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, GFN, MLH, SNA, BTS, TAB, BHJ, AKP, ZTB
- Travel distances (in kilometers) between each pair of airports:
ERF to SNA: 9574
ERF to AKP: 11392
ERF to BHJ: 7394
ERF to MLH: 1775
ERF to TAB: 7794
ERF to BTS: 2104
ERF to ZTB: 5892
ERF to GFN: 17448
GFN to SNA: 13048
GFN to AKP: 13970
GFN to BHJ: 11281
GFN to MLH: 17287
GFN to TAB: 17447
GFN to BTS: 16914
GFN to ZTB: 17792
MLH to SNA: 9526
MLH to AKP: 11337
MLH to BHJ: 7231
MLH to TAB: 7743
MLH to BTS: 1421
MLH to ZTB: 5228
SNA to AKP: 4444
SNA to BHJ: 15450
SNA to TAB: 6368
SNA to BTS: 10023
SNA to ZTB: 5213
BTS to AKP: 11705
BTS to BHJ: 7053
BTS to TAB: 8302
BTS to ZTB: 5807
TAB to AKP: 9785
TAB to BHJ: 14733
TAB to ZTB: 5297
BHJ to AKP: 16905
BHJ to ZTB: 12244
AKP to ZTB: 7658
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": "GFN", "id": 1}, {"name": "MLH", "id": 2}, {"name": "SNA", "id": 3}, {"name": "BTS", "id": 4}, {"name": "TAB", "id": 5}, {"name": "BHJ", "id": 6}, {"name": "AKP", "id": 7}, {"name": "ZTB", "id": 8}], "links": [{"weight": 9574, "source": 0, "target": 3}, {"weight": 11392, "source": 0, "target": 7}, {"weight": 7394, "source": 0, "target": 6}, {"weight": 1775, "source": 0, "target": 2}, {"weight": 7794, "source": 0, "target": 5}, {"weight": 2104, "source": 0, "target": 4}, {"weight": 5892, "source": 0, "target": 8}, {"weight": 17448, "source": 0, "target": 1}, {"weight": 13048, "source": 1, "target": 3}, {"weight": 13970, "source": 1, "target": 7}, {"weight": 11281, "source": 1, "target": 6}, {"weight": 17287, "source": 1, "target": 2}, {"weight": 17447, "source": 1, "target": 5}, {"weight": 16914, "source": 1, "target": 4}, {"weight": 17792, "source": 1, "target": 8}, {"weight": 9526, "source": 2, "target": 3}, {"weight": 11337, "source": 2, "target": 7}, {"weight": 7231, "source": 2, "target": 6}, {"weight": 7743, "source": 2, "target": 5}, {"weight": 1421, "source": 2, "target": 4}, {"weight": 5228, "source": 2, "target": 8}, {"weight": 4444, "source": 3, "target": 7}, {"weight": 15450, "source": 3, "target": 6}, {"weight": 6368, "source": 3, "target": 5}, {"weight": 10023, "source": 3, "target": 4}, {"weight": 5213, "source": 3, "target": 8}, {"weight": 11705, "source": 4, "target": 7}, {"weight": 7053, "source": 4, "target": 6}, {"weight": 8302, "source": 4, "target": 5}, {"weight": 5807, "source": 4, "target": 8}, {"weight": 9785, "source": 5, "target": 7}, {"weight": 14733, "source": 5, "target": 6}, {"weight": 5297, "source": 5, "target": 8}, {"weight": 16905, "source": 6, "target": 7}, {"weight": 12244, "source": 6, "target": 8}, {"weight": 7658, "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, GFN, MLH, SNA, BTS, TAB, BHJ, AKP, ZTB
- Travel distances (in kilometers) between each pair of airports:
ERF to SNA: 9574
ERF to AKP: 11392
ERF to BHJ: 7394
ERF to MLH: 1775
ERF to TAB: 7794
ERF to BTS: 2104
ERF to ZTB: 5892
ERF to GFN: 17448
GFN to SNA: 13048
GFN to AKP: 13970
GFN to BHJ: 11281
GFN to MLH: 17287
GFN to TAB: 17447
GFN to BTS: 16914
GFN to ZTB: 17792
MLH to SNA: 9526
MLH to AKP: 11337
MLH to BHJ: 7231
MLH to TAB: 7743
MLH to BTS: 1421
MLH to ZTB: 5228
SNA to AKP: 4444
SNA to BHJ: 15450
SNA to TAB: 6368
SNA to BTS: 10023
SNA to ZTB: 5213
BTS to AKP: 11705
BTS to BHJ: 7053
BTS to TAB: 8302
BTS to ZTB: 5807
TAB to AKP: 9785
TAB to BHJ: 14733
TAB to ZTB: 5297
BHJ to AKP: 16905
BHJ to ZTB: 12244
AKP to ZTB: 7658
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test