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: UPK, SPC, PYC, NME, UBA, IOQ, BXU, KGQ, OUL
- Travel distances (in kilometers) between each pair of airports:
UPK to KGQ: 24
UPK to BXU: 14653
UPK to UBA: 13484
UPK to NME: 11403
UPK to PYC: 10743
UPK to SPC: 7184
UPK to OUL: 5311
UPK to IOQ: 1466
SPC to BXU: 14282
SPC to UBA: 6700
SPC to NME: 12214
SPC to PYC: 8233
SPC to OUL: 5073
SPC to IOQ: 6903
SPC to KGQ: 7160
PYC to BXU: 17198
PYC to UBA: 5981
PYC to NME: 9117
PYC to OUL: 11068
PYC to IOQ: 10462
PYC to KGQ: 10719
NME to BXU: 14280
NME to UBA: 13464
NME to OUL: 11776
NME to IOQ: 11122
NME to KGQ: 11379
UBA to BXU: 19176
UBA to OUL: 11428
UBA to IOQ: 13203
UBA to KGQ: 13460
IOQ to BXU: 14372
IOQ to OUL: 5030
IOQ to KGQ: 1442
BXU to OUL: 10253
BXU to KGQ: 14629
KGQ to OUL: 5287
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": "UPK", "id": 0}, {"name": "SPC", "id": 1}, {"name": "PYC", "id": 2}, {"name": "NME", "id": 3}, {"name": "UBA", "id": 4}, {"name": "IOQ", "id": 5}, {"name": "BXU", "id": 6}, {"name": "KGQ", "id": 7}, {"name": "OUL", "id": 8}], "links": [{"weight": 24, "source": 0, "target": 7}, {"weight": 14653, "source": 0, "target": 6}, {"weight": 13484, "source": 0, "target": 4}, {"weight": 11403, "source": 0, "target": 3}, {"weight": 10743, "source": 0, "target": 2}, {"weight": 7184, "source": 0, "target": 1}, {"weight": 5311, "source": 0, "target": 8}, {"weight": 1466, "source": 0, "target": 5}, {"weight": 14282, "source": 1, "target": 6}, {"weight": 6700, "source": 1, "target": 4}, {"weight": 12214, "source": 1, "target": 3}, {"weight": 8233, "source": 1, "target": 2}, {"weight": 5073, "source": 1, "target": 8}, {"weight": 6903, "source": 1, "target": 5}, {"weight": 7160, "source": 1, "target": 7}, {"weight": 17198, "source": 2, "target": 6}, {"weight": 5981, "source": 2, "target": 4}, {"weight": 9117, "source": 2, "target": 3}, {"weight": 11068, "source": 2, "target": 8}, {"weight": 10462, "source": 2, "target": 5}, {"weight": 10719, "source": 2, "target": 7}, {"weight": 14280, "source": 3, "target": 6}, {"weight": 13464, "source": 3, "target": 4}, {"weight": 11776, "source": 3, "target": 8}, {"weight": 11122, "source": 3, "target": 5}, {"weight": 11379, "source": 3, "target": 7}, {"weight": 19176, "source": 4, "target": 6}, {"weight": 11428, "source": 4, "target": 8}, {"weight": 13203, "source": 4, "target": 5}, {"weight": 13460, "source": 4, "target": 7}, {"weight": 14372, "source": 5, "target": 6}, {"weight": 5030, "source": 5, "target": 8}, {"weight": 1442, "source": 5, "target": 7}, {"weight": 10253, "source": 6, "target": 8}, {"weight": 14629, "source": 6, "target": 7}, {"weight": 5287, "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: UPK, SPC, PYC, NME, UBA, IOQ, BXU, KGQ, OUL
- Travel distances (in kilometers) between each pair of airports:
UPK to KGQ: 24
UPK to BXU: 14653
UPK to UBA: 13484
UPK to NME: 11403
UPK to PYC: 10743
UPK to SPC: 7184
UPK to OUL: 5311
UPK to IOQ: 1466
SPC to BXU: 14282
SPC to UBA: 6700
SPC to NME: 12214
SPC to PYC: 8233
SPC to OUL: 5073
SPC to IOQ: 6903
SPC to KGQ: 7160
PYC to BXU: 17198
PYC to UBA: 5981
PYC to NME: 9117
PYC to OUL: 11068
PYC to IOQ: 10462
PYC to KGQ: 10719
NME to BXU: 14280
NME to UBA: 13464
NME to OUL: 11776
NME to IOQ: 11122
NME to KGQ: 11379
UBA to BXU: 19176
UBA to OUL: 11428
UBA to IOQ: 13203
UBA to KGQ: 13460
IOQ to BXU: 14372
IOQ to OUL: 5030
IOQ to KGQ: 1442
BXU to OUL: 10253
BXU to KGQ: 14629
KGQ to OUL: 5287
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test