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: TGU, IXB, HUH, CNJ, ZAT, ISU, GAN, YPR, DHM, THL, STL
- Travel distances (in kilometers) between each pair of airports:
TGU to STL: 2821
TGU to IXB: 16126
TGU to THL: 16839
TGU to YPR: 5879
TGU to DHM: 15410
TGU to ZAT: 15363
TGU to ISU: 12608
TGU to CNJ: 16906
TGU to GAN: 17678
TGU to HUH: 10681
IXB to STL: 13560
IXB to THL: 2038
IXB to YPR: 12976
IXB to DHM: 1532
IXB to ZAT: 2074
IXB to ISU: 4207
IXB to CNJ: 8061
IXB to GAN: 3597
IXB to HUH: 15196
HUH to STL: 9345
HUH to THL: 14613
HUH to YPR: 9283
HUH to DHM: 15937
HUH to ZAT: 13232
HUH to ISU: 17897
HUH to CNJ: 7741
HUH to GAN: 16197
CNJ to STL: 15570
CNJ to THL: 7235
CNJ to YPR: 14140
CNJ to DHM: 9306
CNJ to ZAT: 7167
CNJ to ISU: 11901
CNJ to GAN: 8615
ZAT to STL: 12828
ZAT to THL: 1491
ZAT to YPR: 11097
ZAT to DHM: 3256
ZAT to ISU: 5931
ZAT to GAN: 4561
ISU to STL: 10595
ISU to THL: 5985
ISU to YPR: 11951
ISU to DHM: 3491
ISU to GAN: 5079
GAN to STL: 15604
GAN to THL: 4716
GAN to YPR: 15559
GAN to DHM: 3734
YPR to STL: 3702
YPR to THL: 12573
YPR to DHM: 13462
DHM to STL: 12844
DHM to THL: 3310
THL to STL: 14304
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": "TGU", "id": 0}, {"name": "IXB", "id": 1}, {"name": "HUH", "id": 2}, {"name": "CNJ", "id": 3}, {"name": "ZAT", "id": 4}, {"name": "ISU", "id": 5}, {"name": "GAN", "id": 6}, {"name": "YPR", "id": 7}, {"name": "DHM", "id": 8}, {"name": "THL", "id": 9}, {"name": "STL", "id": 10}], "links": [{"weight": 2821, "source": 0, "target": 10}, {"weight": 16126, "source": 0, "target": 1}, {"weight": 16839, "source": 0, "target": 9}, {"weight": 5879, "source": 0, "target": 7}, {"weight": 15410, "source": 0, "target": 8}, {"weight": 15363, "source": 0, "target": 4}, {"weight": 12608, "source": 0, "target": 5}, {"weight": 16906, "source": 0, "target": 3}, {"weight": 17678, "source": 0, "target": 6}, {"weight": 10681, "source": 0, "target": 2}, {"weight": 13560, "source": 1, "target": 10}, {"weight": 2038, "source": 1, "target": 9}, {"weight": 12976, "source": 1, "target": 7}, {"weight": 1532, "source": 1, "target": 8}, {"weight": 2074, "source": 1, "target": 4}, {"weight": 4207, "source": 1, "target": 5}, {"weight": 8061, "source": 1, "target": 3}, {"weight": 3597, "source": 1, "target": 6}, {"weight": 15196, "source": 1, "target": 2}, {"weight": 9345, "source": 2, "target": 10}, {"weight": 14613, "source": 2, "target": 9}, {"weight": 9283, "source": 2, "target": 7}, {"weight": 15937, "source": 2, "target": 8}, {"weight": 13232, "source": 2, "target": 4}, {"weight": 17897, "source": 2, "target": 5}, {"weight": 7741, "source": 2, "target": 3}, {"weight": 16197, "source": 2, "target": 6}, {"weight": 15570, "source": 3, "target": 10}, {"weight": 7235, "source": 3, "target": 9}, {"weight": 14140, "source": 3, "target": 7}, {"weight": 9306, "source": 3, "target": 8}, {"weight": 7167, "source": 3, "target": 4}, {"weight": 11901, "source": 3, "target": 5}, {"weight": 8615, "source": 3, "target": 6}, {"weight": 12828, "source": 4, "target": 10}, {"weight": 1491, "source": 4, "target": 9}, {"weight": 11097, "source": 4, "target": 7}, {"weight": 3256, "source": 4, "target": 8}, {"weight": 5931, "source": 4, "target": 5}, {"weight": 4561, "source": 4, "target": 6}, {"weight": 10595, "source": 5, "target": 10}, {"weight": 5985, "source": 5, "target": 9}, {"weight": 11951, "source": 5, "target": 7}, {"weight": 3491, "source": 5, "target": 8}, {"weight": 5079, "source": 5, "target": 6}, {"weight": 15604, "source": 6, "target": 10}, {"weight": 4716, "source": 6, "target": 9}, {"weight": 15559, "source": 6, "target": 7}, {"weight": 3734, "source": 6, "target": 8}, {"weight": 3702, "source": 7, "target": 10}, {"weight": 12573, "source": 7, "target": 9}, {"weight": 13462, "source": 7, "target": 8}, {"weight": 12844, "source": 8, "target": 10}, {"weight": 3310, "source": 8, "target": 9}, {"weight": 14304, "source": 9, "target": 10}]}
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: TGU, IXB, HUH, CNJ, ZAT, ISU, GAN, YPR, DHM, THL, STL
- Travel distances (in kilometers) between each pair of airports:
TGU to STL: 2821
TGU to IXB: 16126
TGU to THL: 16839
TGU to YPR: 5879
TGU to DHM: 15410
TGU to ZAT: 15363
TGU to ISU: 12608
TGU to CNJ: 16906
TGU to GAN: 17678
TGU to HUH: 10681
IXB to STL: 13560
IXB to THL: 2038
IXB to YPR: 12976
IXB to DHM: 1532
IXB to ZAT: 2074
IXB to ISU: 4207
IXB to CNJ: 8061
IXB to GAN: 3597
IXB to HUH: 15196
HUH to STL: 9345
HUH to THL: 14613
HUH to YPR: 9283
HUH to DHM: 15937
HUH to ZAT: 13232
HUH to ISU: 17897
HUH to CNJ: 7741
HUH to GAN: 16197
CNJ to STL: 15570
CNJ to THL: 7235
CNJ to YPR: 14140
CNJ to DHM: 9306
CNJ to ZAT: 7167
CNJ to ISU: 11901
CNJ to GAN: 8615
ZAT to STL: 12828
ZAT to THL: 1491
ZAT to YPR: 11097
ZAT to DHM: 3256
ZAT to ISU: 5931
ZAT to GAN: 4561
ISU to STL: 10595
ISU to THL: 5985
ISU to YPR: 11951
ISU to DHM: 3491
ISU to GAN: 5079
GAN to STL: 15604
GAN to THL: 4716
GAN to YPR: 15559
GAN to DHM: 3734
YPR to STL: 3702
YPR to THL: 12573
YPR to DHM: 13462
DHM to STL: 12844
DHM to THL: 3310
THL to STL: 14304
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test