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: YQB, PNP, QFN, URY, SCO, YQR, NGE, YWP, TUS
- Travel distances (in kilometers) between each pair of airports:
YQB to TUS: 3722
YQB to YQR: 2581
YQB to PNP: 16246
YQB to SCO: 9035
YQB to QFN: 6548
YQB to NGE: 10104
YQB to URY: 10815
YQB to YWP: 2170
PNP to TUS: 13143
PNP to YQR: 13822
PNP to SCO: 11396
PNP to QFN: 17489
PNP to NGE: 15759
PNP to URY: 12914
PNP to YWP: 15480
QFN to TUS: 8788
QFN to YQR: 7644
QFN to SCO: 7006
QFN to NGE: 9086
QFN to URY: 9627
QFN to YWP: 7643
URY to TUS: 14344
URY to YQR: 13203
URY to SCO: 3363
URY to NGE: 4423
URY to YWP: 12980
SCO to TUS: 11726
SCO to YQR: 10582
SCO to NGE: 5909
SCO to YWP: 10562
YQR to TUS: 2203
YQR to NGE: 12333
YQR to YWP: 1659
NGE to TUS: 13299
NGE to YWP: 11901
YWP to TUS: 3416
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": "YQB", "id": 0}, {"name": "PNP", "id": 1}, {"name": "QFN", "id": 2}, {"name": "URY", "id": 3}, {"name": "SCO", "id": 4}, {"name": "YQR", "id": 5}, {"name": "NGE", "id": 6}, {"name": "YWP", "id": 7}, {"name": "TUS", "id": 8}], "links": [{"weight": 3722, "source": 0, "target": 8}, {"weight": 2581, "source": 0, "target": 5}, {"weight": 16246, "source": 0, "target": 1}, {"weight": 9035, "source": 0, "target": 4}, {"weight": 6548, "source": 0, "target": 2}, {"weight": 10104, "source": 0, "target": 6}, {"weight": 10815, "source": 0, "target": 3}, {"weight": 2170, "source": 0, "target": 7}, {"weight": 13143, "source": 1, "target": 8}, {"weight": 13822, "source": 1, "target": 5}, {"weight": 11396, "source": 1, "target": 4}, {"weight": 17489, "source": 1, "target": 2}, {"weight": 15759, "source": 1, "target": 6}, {"weight": 12914, "source": 1, "target": 3}, {"weight": 15480, "source": 1, "target": 7}, {"weight": 8788, "source": 2, "target": 8}, {"weight": 7644, "source": 2, "target": 5}, {"weight": 7006, "source": 2, "target": 4}, {"weight": 9086, "source": 2, "target": 6}, {"weight": 9627, "source": 2, "target": 3}, {"weight": 7643, "source": 2, "target": 7}, {"weight": 14344, "source": 3, "target": 8}, {"weight": 13203, "source": 3, "target": 5}, {"weight": 3363, "source": 3, "target": 4}, {"weight": 4423, "source": 3, "target": 6}, {"weight": 12980, "source": 3, "target": 7}, {"weight": 11726, "source": 4, "target": 8}, {"weight": 10582, "source": 4, "target": 5}, {"weight": 5909, "source": 4, "target": 6}, {"weight": 10562, "source": 4, "target": 7}, {"weight": 2203, "source": 5, "target": 8}, {"weight": 12333, "source": 5, "target": 6}, {"weight": 1659, "source": 5, "target": 7}, {"weight": 13299, "source": 6, "target": 8}, {"weight": 11901, "source": 6, "target": 7}, {"weight": 3416, "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: YQB, PNP, QFN, URY, SCO, YQR, NGE, YWP, TUS
- Travel distances (in kilometers) between each pair of airports:
YQB to TUS: 3722
YQB to YQR: 2581
YQB to PNP: 16246
YQB to SCO: 9035
YQB to QFN: 6548
YQB to NGE: 10104
YQB to URY: 10815
YQB to YWP: 2170
PNP to TUS: 13143
PNP to YQR: 13822
PNP to SCO: 11396
PNP to QFN: 17489
PNP to NGE: 15759
PNP to URY: 12914
PNP to YWP: 15480
QFN to TUS: 8788
QFN to YQR: 7644
QFN to SCO: 7006
QFN to NGE: 9086
QFN to URY: 9627
QFN to YWP: 7643
URY to TUS: 14344
URY to YQR: 13203
URY to SCO: 3363
URY to NGE: 4423
URY to YWP: 12980
SCO to TUS: 11726
SCO to YQR: 10582
SCO to NGE: 5909
SCO to YWP: 10562
YQR to TUS: 2203
YQR to NGE: 12333
YQR to YWP: 1659
NGE to TUS: 13299
NGE to YWP: 11901
YWP to TUS: 3416
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test