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: LUN, HLH, CJS, YYR, MUK, GFK, DMK, NSI, LRH
- Travel distances (in kilometers) between each pair of airports:
LUN to CJS: 15620
LUN to GFK: 14378
LUN to LRH: 8563
LUN to YYR: 12777
LUN to NSI: 3302
LUN to DMK: 9589
LUN to HLH: 11800
LUN to MUK: 17491
HLH to CJS: 11506
HLH to GFK: 11270
HLH to LRH: 9420
HLH to YYR: 13264
HLH to NSI: 11880
HLH to DMK: 4112
HLH to MUK: 12974
CJS to GFK: 3128
CJS to LRH: 9368
CJS to YYR: 5129
CJS to NSI: 12804
CJS to DMK: 14519
CJS to MUK: 9221
YYR to GFK: 3377
YYR to LRH: 5305
YYR to NSI: 10003
YYR to DMK: 14120
YYR to MUK: 13184
MUK to GFK: 10172
MUK to LRH: 17165
MUK to NSI: 19339
MUK to DMK: 12852
GFK to LRH: 7655
GFK to NSI: 11503
GFK to DMK: 14560
DMK to LRH: 9868
DMK to NSI: 10385
NSI to LRH: 5555
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": "LUN", "id": 0}, {"name": "HLH", "id": 1}, {"name": "CJS", "id": 2}, {"name": "YYR", "id": 3}, {"name": "MUK", "id": 4}, {"name": "GFK", "id": 5}, {"name": "DMK", "id": 6}, {"name": "NSI", "id": 7}, {"name": "LRH", "id": 8}], "links": [{"weight": 15620, "source": 0, "target": 2}, {"weight": 14378, "source": 0, "target": 5}, {"weight": 8563, "source": 0, "target": 8}, {"weight": 12777, "source": 0, "target": 3}, {"weight": 3302, "source": 0, "target": 7}, {"weight": 9589, "source": 0, "target": 6}, {"weight": 11800, "source": 0, "target": 1}, {"weight": 17491, "source": 0, "target": 4}, {"weight": 11506, "source": 1, "target": 2}, {"weight": 11270, "source": 1, "target": 5}, {"weight": 9420, "source": 1, "target": 8}, {"weight": 13264, "source": 1, "target": 3}, {"weight": 11880, "source": 1, "target": 7}, {"weight": 4112, "source": 1, "target": 6}, {"weight": 12974, "source": 1, "target": 4}, {"weight": 3128, "source": 2, "target": 5}, {"weight": 9368, "source": 2, "target": 8}, {"weight": 5129, "source": 2, "target": 3}, {"weight": 12804, "source": 2, "target": 7}, {"weight": 14519, "source": 2, "target": 6}, {"weight": 9221, "source": 2, "target": 4}, {"weight": 3377, "source": 3, "target": 5}, {"weight": 5305, "source": 3, "target": 8}, {"weight": 10003, "source": 3, "target": 7}, {"weight": 14120, "source": 3, "target": 6}, {"weight": 13184, "source": 3, "target": 4}, {"weight": 10172, "source": 4, "target": 5}, {"weight": 17165, "source": 4, "target": 8}, {"weight": 19339, "source": 4, "target": 7}, {"weight": 12852, "source": 4, "target": 6}, {"weight": 7655, "source": 5, "target": 8}, {"weight": 11503, "source": 5, "target": 7}, {"weight": 14560, "source": 5, "target": 6}, {"weight": 9868, "source": 6, "target": 8}, {"weight": 10385, "source": 6, "target": 7}, {"weight": 5555, "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: LUN, HLH, CJS, YYR, MUK, GFK, DMK, NSI, LRH
- Travel distances (in kilometers) between each pair of airports:
LUN to CJS: 15620
LUN to GFK: 14378
LUN to LRH: 8563
LUN to YYR: 12777
LUN to NSI: 3302
LUN to DMK: 9589
LUN to HLH: 11800
LUN to MUK: 17491
HLH to CJS: 11506
HLH to GFK: 11270
HLH to LRH: 9420
HLH to YYR: 13264
HLH to NSI: 11880
HLH to DMK: 4112
HLH to MUK: 12974
CJS to GFK: 3128
CJS to LRH: 9368
CJS to YYR: 5129
CJS to NSI: 12804
CJS to DMK: 14519
CJS to MUK: 9221
YYR to GFK: 3377
YYR to LRH: 5305
YYR to NSI: 10003
YYR to DMK: 14120
YYR to MUK: 13184
MUK to GFK: 10172
MUK to LRH: 17165
MUK to NSI: 19339
MUK to DMK: 12852
GFK to LRH: 7655
GFK to NSI: 11503
GFK to DMK: 14560
DMK to LRH: 9868
DMK to NSI: 10385
NSI to LRH: 5555
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test