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: ERF, HIB, ZAD, TCZ, ABL, YVZ, APO, WRO, LOH
- Travel distances (in kilometers) between each pair of airports:
ERF to ZAD: 2217
ERF to WRO: 1966
ERF to ABL: 11935
ERF to TCZ: 9602
ERF to APO: 9764
ERF to HIB: 7827
ERF to LOH: 10500
ERF to YVZ: 8028
HIB to ZAD: 8163
HIB to WRO: 7847
HIB to ABL: 5408
HIB to TCZ: 13449
HIB to APO: 5488
HIB to LOH: 5972
HIB to YVZ: 1367
ZAD to WRO: 1022
ZAD to ABL: 12442
ZAD to TCZ: 8675
ZAD to APO: 10033
ZAD to LOH: 10769
ZAD to YVZ: 8651
TCZ to WRO: 8072
TCZ to ABL: 14463
TCZ to APO: 17665
TCZ to LOH: 18098
TCZ to YVZ: 13180
ABL to WRO: 11939
ABL to APO: 10168
ABL to LOH: 10505
ABL to YVZ: 5779
YVZ to WRO: 8354
YVZ to APO: 6295
YVZ to LOH: 6779
APO to WRO: 10101
APO to LOH: 1479
WRO to LOH: 10837
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": "ERF", "id": 0}, {"name": "HIB", "id": 1}, {"name": "ZAD", "id": 2}, {"name": "TCZ", "id": 3}, {"name": "ABL", "id": 4}, {"name": "YVZ", "id": 5}, {"name": "APO", "id": 6}, {"name": "WRO", "id": 7}, {"name": "LOH", "id": 8}], "links": [{"weight": 2217, "source": 0, "target": 2}, {"weight": 1966, "source": 0, "target": 7}, {"weight": 11935, "source": 0, "target": 4}, {"weight": 9602, "source": 0, "target": 3}, {"weight": 9764, "source": 0, "target": 6}, {"weight": 7827, "source": 0, "target": 1}, {"weight": 10500, "source": 0, "target": 8}, {"weight": 8028, "source": 0, "target": 5}, {"weight": 8163, "source": 1, "target": 2}, {"weight": 7847, "source": 1, "target": 7}, {"weight": 5408, "source": 1, "target": 4}, {"weight": 13449, "source": 1, "target": 3}, {"weight": 5488, "source": 1, "target": 6}, {"weight": 5972, "source": 1, "target": 8}, {"weight": 1367, "source": 1, "target": 5}, {"weight": 1022, "source": 2, "target": 7}, {"weight": 12442, "source": 2, "target": 4}, {"weight": 8675, "source": 2, "target": 3}, {"weight": 10033, "source": 2, "target": 6}, {"weight": 10769, "source": 2, "target": 8}, {"weight": 8651, "source": 2, "target": 5}, {"weight": 8072, "source": 3, "target": 7}, {"weight": 14463, "source": 3, "target": 4}, {"weight": 17665, "source": 3, "target": 6}, {"weight": 18098, "source": 3, "target": 8}, {"weight": 13180, "source": 3, "target": 5}, {"weight": 11939, "source": 4, "target": 7}, {"weight": 10168, "source": 4, "target": 6}, {"weight": 10505, "source": 4, "target": 8}, {"weight": 5779, "source": 4, "target": 5}, {"weight": 8354, "source": 5, "target": 7}, {"weight": 6295, "source": 5, "target": 6}, {"weight": 6779, "source": 5, "target": 8}, {"weight": 10101, "source": 6, "target": 7}, {"weight": 1479, "source": 6, "target": 8}, {"weight": 10837, "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: ERF, HIB, ZAD, TCZ, ABL, YVZ, APO, WRO, LOH
- Travel distances (in kilometers) between each pair of airports:
ERF to ZAD: 2217
ERF to WRO: 1966
ERF to ABL: 11935
ERF to TCZ: 9602
ERF to APO: 9764
ERF to HIB: 7827
ERF to LOH: 10500
ERF to YVZ: 8028
HIB to ZAD: 8163
HIB to WRO: 7847
HIB to ABL: 5408
HIB to TCZ: 13449
HIB to APO: 5488
HIB to LOH: 5972
HIB to YVZ: 1367
ZAD to WRO: 1022
ZAD to ABL: 12442
ZAD to TCZ: 8675
ZAD to APO: 10033
ZAD to LOH: 10769
ZAD to YVZ: 8651
TCZ to WRO: 8072
TCZ to ABL: 14463
TCZ to APO: 17665
TCZ to LOH: 18098
TCZ to YVZ: 13180
ABL to WRO: 11939
ABL to APO: 10168
ABL to LOH: 10505
ABL to YVZ: 5779
YVZ to WRO: 8354
YVZ to APO: 6295
YVZ to LOH: 6779
APO to WRO: 10101
APO to LOH: 1479
WRO to LOH: 10837
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test