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: FRE, TID, JHS, IGD, SLH, BPX, PGF, HIR, JER
- Travel distances (in kilometers) between each pair of airports:
FRE to HIR: 154
FRE to PGF: 16881
FRE to JER: 16496
FRE to TID: 17085
FRE to BPX: 8629
FRE to JHS: 18598
FRE to SLH: 1893
FRE to IGD: 15353
TID to PGF: 2050
TID to JER: 1932
TID to BPX: 8961
TID to HIR: 16931
TID to JHS: 5455
TID to SLH: 18670
TID to IGD: 3755
JHS to PGF: 4641
JHS to JER: 3782
JHS to BPX: 11386
JHS to HIR: 18444
JHS to SLH: 18333
JHS to IGD: 6843
IGD to PGF: 4180
IGD to JER: 3848
IGD to BPX: 7155
IGD to HIR: 15199
IGD to SLH: 16938
SLH to PGF: 18375
SLH to JER: 17877
SLH to BPX: 10214
SLH to HIR: 1739
BPX to PGF: 9281
BPX to JER: 8899
BPX to HIR: 8475
PGF to JER: 1228
PGF to HIR: 16727
HIR to JER: 16342
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": "FRE", "id": 0}, {"name": "TID", "id": 1}, {"name": "JHS", "id": 2}, {"name": "IGD", "id": 3}, {"name": "SLH", "id": 4}, {"name": "BPX", "id": 5}, {"name": "PGF", "id": 6}, {"name": "HIR", "id": 7}, {"name": "JER", "id": 8}], "links": [{"weight": 154, "source": 0, "target": 7}, {"weight": 16881, "source": 0, "target": 6}, {"weight": 16496, "source": 0, "target": 8}, {"weight": 17085, "source": 0, "target": 1}, {"weight": 8629, "source": 0, "target": 5}, {"weight": 18598, "source": 0, "target": 2}, {"weight": 1893, "source": 0, "target": 4}, {"weight": 15353, "source": 0, "target": 3}, {"weight": 2050, "source": 1, "target": 6}, {"weight": 1932, "source": 1, "target": 8}, {"weight": 8961, "source": 1, "target": 5}, {"weight": 16931, "source": 1, "target": 7}, {"weight": 5455, "source": 1, "target": 2}, {"weight": 18670, "source": 1, "target": 4}, {"weight": 3755, "source": 1, "target": 3}, {"weight": 4641, "source": 2, "target": 6}, {"weight": 3782, "source": 2, "target": 8}, {"weight": 11386, "source": 2, "target": 5}, {"weight": 18444, "source": 2, "target": 7}, {"weight": 18333, "source": 2, "target": 4}, {"weight": 6843, "source": 2, "target": 3}, {"weight": 4180, "source": 3, "target": 6}, {"weight": 3848, "source": 3, "target": 8}, {"weight": 7155, "source": 3, "target": 5}, {"weight": 15199, "source": 3, "target": 7}, {"weight": 16938, "source": 3, "target": 4}, {"weight": 18375, "source": 4, "target": 6}, {"weight": 17877, "source": 4, "target": 8}, {"weight": 10214, "source": 4, "target": 5}, {"weight": 1739, "source": 4, "target": 7}, {"weight": 9281, "source": 5, "target": 6}, {"weight": 8899, "source": 5, "target": 8}, {"weight": 8475, "source": 5, "target": 7}, {"weight": 1228, "source": 6, "target": 8}, {"weight": 16727, "source": 6, "target": 7}, {"weight": 16342, "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: FRE, TID, JHS, IGD, SLH, BPX, PGF, HIR, JER
- Travel distances (in kilometers) between each pair of airports:
FRE to HIR: 154
FRE to PGF: 16881
FRE to JER: 16496
FRE to TID: 17085
FRE to BPX: 8629
FRE to JHS: 18598
FRE to SLH: 1893
FRE to IGD: 15353
TID to PGF: 2050
TID to JER: 1932
TID to BPX: 8961
TID to HIR: 16931
TID to JHS: 5455
TID to SLH: 18670
TID to IGD: 3755
JHS to PGF: 4641
JHS to JER: 3782
JHS to BPX: 11386
JHS to HIR: 18444
JHS to SLH: 18333
JHS to IGD: 6843
IGD to PGF: 4180
IGD to JER: 3848
IGD to BPX: 7155
IGD to HIR: 15199
IGD to SLH: 16938
SLH to PGF: 18375
SLH to JER: 17877
SLH to BPX: 10214
SLH to HIR: 1739
BPX to PGF: 9281
BPX to JER: 8899
BPX to HIR: 8475
PGF to JER: 1228
PGF to HIR: 16727
HIR to JER: 16342
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test