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: DNK, ERC, OVB, SZX, YAT, MCI, GFF, TLV, IRC
- Travel distances (in kilometers) between each pair of airports:
DNK to TLV: 1817
DNK to OVB: 3596
DNK to SZX: 7887
DNK to IRC: 12290
DNK to MCI: 9199
DNK to ERC: 1905
DNK to YAT: 8853
DNK to GFF: 15218
ERC to OVB: 4711
ERC to SZX: 8457
ERC to TLV: 1981
ERC to IRC: 13534
ERC to MCI: 10349
ERC to YAT: 9754
ERC to GFF: 15625
OVB to SZX: 4657
OVB to TLV: 4535
OVB to IRC: 14320
OVB to MCI: 11290
OVB to YAT: 11098
OVB to GFF: 12327
SZX to TLV: 7782
SZX to IRC: 13086
SZX to MCI: 12808
SZX to YAT: 13605
SZX to GFF: 8304
YAT to TLV: 9956
YAT to IRC: 6299
YAT to MCI: 2433
YAT to GFF: 16548
MCI to TLV: 10568
MCI to IRC: 5060
MCI to GFF: 14720
GFF to TLV: 14639
GFF to IRC: 13741
TLV to IRC: 13756
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": "DNK", "id": 0}, {"name": "ERC", "id": 1}, {"name": "OVB", "id": 2}, {"name": "SZX", "id": 3}, {"name": "YAT", "id": 4}, {"name": "MCI", "id": 5}, {"name": "GFF", "id": 6}, {"name": "TLV", "id": 7}, {"name": "IRC", "id": 8}], "links": [{"weight": 1817, "source": 0, "target": 7}, {"weight": 3596, "source": 0, "target": 2}, {"weight": 7887, "source": 0, "target": 3}, {"weight": 12290, "source": 0, "target": 8}, {"weight": 9199, "source": 0, "target": 5}, {"weight": 1905, "source": 0, "target": 1}, {"weight": 8853, "source": 0, "target": 4}, {"weight": 15218, "source": 0, "target": 6}, {"weight": 4711, "source": 1, "target": 2}, {"weight": 8457, "source": 1, "target": 3}, {"weight": 1981, "source": 1, "target": 7}, {"weight": 13534, "source": 1, "target": 8}, {"weight": 10349, "source": 1, "target": 5}, {"weight": 9754, "source": 1, "target": 4}, {"weight": 15625, "source": 1, "target": 6}, {"weight": 4657, "source": 2, "target": 3}, {"weight": 4535, "source": 2, "target": 7}, {"weight": 14320, "source": 2, "target": 8}, {"weight": 11290, "source": 2, "target": 5}, {"weight": 11098, "source": 2, "target": 4}, {"weight": 12327, "source": 2, "target": 6}, {"weight": 7782, "source": 3, "target": 7}, {"weight": 13086, "source": 3, "target": 8}, {"weight": 12808, "source": 3, "target": 5}, {"weight": 13605, "source": 3, "target": 4}, {"weight": 8304, "source": 3, "target": 6}, {"weight": 9956, "source": 4, "target": 7}, {"weight": 6299, "source": 4, "target": 8}, {"weight": 2433, "source": 4, "target": 5}, {"weight": 16548, "source": 4, "target": 6}, {"weight": 10568, "source": 5, "target": 7}, {"weight": 5060, "source": 5, "target": 8}, {"weight": 14720, "source": 5, "target": 6}, {"weight": 14639, "source": 6, "target": 7}, {"weight": 13741, "source": 6, "target": 8}, {"weight": 13756, "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: DNK, ERC, OVB, SZX, YAT, MCI, GFF, TLV, IRC
- Travel distances (in kilometers) between each pair of airports:
DNK to TLV: 1817
DNK to OVB: 3596
DNK to SZX: 7887
DNK to IRC: 12290
DNK to MCI: 9199
DNK to ERC: 1905
DNK to YAT: 8853
DNK to GFF: 15218
ERC to OVB: 4711
ERC to SZX: 8457
ERC to TLV: 1981
ERC to IRC: 13534
ERC to MCI: 10349
ERC to YAT: 9754
ERC to GFF: 15625
OVB to SZX: 4657
OVB to TLV: 4535
OVB to IRC: 14320
OVB to MCI: 11290
OVB to YAT: 11098
OVB to GFF: 12327
SZX to TLV: 7782
SZX to IRC: 13086
SZX to MCI: 12808
SZX to YAT: 13605
SZX to GFF: 8304
YAT to TLV: 9956
YAT to IRC: 6299
YAT to MCI: 2433
YAT to GFF: 16548
MCI to TLV: 10568
MCI to IRC: 5060
MCI to GFF: 14720
GFF to TLV: 14639
GFF to IRC: 13741
TLV to IRC: 13756
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test