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: MEL, OIM, BHK, AKK, LRH, SYZ, SHD, ZQN, YPH
- Travel distances (in kilometers) between each pair of airports:
MEL to ZQN: 2145
MEL to YPH: 16869
MEL to BHK: 12085
MEL to AKK: 13889
MEL to LRH: 17127
MEL to SYZ: 12194
MEL to OIM: 8573
MEL to SHD: 16541
OIM to YPH: 11315
OIM to BHK: 6563
OIM to AKK: 10670
OIM to LRH: 10440
OIM to SYZ: 8122
OIM to ZQN: 10052
OIM to SHD: 11559
BHK to YPH: 11291
BHK to AKK: 14670
BHK to LRH: 5296
BHK to SYZ: 3165
BHK to ZQN: 14206
BHK to SHD: 10633
AKK to YPH: 6583
AKK to LRH: 11134
AKK to SYZ: 15315
AKK to ZQN: 13127
AKK to SHD: 6187
LRH to YPH: 6889
LRH to SYZ: 4976
LRH to ZQN: 19272
LRH to SHD: 6492
SYZ to YPH: 11136
SYZ to ZQN: 14339
SYZ to SHD: 11049
SHD to YPH: 2415
SHD to ZQN: 15329
ZQN to YPH: 15798
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": "MEL", "id": 0}, {"name": "OIM", "id": 1}, {"name": "BHK", "id": 2}, {"name": "AKK", "id": 3}, {"name": "LRH", "id": 4}, {"name": "SYZ", "id": 5}, {"name": "SHD", "id": 6}, {"name": "ZQN", "id": 7}, {"name": "YPH", "id": 8}], "links": [{"weight": 2145, "source": 0, "target": 7}, {"weight": 16869, "source": 0, "target": 8}, {"weight": 12085, "source": 0, "target": 2}, {"weight": 13889, "source": 0, "target": 3}, {"weight": 17127, "source": 0, "target": 4}, {"weight": 12194, "source": 0, "target": 5}, {"weight": 8573, "source": 0, "target": 1}, {"weight": 16541, "source": 0, "target": 6}, {"weight": 11315, "source": 1, "target": 8}, {"weight": 6563, "source": 1, "target": 2}, {"weight": 10670, "source": 1, "target": 3}, {"weight": 10440, "source": 1, "target": 4}, {"weight": 8122, "source": 1, "target": 5}, {"weight": 10052, "source": 1, "target": 7}, {"weight": 11559, "source": 1, "target": 6}, {"weight": 11291, "source": 2, "target": 8}, {"weight": 14670, "source": 2, "target": 3}, {"weight": 5296, "source": 2, "target": 4}, {"weight": 3165, "source": 2, "target": 5}, {"weight": 14206, "source": 2, "target": 7}, {"weight": 10633, "source": 2, "target": 6}, {"weight": 6583, "source": 3, "target": 8}, {"weight": 11134, "source": 3, "target": 4}, {"weight": 15315, "source": 3, "target": 5}, {"weight": 13127, "source": 3, "target": 7}, {"weight": 6187, "source": 3, "target": 6}, {"weight": 6889, "source": 4, "target": 8}, {"weight": 4976, "source": 4, "target": 5}, {"weight": 19272, "source": 4, "target": 7}, {"weight": 6492, "source": 4, "target": 6}, {"weight": 11136, "source": 5, "target": 8}, {"weight": 14339, "source": 5, "target": 7}, {"weight": 11049, "source": 5, "target": 6}, {"weight": 2415, "source": 6, "target": 8}, {"weight": 15329, "source": 6, "target": 7}, {"weight": 15798, "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: MEL, OIM, BHK, AKK, LRH, SYZ, SHD, ZQN, YPH
- Travel distances (in kilometers) between each pair of airports:
MEL to ZQN: 2145
MEL to YPH: 16869
MEL to BHK: 12085
MEL to AKK: 13889
MEL to LRH: 17127
MEL to SYZ: 12194
MEL to OIM: 8573
MEL to SHD: 16541
OIM to YPH: 11315
OIM to BHK: 6563
OIM to AKK: 10670
OIM to LRH: 10440
OIM to SYZ: 8122
OIM to ZQN: 10052
OIM to SHD: 11559
BHK to YPH: 11291
BHK to AKK: 14670
BHK to LRH: 5296
BHK to SYZ: 3165
BHK to ZQN: 14206
BHK to SHD: 10633
AKK to YPH: 6583
AKK to LRH: 11134
AKK to SYZ: 15315
AKK to ZQN: 13127
AKK to SHD: 6187
LRH to YPH: 6889
LRH to SYZ: 4976
LRH to ZQN: 19272
LRH to SHD: 6492
SYZ to YPH: 11136
SYZ to ZQN: 14339
SYZ to SHD: 11049
SHD to YPH: 2415
SHD to ZQN: 15329
ZQN to YPH: 15798
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test