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: CKZ, AVV, NPL, MKE, STD, RBY, BGI, UTS, MDK
- Travel distances (in kilometers) between each pair of airports:
CKZ to RBY: 13692
CKZ to BGI: 10090
CKZ to MKE: 9757
CKZ to MDK: 6775
CKZ to AVV: 15909
CKZ to NPL: 17501
CKZ to STD: 11288
CKZ to UTS: 4117
AVV to RBY: 14177
AVV to BGI: 17875
AVV to MKE: 15635
AVV to MDK: 15137
AVV to NPL: 3142
AVV to STD: 17649
AVV to UTS: 15192
NPL to RBY: 12568
NPL to BGI: 15661
NPL to MKE: 13534
NPL to MDK: 16769
NPL to STD: 15435
NPL to UTS: 16271
MKE to RBY: 5297
MKE to BGI: 4317
MKE to MDK: 12040
MKE to STD: 4801
MKE to UTS: 9144
STD to RBY: 10040
STD to BGI: 1500
STD to MDK: 12308
STD to UTS: 11803
RBY to BGI: 9568
RBY to MDK: 17315
RBY to UTS: 12933
BGI to MDK: 11523
BGI to UTS: 10347
UTS to MDK: 9007
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": "CKZ", "id": 0}, {"name": "AVV", "id": 1}, {"name": "NPL", "id": 2}, {"name": "MKE", "id": 3}, {"name": "STD", "id": 4}, {"name": "RBY", "id": 5}, {"name": "BGI", "id": 6}, {"name": "UTS", "id": 7}, {"name": "MDK", "id": 8}], "links": [{"weight": 13692, "source": 0, "target": 5}, {"weight": 10090, "source": 0, "target": 6}, {"weight": 9757, "source": 0, "target": 3}, {"weight": 6775, "source": 0, "target": 8}, {"weight": 15909, "source": 0, "target": 1}, {"weight": 17501, "source": 0, "target": 2}, {"weight": 11288, "source": 0, "target": 4}, {"weight": 4117, "source": 0, "target": 7}, {"weight": 14177, "source": 1, "target": 5}, {"weight": 17875, "source": 1, "target": 6}, {"weight": 15635, "source": 1, "target": 3}, {"weight": 15137, "source": 1, "target": 8}, {"weight": 3142, "source": 1, "target": 2}, {"weight": 17649, "source": 1, "target": 4}, {"weight": 15192, "source": 1, "target": 7}, {"weight": 12568, "source": 2, "target": 5}, {"weight": 15661, "source": 2, "target": 6}, {"weight": 13534, "source": 2, "target": 3}, {"weight": 16769, "source": 2, "target": 8}, {"weight": 15435, "source": 2, "target": 4}, {"weight": 16271, "source": 2, "target": 7}, {"weight": 5297, "source": 3, "target": 5}, {"weight": 4317, "source": 3, "target": 6}, {"weight": 12040, "source": 3, "target": 8}, {"weight": 4801, "source": 3, "target": 4}, {"weight": 9144, "source": 3, "target": 7}, {"weight": 10040, "source": 4, "target": 5}, {"weight": 1500, "source": 4, "target": 6}, {"weight": 12308, "source": 4, "target": 8}, {"weight": 11803, "source": 4, "target": 7}, {"weight": 9568, "source": 5, "target": 6}, {"weight": 17315, "source": 5, "target": 8}, {"weight": 12933, "source": 5, "target": 7}, {"weight": 11523, "source": 6, "target": 8}, {"weight": 10347, "source": 6, "target": 7}, {"weight": 9007, "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: CKZ, AVV, NPL, MKE, STD, RBY, BGI, UTS, MDK
- Travel distances (in kilometers) between each pair of airports:
CKZ to RBY: 13692
CKZ to BGI: 10090
CKZ to MKE: 9757
CKZ to MDK: 6775
CKZ to AVV: 15909
CKZ to NPL: 17501
CKZ to STD: 11288
CKZ to UTS: 4117
AVV to RBY: 14177
AVV to BGI: 17875
AVV to MKE: 15635
AVV to MDK: 15137
AVV to NPL: 3142
AVV to STD: 17649
AVV to UTS: 15192
NPL to RBY: 12568
NPL to BGI: 15661
NPL to MKE: 13534
NPL to MDK: 16769
NPL to STD: 15435
NPL to UTS: 16271
MKE to RBY: 5297
MKE to BGI: 4317
MKE to MDK: 12040
MKE to STD: 4801
MKE to UTS: 9144
STD to RBY: 10040
STD to BGI: 1500
STD to MDK: 12308
STD to UTS: 11803
RBY to BGI: 9568
RBY to MDK: 17315
RBY to UTS: 12933
BGI to MDK: 11523
BGI to UTS: 10347
UTS to MDK: 9007
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test