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: ZFN, LIR, KIH, EOH, YSJ, ULZ, YTL, RGL, MXX
- Travel distances (in kilometers) between each pair of airports:
ZFN to LIR: 7011
ZFN to RGL: 14448
ZFN to EOH: 8236
ZFN to YSJ: 4502
ZFN to KIH: 13579
ZFN to ULZ: 12866
ZFN to MXX: 8959
ZFN to YTL: 3667
LIR to RGL: 7492
LIR to EOH: 1473
LIR to YSJ: 4654
LIR to KIH: 14222
LIR to ULZ: 15845
LIR to MXX: 10059
LIR to YTL: 5336
KIH to RGL: 16136
KIH to EOH: 13831
KIH to YSJ: 10142
KIH to ULZ: 6040
KIH to MXX: 5218
KIH to YTL: 12666
EOH to RGL: 6784
EOH to YSJ: 5050
EOH to ULZ: 16515
EOH to MXX: 10331
EOH to YTL: 6214
YSJ to RGL: 11237
YSJ to ULZ: 12660
YSJ to MXX: 6475
YSJ to YTL: 2717
ULZ to RGL: 20934
ULZ to MXX: 6831
ULZ to YTL: 13084
YTL to RGL: 12531
YTL to MXX: 8163
RGL to MXX: 14929
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": "ZFN", "id": 0}, {"name": "LIR", "id": 1}, {"name": "KIH", "id": 2}, {"name": "EOH", "id": 3}, {"name": "YSJ", "id": 4}, {"name": "ULZ", "id": 5}, {"name": "YTL", "id": 6}, {"name": "RGL", "id": 7}, {"name": "MXX", "id": 8}], "links": [{"weight": 7011, "source": 0, "target": 1}, {"weight": 14448, "source": 0, "target": 7}, {"weight": 8236, "source": 0, "target": 3}, {"weight": 4502, "source": 0, "target": 4}, {"weight": 13579, "source": 0, "target": 2}, {"weight": 12866, "source": 0, "target": 5}, {"weight": 8959, "source": 0, "target": 8}, {"weight": 3667, "source": 0, "target": 6}, {"weight": 7492, "source": 1, "target": 7}, {"weight": 1473, "source": 1, "target": 3}, {"weight": 4654, "source": 1, "target": 4}, {"weight": 14222, "source": 1, "target": 2}, {"weight": 15845, "source": 1, "target": 5}, {"weight": 10059, "source": 1, "target": 8}, {"weight": 5336, "source": 1, "target": 6}, {"weight": 16136, "source": 2, "target": 7}, {"weight": 13831, "source": 2, "target": 3}, {"weight": 10142, "source": 2, "target": 4}, {"weight": 6040, "source": 2, "target": 5}, {"weight": 5218, "source": 2, "target": 8}, {"weight": 12666, "source": 2, "target": 6}, {"weight": 6784, "source": 3, "target": 7}, {"weight": 5050, "source": 3, "target": 4}, {"weight": 16515, "source": 3, "target": 5}, {"weight": 10331, "source": 3, "target": 8}, {"weight": 6214, "source": 3, "target": 6}, {"weight": 11237, "source": 4, "target": 7}, {"weight": 12660, "source": 4, "target": 5}, {"weight": 6475, "source": 4, "target": 8}, {"weight": 2717, "source": 4, "target": 6}, {"weight": 20934, "source": 5, "target": 7}, {"weight": 6831, "source": 5, "target": 8}, {"weight": 13084, "source": 5, "target": 6}, {"weight": 12531, "source": 6, "target": 7}, {"weight": 8163, "source": 6, "target": 8}, {"weight": 14929, "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: ZFN, LIR, KIH, EOH, YSJ, ULZ, YTL, RGL, MXX
- Travel distances (in kilometers) between each pair of airports:
ZFN to LIR: 7011
ZFN to RGL: 14448
ZFN to EOH: 8236
ZFN to YSJ: 4502
ZFN to KIH: 13579
ZFN to ULZ: 12866
ZFN to MXX: 8959
ZFN to YTL: 3667
LIR to RGL: 7492
LIR to EOH: 1473
LIR to YSJ: 4654
LIR to KIH: 14222
LIR to ULZ: 15845
LIR to MXX: 10059
LIR to YTL: 5336
KIH to RGL: 16136
KIH to EOH: 13831
KIH to YSJ: 10142
KIH to ULZ: 6040
KIH to MXX: 5218
KIH to YTL: 12666
EOH to RGL: 6784
EOH to YSJ: 5050
EOH to ULZ: 16515
EOH to MXX: 10331
EOH to YTL: 6214
YSJ to RGL: 11237
YSJ to ULZ: 12660
YSJ to MXX: 6475
YSJ to YTL: 2717
ULZ to RGL: 20934
ULZ to MXX: 6831
ULZ to YTL: 13084
YTL to RGL: 12531
YTL to MXX: 8163
RGL to MXX: 14929
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test