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: HVB, KIF, GMB, IIL, DLU, RJA, RBR, KGS, BDL
- Travel distances (in kilometers) between each pair of airports:
HVB to KGS: 15545
HVB to DLU: 8607
HVB to RJA: 10045
HVB to BDL: 15820
HVB to RBR: 17472
HVB to IIL: 13541
HVB to GMB: 14458
HVB to KIF: 14739
KIF to KGS: 9949
KIF to DLU: 13305
KIF to RJA: 14798
KIF to BDL: 2130
KIF to RBR: 8541
KIF to IIL: 12283
KIF to GMB: 13508
GMB to KGS: 4273
GMB to DLU: 7705
GMB to RJA: 5285
GMB to BDL: 11941
GMB to RBR: 13298
GMB to IIL: 4211
IIL to KGS: 3421
IIL to DLU: 5950
IIL to RJA: 4611
IIL to BDL: 10666
IIL to RBR: 14733
DLU to KGS: 8034
DLU to RJA: 3281
DLU to BDL: 13368
DLU to RBR: 19022
RJA to KGS: 6228
RJA to BDL: 13709
RJA to RBR: 17424
RBR to KGS: 12102
RBR to BDL: 6726
KGS to BDL: 8324
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": "HVB", "id": 0}, {"name": "KIF", "id": 1}, {"name": "GMB", "id": 2}, {"name": "IIL", "id": 3}, {"name": "DLU", "id": 4}, {"name": "RJA", "id": 5}, {"name": "RBR", "id": 6}, {"name": "KGS", "id": 7}, {"name": "BDL", "id": 8}], "links": [{"weight": 15545, "source": 0, "target": 7}, {"weight": 8607, "source": 0, "target": 4}, {"weight": 10045, "source": 0, "target": 5}, {"weight": 15820, "source": 0, "target": 8}, {"weight": 17472, "source": 0, "target": 6}, {"weight": 13541, "source": 0, "target": 3}, {"weight": 14458, "source": 0, "target": 2}, {"weight": 14739, "source": 0, "target": 1}, {"weight": 9949, "source": 1, "target": 7}, {"weight": 13305, "source": 1, "target": 4}, {"weight": 14798, "source": 1, "target": 5}, {"weight": 2130, "source": 1, "target": 8}, {"weight": 8541, "source": 1, "target": 6}, {"weight": 12283, "source": 1, "target": 3}, {"weight": 13508, "source": 1, "target": 2}, {"weight": 4273, "source": 2, "target": 7}, {"weight": 7705, "source": 2, "target": 4}, {"weight": 5285, "source": 2, "target": 5}, {"weight": 11941, "source": 2, "target": 8}, {"weight": 13298, "source": 2, "target": 6}, {"weight": 4211, "source": 2, "target": 3}, {"weight": 3421, "source": 3, "target": 7}, {"weight": 5950, "source": 3, "target": 4}, {"weight": 4611, "source": 3, "target": 5}, {"weight": 10666, "source": 3, "target": 8}, {"weight": 14733, "source": 3, "target": 6}, {"weight": 8034, "source": 4, "target": 7}, {"weight": 3281, "source": 4, "target": 5}, {"weight": 13368, "source": 4, "target": 8}, {"weight": 19022, "source": 4, "target": 6}, {"weight": 6228, "source": 5, "target": 7}, {"weight": 13709, "source": 5, "target": 8}, {"weight": 17424, "source": 5, "target": 6}, {"weight": 12102, "source": 6, "target": 7}, {"weight": 6726, "source": 6, "target": 8}, {"weight": 8324, "source": 7, "target": 8}]}
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: HVB, KIF, GMB, IIL, DLU, RJA, RBR, KGS, BDL
- Travel distances (in kilometers) between each pair of airports:
HVB to KGS: 15545
HVB to DLU: 8607
HVB to RJA: 10045
HVB to BDL: 15820
HVB to RBR: 17472
HVB to IIL: 13541
HVB to GMB: 14458
HVB to KIF: 14739
KIF to KGS: 9949
KIF to DLU: 13305
KIF to RJA: 14798
KIF to BDL: 2130
KIF to RBR: 8541
KIF to IIL: 12283
KIF to GMB: 13508
GMB to KGS: 4273
GMB to DLU: 7705
GMB to RJA: 5285
GMB to BDL: 11941
GMB to RBR: 13298
GMB to IIL: 4211
IIL to KGS: 3421
IIL to DLU: 5950
IIL to RJA: 4611
IIL to BDL: 10666
IIL to RBR: 14733
DLU to KGS: 8034
DLU to RJA: 3281
DLU to BDL: 13368
DLU to RBR: 19022
RJA to KGS: 6228
RJA to BDL: 13709
RJA to RBR: 17424
RBR to KGS: 12102
RBR to BDL: 6726
KGS to BDL: 8324
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test