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: DUS, TWB, CGI, XNA, AUR, CFR, JUZ, YYU, UIO, AKU, YIF, QUB, CNM, DIN, PMO, PKA
- Travel distances (in kilometers) between each pair of airports:
DUS to UIO: 9693
DUS to PMO: 1539
DUS to PKA: 10991
DUS to XNA: 7627
DUS to CGI: 7386
DUS to AUR: 1240
DUS to CFR: 1027
DUS to AKU: 6454
DUS to JUZ: 9427
DUS to YYU: 6848
DUS to QUB: 2829
DUS to CNM: 8809
DUS to TWB: 16271
DUS to YIF: 4881
DUS to DIN: 9081
TWB to UIO: 15838
TWB to PMO: 16347
TWB to PKA: 12793
TWB to XNA: 13853
TWB to CGI: 14391
TWB to AUR: 17107
TWB to CFR: 16894
TWB to AKU: 10845
TWB to JUZ: 7695
TWB to YYU: 15001
TWB to QUB: 16937
TWB to CNM: 13109
TWB to YIF: 16925
TWB to DIN: 8199
CGI to UIO: 4739
CGI to PMO: 8622
CGI to PKA: 5594
CGI to XNA: 1437
CGI to AUR: 7691
CGI to CFR: 7478
CGI to AKU: 13057
CGI to JUZ: 12906
CGI to YYU: 1915
CGI to QUB: 9706
CGI to CNM: 2087
CGI to YIF: 3068
CGI to DIN: 13782
XNA to UIO: 4501
XNA to PMO: 8881
XNA to PKA: 5501
XNA to AUR: 7950
XNA to CFR: 7737
XNA to AKU: 13298
XNA to JUZ: 12747
XNA to YYU: 2174
XNA to QUB: 9965
XNA to CNM: 1734
XNA to YIF: 3327
XNA to DIN: 13893
AUR to UIO: 9783
AUR to PMO: 1878
AUR to PKA: 11466
AUR to CFR: 637
AUR to AKU: 7290
AUR to JUZ: 10287
AUR to YYU: 7135
AUR to QUB: 3105
AUR to CNM: 9181
AUR to YIF: 5172
AUR to DIN: 9915
CFR to UIO: 9570
CFR to PMO: 1665
CFR to PKA: 11253
CFR to AKU: 7077
CFR to JUZ: 10074
CFR to YYU: 6922
CFR to QUB: 2855
CFR to CNM: 8968
CFR to YIF: 4959
CFR to DIN: 9702
JUZ to UIO: 16932
JUZ to PMO: 9826
JUZ to PKA: 13145
JUZ to AKU: 4311
JUZ to YYU: 12945
JUZ to QUB: 10725
JUZ to CNM: 12412
JUZ to YIF: 14142
JUZ to DIN: 2025
YYU to UIO: 5559
YYU to PMO: 8066
YYU to PKA: 6003
YYU to AKU: 12533
YYU to QUB: 9150
YYU to CNM: 3306
YYU to YIF: 2514
YYU to DIN: 13865
UIO to PMO: 10202
UIO to PKA: 9693
UIO to AKU: 16015
UIO to QUB: 10971
UIO to CNM: 5360
UIO to YIF: 6399
UIO to DIN: 17966
AKU to PMO: 6829
AKU to PKA: 14739
AKU to QUB: 7728
AKU to CNM: 14023
AKU to YIF: 11273
AKU to DIN: 3773
YIF to PMO: 6197
YIF to PKA: 7549
YIF to QUB: 7424
YIF to CNM: 4682
YIF to DIN: 13906
QUB to PMO: 1429
QUB to PKA: 13718
QUB to CNM: 11311
QUB to DIN: 10488
CNM to PMO: 10191
CNM to PKA: 5223
CNM to DIN: 13558
DIN to PMO: 9589
DIN to PKA: 14274
PMO to PKA: 12490
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": "DUS", "id": 0}, {"name": "TWB", "id": 1}, {"name": "CGI", "id": 2}, {"name": "XNA", "id": 3}, {"name": "AUR", "id": 4}, {"name": "CFR", "id": 5}, {"name": "JUZ", "id": 6}, {"name": "YYU", "id": 7}, {"name": "UIO", "id": 8}, {"name": "AKU", "id": 9}, {"name": "YIF", "id": 10}, {"name": "QUB", "id": 11}, {"name": "CNM", "id": 12}, {"name": "DIN", "id": 13}, {"name": "PMO", "id": 14}, {"name": "PKA", "id": 15}], "links": [{"weight": 9693, "source": 0, "target": 8}, {"weight": 1539, "source": 0, "target": 14}, {"weight": 10991, "source": 0, "target": 15}, {"weight": 7627, "source": 0, "target": 3}, {"weight": 7386, "source": 0, "target": 2}, {"weight": 1240, "source": 0, "target": 4}, {"weight": 1027, "source": 0, "target": 5}, {"weight": 6454, "source": 0, "target": 9}, {"weight": 9427, "source": 0, "target": 6}, {"weight": 6848, "source": 0, "target": 7}, {"weight": 2829, "source": 0, "target": 11}, {"weight": 8809, "source": 0, "target": 12}, {"weight": 16271, "source": 0, "target": 1}, {"weight": 4881, "source": 0, "target": 10}, {"weight": 9081, "source": 0, "target": 13}, {"weight": 15838, "source": 1, "target": 8}, {"weight": 16347, "source": 1, "target": 14}, {"weight": 12793, "source": 1, "target": 15}, {"weight": 13853, "source": 1, "target": 3}, {"weight": 14391, "source": 1, "target": 2}, {"weight": 17107, "source": 1, "target": 4}, {"weight": 16894, "source": 1, "target": 5}, {"weight": 10845, "source": 1, "target": 9}, {"weight": 7695, "source": 1, "target": 6}, {"weight": 15001, "source": 1, "target": 7}, {"weight": 16937, "source": 1, "target": 11}, {"weight": 13109, "source": 1, "target": 12}, {"weight": 16925, "source": 1, "target": 10}, {"weight": 8199, "source": 1, "target": 13}, {"weight": 4739, "source": 2, "target": 8}, {"weight": 8622, "source": 2, "target": 14}, {"weight": 5594, "source": 2, "target": 15}, {"weight": 1437, "source": 2, "target": 3}, {"weight": 7691, "source": 2, "target": 4}, {"weight": 7478, "source": 2, "target": 5}, {"weight": 13057, "source": 2, "target": 9}, {"weight": 12906, "source": 2, "target": 6}, {"weight": 1915, "source": 2, "target": 7}, {"weight": 9706, "source": 2, "target": 11}, {"weight": 2087, "source": 2, "target": 12}, {"weight": 3068, "source": 2, "target": 10}, {"weight": 13782, "source": 2, "target": 13}, {"weight": 4501, "source": 3, "target": 8}, {"weight": 8881, "source": 3, "target": 14}, {"weight": 5501, "source": 3, "target": 15}, {"weight": 7950, "source": 3, "target": 4}, {"weight": 7737, "source": 3, "target": 5}, {"weight": 13298, "source": 3, "target": 9}, {"weight": 12747, "source": 3, "target": 6}, {"weight": 2174, "source": 3, "target": 7}, {"weight": 9965, "source": 3, "target": 11}, {"weight": 1734, "source": 3, "target": 12}, {"weight": 3327, "source": 3, "target": 10}, {"weight": 13893, "source": 3, "target": 13}, {"weight": 9783, "source": 4, "target": 8}, {"weight": 1878, "source": 4, "target": 14}, {"weight": 11466, "source": 4, "target": 15}, {"weight": 637, "source": 4, "target": 5}, {"weight": 7290, "source": 4, "target": 9}, {"weight": 10287, "source": 4, "target": 6}, {"weight": 7135, "source": 4, "target": 7}, {"weight": 3105, "source": 4, "target": 11}, {"weight": 9181, "source": 4, "target": 12}, {"weight": 5172, "source": 4, "target": 10}, {"weight": 9915, "source": 4, "target": 13}, {"weight": 9570, "source": 5, "target": 8}, {"weight": 1665, "source": 5, "target": 14}, {"weight": 11253, "source": 5, "target": 15}, {"weight": 7077, "source": 5, "target": 9}, {"weight": 10074, "source": 5, "target": 6}, {"weight": 6922, "source": 5, "target": 7}, {"weight": 2855, "source": 5, "target": 11}, {"weight": 8968, "source": 5, "target": 12}, {"weight": 4959, "source": 5, "target": 10}, {"weight": 9702, "source": 5, "target": 13}, {"weight": 16932, "source": 6, "target": 8}, {"weight": 9826, "source": 6, "target": 14}, {"weight": 13145, "source": 6, "target": 15}, {"weight": 4311, "source": 6, "target": 9}, {"weight": 12945, "source": 6, "target": 7}, {"weight": 10725, "source": 6, "target": 11}, {"weight": 12412, "source": 6, "target": 12}, {"weight": 14142, "source": 6, "target": 10}, {"weight": 2025, "source": 6, "target": 13}, {"weight": 5559, "source": 7, "target": 8}, {"weight": 8066, "source": 7, "target": 14}, {"weight": 6003, "source": 7, "target": 15}, {"weight": 12533, "source": 7, "target": 9}, {"weight": 9150, "source": 7, "target": 11}, {"weight": 3306, "source": 7, "target": 12}, {"weight": 2514, "source": 7, "target": 10}, {"weight": 13865, "source": 7, "target": 13}, {"weight": 10202, "source": 8, "target": 14}, {"weight": 9693, "source": 8, "target": 15}, {"weight": 16015, "source": 8, "target": 9}, {"weight": 10971, "source": 8, "target": 11}, {"weight": 5360, "source": 8, "target": 12}, {"weight": 6399, "source": 8, "target": 10}, {"weight": 17966, "source": 8, "target": 13}, {"weight": 6829, "source": 9, "target": 14}, {"weight": 14739, "source": 9, "target": 15}, {"weight": 7728, "source": 9, "target": 11}, {"weight": 14023, "source": 9, "target": 12}, {"weight": 11273, "source": 9, "target": 10}, {"weight": 3773, "source": 9, "target": 13}, {"weight": 6197, "source": 10, "target": 14}, {"weight": 7549, "source": 10, "target": 15}, {"weight": 7424, "source": 10, "target": 11}, {"weight": 4682, "source": 10, "target": 12}, {"weight": 13906, "source": 10, "target": 13}, {"weight": 1429, "source": 11, "target": 14}, {"weight": 13718, "source": 11, "target": 15}, {"weight": 11311, "source": 11, "target": 12}, {"weight": 10488, "source": 11, "target": 13}, {"weight": 10191, "source": 12, "target": 14}, {"weight": 5223, "source": 12, "target": 15}, {"weight": 13558, "source": 12, "target": 13}, {"weight": 9589, "source": 13, "target": 14}, {"weight": 14274, "source": 13, "target": 15}, {"weight": 12490, "source": 14, "target": 15}]}
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: DUS, TWB, CGI, XNA, AUR, CFR, JUZ, YYU, UIO, AKU, YIF, QUB, CNM, DIN, PMO, PKA
- Travel distances (in kilometers) between each pair of airports:
DUS to UIO: 9693
DUS to PMO: 1539
DUS to PKA: 10991
DUS to XNA: 7627
DUS to CGI: 7386
DUS to AUR: 1240
DUS to CFR: 1027
DUS to AKU: 6454
DUS to JUZ: 9427
DUS to YYU: 6848
DUS to QUB: 2829
DUS to CNM: 8809
DUS to TWB: 16271
DUS to YIF: 4881
DUS to DIN: 9081
TWB to UIO: 15838
TWB to PMO: 16347
TWB to PKA: 12793
TWB to XNA: 13853
TWB to CGI: 14391
TWB to AUR: 17107
TWB to CFR: 16894
TWB to AKU: 10845
TWB to JUZ: 7695
TWB to YYU: 15001
TWB to QUB: 16937
TWB to CNM: 13109
TWB to YIF: 16925
TWB to DIN: 8199
CGI to UIO: 4739
CGI to PMO: 8622
CGI to PKA: 5594
CGI to XNA: 1437
CGI to AUR: 7691
CGI to CFR: 7478
CGI to AKU: 13057
CGI to JUZ: 12906
CGI to YYU: 1915
CGI to QUB: 9706
CGI to CNM: 2087
CGI to YIF: 3068
CGI to DIN: 13782
XNA to UIO: 4501
XNA to PMO: 8881
XNA to PKA: 5501
XNA to AUR: 7950
XNA to CFR: 7737
XNA to AKU: 13298
XNA to JUZ: 12747
XNA to YYU: 2174
XNA to QUB: 9965
XNA to CNM: 1734
XNA to YIF: 3327
XNA to DIN: 13893
AUR to UIO: 9783
AUR to PMO: 1878
AUR to PKA: 11466
AUR to CFR: 637
AUR to AKU: 7290
AUR to JUZ: 10287
AUR to YYU: 7135
AUR to QUB: 3105
AUR to CNM: 9181
AUR to YIF: 5172
AUR to DIN: 9915
CFR to UIO: 9570
CFR to PMO: 1665
CFR to PKA: 11253
CFR to AKU: 7077
CFR to JUZ: 10074
CFR to YYU: 6922
CFR to QUB: 2855
CFR to CNM: 8968
CFR to YIF: 4959
CFR to DIN: 9702
JUZ to UIO: 16932
JUZ to PMO: 9826
JUZ to PKA: 13145
JUZ to AKU: 4311
JUZ to YYU: 12945
JUZ to QUB: 10725
JUZ to CNM: 12412
JUZ to YIF: 14142
JUZ to DIN: 2025
YYU to UIO: 5559
YYU to PMO: 8066
YYU to PKA: 6003
YYU to AKU: 12533
YYU to QUB: 9150
YYU to CNM: 3306
YYU to YIF: 2514
YYU to DIN: 13865
UIO to PMO: 10202
UIO to PKA: 9693
UIO to AKU: 16015
UIO to QUB: 10971
UIO to CNM: 5360
UIO to YIF: 6399
UIO to DIN: 17966
AKU to PMO: 6829
AKU to PKA: 14739
AKU to QUB: 7728
AKU to CNM: 14023
AKU to YIF: 11273
AKU to DIN: 3773
YIF to PMO: 6197
YIF to PKA: 7549
YIF to QUB: 7424
YIF to CNM: 4682
YIF to DIN: 13906
QUB to PMO: 1429
QUB to PKA: 13718
QUB to CNM: 11311
QUB to DIN: 10488
CNM to PMO: 10191
CNM to PKA: 5223
CNM to DIN: 13558
DIN to PMO: 9589
DIN to PKA: 14274
PMO to PKA: 12490
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test