight": 11510, "source": 5, "target": 14}, {"weight": 4784, "source": 5, "target": 9}, {"weight": 2922, "source": 5, "target": 10}, {"weight": 7705, "source": 5, "target": 12}, {"weight": 2022, "source": 5, "target": 8}, {"weight": 7014, "source": 5, "target": 7}, {"weight": 2811, "source": 5, "target": 13}, {"weight": 1677, "source": 5, "target": 11}, {"weight": 14185, "source": 6, "target": 15}, {"weight": 14814, "source": 6, "target": 14}, {"weight": 2180, "source": 6, "target": 9}, {"weight": 1908, "source": 6, "target": 10}, {"weight": 10570, "source": 6, "target": 12}, {"weight": 4428, "source": 6, "target": 8}, {"weight": 7105, "source": 6, "target": 7}, {"weight": 2286, "source": 6, "target": 13}, {"weight": 5228, "source": 6, "target": 11}, {"weight": 13097, "source": 7, "target": 15}, {"weight": 13726, "source": 7, "target": 14}, {"weight": 5064, "source": 7, "target": 9}, {"weight": 7932, "source": 7, "target": 10}, {"weight": 13533, "source": 7, "target": 12}, {"weight": 8873, "source": 7, "target": 8}, {"weight": 7574, "source": 7, "target": 13}, {"weight": 8290, "source": 7, "target": 11}, {"weight": 10481, "source": 8, "target": 15}, {"weight": 11110, "source": 8, "target": 14}, {"weight": 5987, "source": 8, "target": 9}, {"weight": 3320, "source": 8, "target": 10}, {"weight": 6865, "source": 8, "target": 12}, {"weight": 3587, "source": 8, "target": 13}, {"weight": 2764, "source": 8, "target": 11}, {"weight": 15036, "source": 9, "target": 15}, {"weight": 15665, "source": 9, "target": 14}, {"weight": 3502, "source": 9, "target": 10}, {"weight": 12185, "source": 9, "target": 12}, {"weight": 3557, "source": 9, "target": 13}, {"weight": 6075, "source": 9, "target": 11}, {"weight": 13077, "source": 10, "target": 15}, {"weight": 13706, "source": 10, "target": 14}, {"weight": 9487, "source": 10, "target": 12}, {"weight": 1410, "source": 10, "target": 13}, {"weight": 4270, "source": 10, "target": 11}, {"weight": 11189, "source": 11, "target": 15}, {"weight": 11818, "source": 11, "target": 14}, {"weight": 8025, "source": 11, "target": 12}, {"weight": 4225, "source": 11, "target": 13}, {"weight": 6439, "source": 12, "target": 15}, {"weight": 6786, "source": 12, "target": 14}, {"weight": 9792, "source": 12, "target": 13}, {"weight": 13237, "source": 13, "target": 15}, {"weight": 13866, "source": 13, "target": 14}, {"weight": 1599, "source": 14, "target": 15}]}
You are required to solve the Travelling Salesman Problem for an undirected flight route network. Your objective is to determine the shortest possible route that visits each of the listed airports exactly once and returns to the starting point.

**Problem to Solve**

- Airports to visit: LOE, YAK, UTN, RGK, HOR, TKU, HRG, KGT, WAT, AUH, AOK, HVG, SAV, ASR, IAN, IRC
- Travel distances (in kilometers) between each pair of airports:
LOE to TKU: 8702
LOE to HRG: 7552
LOE to IRC: 15070
LOE to IAN: 15699
LOE to AUH: 5473
LOE to AOK: 8729
LOE to SAV: 15506
LOE to YAK: 14179
LOE to WAT: 10493
LOE to KGT: 2486
LOE to ASR: 8447
LOE to HOR: 12708
LOE to RGK: 10753
LOE to UTN: 10764
LOE to HVG: 9991
YAK to TKU: 9990
YAK to HRG: 13294
YAK to IRC: 1223
YAK to IAN: 1570
YAK to AUH: 14145
YAK to AOK: 12186
YAK to SAV: 5626
YAK to WAT: 9590
YAK to KGT: 12206
YAK to ASR: 12346
YAK to HOR: 9873
YAK to RGK: 14085
YAK to UTN: 19228
YAK to HVG: 10298
UTN to TKU: 10409
UTN to HRG: 7134
UTN to IRC: 19883
UTN to IAN: 20230
UTN to AUH: 7032
UTN to AOK: 8505
UTN to SAV: 14659
UTN to WAT: 10321
UTN to KGT: 11262
UTN to ASR: 8873
UTN to HOR: 10586
UTN to RGK: 12964
UTN to HVG: 11815
RGK to TKU: 4201
RGK to HRG: 6271
RGK to IRC: 14976
RGK to IAN: 15605
RGK to AUH: 6821
RGK to AOK: 5493
RGK to SAV: 11812
RGK to WAT: 6038
RGK to KGT: 9300
RGK to ASR: 5424
RGK to HOR: 8428
RGK to HVG: 5486
HOR to TKU: 4446
HOR to HRG: 5904
HOR to IRC: 10545
HOR to IAN: 10892
HOR to AUH: 7796
HOR to AOK: 4934
HOR to SAV: 5571
HOR to WAT: 3448
HOR to KGT: 11269
HOR to ASR: 5474
HOR to HVG: 5361
TKU to HRG: 3822
TKU to IRC: 10881
TKU to IAN: 11510
TKU to AUH: 4784
TKU to AOK: 2922
TKU to SAV: 7705
TKU to WAT: 2022
TKU to KGT: 7014
TKU to ASR: 2811
TKU to HVG: 1677
HRG to IRC: 14185
HRG to IAN: 14814
HRG to AUH: 2180
HRG to AOK: 1908
HRG to SAV: 10570
HRG to WAT: 4428
HRG to KGT: 7105
HRG to ASR: 2286
HRG to HVG: 5228
KGT to IRC: 13097
KGT to IAN: 13726
KGT to AUH: 5064
KGT to AOK: 7932
KGT to SAV: 13533
KGT to WAT: 8873
KGT to ASR: 7574
KGT to HVG: 8290
WAT to IRC: 10481
WAT to IAN: 11110
WAT to AUH: 5987
WAT to AOK: 3320
WAT to SAV: 6865
WAT to ASR: 3587
WAT to HVG: 2764
AUH to IRC: 15036
AUH to IAN: 15665
AUH to AOK: 3502
AUH to SAV: 12185
AUH to ASR: 3557
AUH to HVG: 6075
AOK to IRC: 13077
AOK to IAN: 13706
AOK to SAV: 9487
AOK to ASR: 1410
AOK to HVG: 4270
HVG to IRC: 11189
HVG to IAN: 11818
HVG to SAV: 8025
HVG to ASR: 4225
SAV to IRC: 6439
SAV to IAN: 6786
SAV to ASR: 9792
ASR to IRC: 13237
ASR to IAN: 13866
IAN to IRC: 1599
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test