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: LRD, ECP, JGS, XKS, SMS, BMU, VCP, ATM, RAI, ELC, FDH, OMS, NRA, SLY, SPR, SBZ, DAC, YEG, ASB
- Travel distances (in kilometers) between each pair of airports:
LRD to FDH: 9148
LRD to DAC: 15199
LRD to YEG: 3261
LRD to SPR: 2096
LRD to VCP: 8489
LRD to ATM: 6754
LRD to ECP: 1863
LRD to RAI: 8501
LRD to ASB: 12483
LRD to JGS: 13280
LRD to BMU: 16644
LRD to OMS: 12043
LRD to SLY: 11970
LRD to SBZ: 10118
LRD to SMS: 17138
LRD to ELC: 17030
LRD to XKS: 3475
LRD to NRA: 14632
ECP to FDH: 8030
ECP to DAC: 14666
ECP to YEG: 3486
ECP to SPR: 2272
ECP to VCP: 7839
ECP to ATM: 6104
ECP to RAI: 7328
ECP to ASB: 11580
ECP to JGS: 13341
ECP to BMU: 17292
ECP to OMS: 11061
ECP to SLY: 11067
ECP to SBZ: 9007
ECP to SMS: 15967
ECP to ELC: 18039
ECP to XKS: 3197
ECP to NRA: 15558
JGS to FDH: 9056
JGS to DAC: 2747
JGS to YEG: 10775
JGS to SPR: 14642
JGS to VCP: 18219
JGS to ATM: 17693
JGS to RAI: 13688
JGS to ASB: 5636
JGS to BMU: 4362
JGS to OMS: 4996
JGS to SLY: 5944
JGS to SBZ: 8491
JGS to SMS: 9247
JGS to ELC: 5279
JGS to XKS: 12658
JGS to NRA: 8282
XKS to FDH: 8224
XKS to DAC: 14553
XKS to YEG: 2014
XKS to SPR: 4650
XKS to VCP: 9970
XKS to ATM: 8029
XKS to RAI: 7784
XKS to ASB: 11638
XKS to BMU: 15962
XKS to OMS: 11119
XKS to SLY: 11125
XKS to SBZ: 9194
XKS to SMS: 16595
XKS to ELC: 16712
XKS to NRA: 15628
SMS to FDH: 8977
SMS to DAC: 6980
SMS to YEG: 16191
SMS to SPR: 16428
SMS to VCP: 10392
SMS to ATM: 12814
SMS to RAI: 9276
SMS to ASB: 7238
SMS to BMU: 8735
SMS to OMS: 9498
SMS to SLY: 10251
SMS to SBZ: 7945
SMS to ELC: 10013
SMS to NRA: 10563
BMU to FDH: 12396
BMU to DAC: 4913
BMU to YEG: 14187
BMU to SPR: 18277
BMU to VCP: 18633
BMU to ATM: 20398
BMU to RAI: 16135
BMU to ASB: 8216
BMU to OMS: 8795
BMU to SLY: 9743
BMU to SBZ: 11350
BMU to ELC: 2662
BMU to NRA: 5445
VCP to FDH: 9799
VCP to DAC: 15770
VCP to YEG: 10655
VCP to SPR: 6606
VCP to ATM: 2875
VCP to RAI: 4989
VCP to ASB: 13179
VCP to OMS: 14047
VCP to SLY: 13778
VCP to SBZ: 10808
VCP to ELC: 17838
VCP to NRA: 14609
ATM to FDH: 9073
ATM to DAC: 16060
ATM to YEG: 8920
ATM to SPR: 4871
ATM to RAI: 4263
ATM to ASB: 12715
ATM to OMS: 13085
ATM to SLY: 12828
ATM to SBZ: 10082
ATM to ELC: 20545
ATM to NRA: 17316
RAI to FDH: 4810
RAI to DAC: 11797
RAI to YEG: 8796
RAI to SPR: 8718
RAI to ASB: 8452
RAI to OMS: 9076
RAI to SLY: 8807
RAI to SBZ: 5819
RAI to ELC: 17957
RAI to NRA: 18820
ELC to FDH: 14184
ELC to DAC: 6748
ELC to YEG: 14937
ELC to SPR: 18451
ELC to ASB: 10035
ELC to OMS: 9899
ELC to SLY: 10847
ELC to SBZ: 13172
ELC to NRA: 4101
FDH to DAC: 7650
FDH to YEG: 7581
FDH to SPR: 9323
FDH to ASB: 4237
FDH to OMS: 4448
FDH to SLY: 4190
FDH to SBZ: 1516
FDH to NRA: 17093
OMS to DAC: 4555
OMS to YEG: 10250
OMS to SPR: 12469
OMS to ASB: 3118
OMS to SLY: 1691
OMS to SBZ: 3942
OMS to NRA: 12887
NRA to DAC: 9518
NRA to YEG: 13745
NRA to SPR: 16053
NRA to ASB: 12897
NRA to SLY: 13835
NRA to SBZ: 16045
SLY to DAC: 5843
SLY to YEG: 10256
SLY to SPR: 12475
SLY to ASB: 3871
SLY to SBZ: 4248
SPR to DAC: 16151
SPR to YEG: 4595
SPR to ASB: 12988
SPR to SBZ: 10297
SBZ to DAC: 6618
SBZ to YEG: 8543
SBZ to ASB: 3203
DAC to YEG: 12670
DAC to ASB: 3451
YEG to ASB: 10769
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": "LRD", "id": 0}, {"name": "ECP", "id": 1}, {"name": "JGS", "id": 2}, {"name": "XKS", "id": 3}, {"name": "SMS", "id": 4}, {"name": "BMU", "id": 5}, {"name": "VCP", "id": 6}, {"name": "ATM", "id": 7}, {"name": "RAI", "id": 8}, {"name": "ELC", "id": 9}, {"name": "FDH", "id": 10}, {"name": "OMS", "id": 11}, {"name": "NRA", "id": 12}, {"name": "SLY", "id": 13}, {"name": "SPR", "id": 14}, {"name": "SBZ", "id": 15}, {"name": "DAC", "id": 16}, {"name": "YEG", "id": 17}, {"name": "ASB", "id": 18}], "links": [{"weight": 9148, "source": 0, "target": 10}, {"weight": 15199, "source": 0, "target": 16}, {"weight": 3261, "source": 0, "target": 17}, {"weight": 2096, "source": 0, "target": 14}, {"weight": 8489, "source": 0, "target": 6}, {"weight": 6754, "source": 0, "target": 7}, {"weight": 1863, "source": 0, "target": 1}, {"weight": 8501, "source": 0, "target": 8}, {"weight": 12483, "source": 0, "target": 18}, {"weight": 13280, "source": 0, "target": 2}, {"weight": 16644, "source": 0, "target": 5}, {"weight": 12043, "source": 0, "target": 11}, {"weight": 11970, "source": 0, "target": 13}, {"weight": 10118, "source": 0, "target": 15}, {"weight": 17138, "source": 0, "target": 4}, {"weight": 17030, "source": 0, "target": 9}, {"weight": 3475, "source": 0, "target": 3}, {"weight": 14632, "source": 0, "target": 12}, {"weight": 8030, "source": 1, "target": 10}, {"weight": 14666, "source": 1, "target": 16}, {"weight": 3486, "source": 1, "target": 17}, {"weight": 2272, "source": 1, "target": 14}, {"weight": 7839, "source": 1, "target": 6}, {"weight": 6104, "source": 1, "target": 7}, {"weight": 7328, "source": 1, "target": 8}, {"weight": 11580, "source": 1, "target": 18}, {"weight": 13341, "source": 1, "target": 2}, {"weight": 17292, "source": 1, "target": 5}, {"weight": 11061, "source": 1, "target": 11}, {"weight": 11067, "source": 1, "target": 13}, {"weight": 9007, "source": 1, "target": 15}, {"weight": 15967, "source": 1, "target": 4}, {"weight": 18039, "source": 1, "target": 9}, {"weight": 3197, "source": 1, "target": 3}, {"weight": 15558, "source": 1, "target": 12}, {"weight": 9056, "source": 2, "target": 10}, {"weight": 2747, "source": 2, "target": 16}, {"weight": 10775, "source": 2, "target": 17}, {"weight": 14642, "source": 2, "target": 14}, {"weight": 18219, "source": 2, "target": 6}, {"weight": 17693, "source": 2, "target": 7}, {"weight": 13688, "source": 2, "target": 8}, {"weight": 5636, "source": 2, "target": 18}, {"weight": 4362, "source": 2, "target": 5}, {"weight": 4996, "source": 2, "target": 11}, {"weight": 5944, "source": 2, "target": 13}, {"weight": 8491, "source": 2, "target": 15}, {"weight": 9247, "source": 2, "target": 4}, {"weight": 5279, "source": 2, "target": 9}, {"weight": 12658, "source": 2, "target": 3}, {"weight": 8282, "source": 2, "target": 12}, {"weight": 8224, "source": 3, "target": 10}, {"weight": 14553, "source": 3, "target": 16}, {"weight": 2014, "source": 3, "target": 17}, {"weight": 4650, "source": 3, "target": 14}, {"weight": 9970, "source": 3, "target": 6}, {"weight": 8029, "source": 3, "target": 7}, {"weight": 7784, "source": 3, "target": 8}, {"weight": 11638, "source": 3, "target": 18}, {"weight": 15962, "source": 3, "target": 5}, {"weight": 11119, "source": 3, "target": 11}, {"weight": 11125, "source": 3, "target": 13}, {"weight": 9194, "source": 3, "target": 15}, {"weight": 16595, "source": 3, "target": 4}, {"weight": 16712, "source": 3, "target": 9}, {"weight": 15628, "source": 3, "target": 12}, {"weight": 8977, "source": 4, "target": 10}, {"weight": 6980, "source": 4, "target": 16}, {"weight": 16191, "source": 4, "target": 17}, {"weight": 16428, "source": 4, "target": 14}, {"weight": 10392, "source": 4, "target": 6}, {"weight": 12814, "source": 4, "target": 7}, {"weight": 9276, "source": 4, "target": 8}, {"weight": 7238, "source": 4, "target": 18}, {"weight": 8735, "source": 4, "target": 5}, {"weight": 9498, "source": 4, "target": 11}, {"weight": 10251, "source": 4, "target": 13}, {"weight": 7945, "source": 4, "target": 15}, {"weight": 10013, "source": 4, "target": 9}, {"weight": 10563, "source": 4, "target": 12}, {"weight": 12396, "source": 5, "target": 10}, {"weight": 4913, "source": 5, "target": 16}, {"weight": 14187, "source": 5, "target": 17}, {"weight": 18277, "source": 5, "target": 14}, {"weight": 18633, "source": 5, "target": 6}, {"weight": 20398, "source": 5, "target": 7}, {"weight": 16135, "source": 5, "target": 8}, {"weight": 8216, "source": 5, "target": 18}, {"weight": 8795, "source": 5, "target": 11}, {"weight": 9743, "source": 5, "target": 13}, {"weight": 11350, "source": 5, "target": 15}, {"weight": 2662, "source": 5, "target": 9}, {"weight": 5445, "source": 5, "target": 12}, {"weight": 9799, "source": 6, "target": 10}, {"weight": 15770, "source": 6, "target": 16}, {"weight": 10655, "source": 6, "target": 17}, {"weight": 6606, "source": 6, "target": 14}, {"weight": 2875, "source": 6, "target": 7}, {"weight": 4989, "source": 6, "target": 8}, {"weight": 13179, "source": 6, "target": 18}, {"weight": 14047, "source": 6, "target": 11}, {"weight": 13778, "source": 6, "target": 13}, {"weight": 10808, "source": 6, "target": 15}, {"weight": 17838, "source": 6, "target": 9}, {"weight": 14609, "source": 6, "target": 12}, {"weight": 9073, "source": 7, "target": 10}, {"weight": 16060, "source": 7, "target": 16}, {"weight": 8920, "source": 7, "target": 17}, {"weight": 4871, "source": 7, "target": 14}, {"weight": 4263, "source": 7, "target": 8}, {"weight": 12715, "source": 7, "target": 18}, {"weight": 13085, "source": 7, "target": 11}, {"weight": 12828, "source": 7, "target": 13}, {"weight": 10082, "source": 7, "target": 15}, {"weight": 20545, "source": 7, "target": 9}, {"weight": 17316, "source": 7, "target": 12}, {"weight": 4810, "source": 8, "target": 10}, {"weight": 11797, "source": 8, "target": 16}, {"weight": 8796, "source": 8, "target": 17}, {"weight": 8718, "source": 8, "target": 14}, {"weight": 8452, "source": 8, "target": 18}, {"weight": 9076, "source": 8, "target": 11}, {"weight": 8807, "source": 8, "target": 13}, {"weight": 5819, "source": 8, "target": 15}, {"weight": 17957, "source": 8, "target": 9}, {"weight": 18820, "source": 8, "target": 12}, {"weight": 14184, "source": 9, "target": 10}, {"weight": 6748, "source": 9, "target": 16}, {"weight": 14937, "source": 9, "target": 17}, {"weight": 18451, "source": 9, "target": 14}, {"weight": 10035, "source": 9, "target": 18}, {"weight": 9899, "source": 9, "target": 11}, {"weight": 10847, "source": 9, "target": 13}, {"weight": 13172, "source": 9, "target": 15}, {"weight": 4101, "source": 9, "target": 12}, {"weight": 7650, "source": 10, "target": 16}, {"weight": 7581, "source": 10, "target": 17}, {"weight": 9323, "source": 10, "target": 14}, {"weight": 4237, "source": 10, "target": 18}, {"weight": 4448, "source": 10, "target": 11}, {"weight": 4190, "source": 10, "target": 13}, {"weight": 1516, "source": 10, "target": 15}, {"weight": 17093, "source": 10, "target": 12}, {"weight": 4555, "source": 11, "target": 16}, {"weight": 10250, "source": 11, "target": 17}, {"weight": 12469, "source": 11, "target": 14}, {"weight": 3118, "source": 11, "target": 18}, {"weight": 1691, "source": 11, "target": 13}, {"weight": 3942, "source": 11, "target": 15}, {"weight": 12887, "source": 11, "target": 12}, {"weight": 9518, "source": 12, "target": 16}, {"weight": 13745, "source": 12, "target": 17}, {"weight": 16053, "source": 12, "target": 14}, {"weight": 12897, "source": 12, "target": 18}, {"weight": 13835, "source": 12, "target": 13}, {"weight": 16045, "source": 12, "target": 15}, {"weight": 5843, "source": 13, "target": 16}, {"weight": 10256, "source": 13, "target": 17}, {"weight": 12475, "source": 13, "target": 14}, {"weight": 3871, "source": 13, "target": 18}, {"weight": 4248, "source": 13, "target": 15}, {"weight": 16151, "source": 14, "target": 16}, {"weight": 4595, "source": 14, "target": 17}, {"weight": 12988, "source": 14, "target": 18}, {"weight": 10297, "source": 14, "target": 15}, {"weight": 6618, "source": 15, "target": 16}, {"weight": 8543, "source": 15, "target": 17}, {"weight": 3203, "source": 15, "target": 18}, {"weight": 12670, "source": 16, "target": 17}, {"weight": 3451, "source": 16, "target": 18}, {"weight": 10769, "source": 17, "target": 18}]}
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: LRD, ECP, JGS, XKS, SMS, BMU, VCP, ATM, RAI, ELC, FDH, OMS, NRA, SLY, SPR, SBZ, DAC, YEG, ASB
- Travel distances (in kilometers) between each pair of airports:
LRD to FDH: 9148
LRD to DAC: 15199
LRD to YEG: 3261
LRD to SPR: 2096
LRD to VCP: 8489
LRD to ATM: 6754
LRD to ECP: 1863
LRD to RAI: 8501
LRD to ASB: 12483
LRD to JGS: 13280
LRD to BMU: 16644
LRD to OMS: 12043
LRD to SLY: 11970
LRD to SBZ: 10118
LRD to SMS: 17138
LRD to ELC: 17030
LRD to XKS: 3475
LRD to NRA: 14632
ECP to FDH: 8030
ECP to DAC: 14666
ECP to YEG: 3486
ECP to SPR: 2272
ECP to VCP: 7839
ECP to ATM: 6104
ECP to RAI: 7328
ECP to ASB: 11580
ECP to JGS: 13341
ECP to BMU: 17292
ECP to OMS: 11061
ECP to SLY: 11067
ECP to SBZ: 9007
ECP to SMS: 15967
ECP to ELC: 18039
ECP to XKS: 3197
ECP to NRA: 15558
JGS to FDH: 9056
JGS to DAC: 2747
JGS to YEG: 10775
JGS to SPR: 14642
JGS to VCP: 18219
JGS to ATM: 17693
JGS to RAI: 13688
JGS to ASB: 5636
JGS to BMU: 4362
JGS to OMS: 4996
JGS to SLY: 5944
JGS to SBZ: 8491
JGS to SMS: 9247
JGS to ELC: 5279
JGS to XKS: 12658
JGS to NRA: 8282
XKS to FDH: 8224
XKS to DAC: 14553
XKS to YEG: 2014
XKS to SPR: 4650
XKS to VCP: 9970
XKS to ATM: 8029
XKS to RAI: 7784
XKS to ASB: 11638
XKS to BMU: 15962
XKS to OMS: 11119
XKS to SLY: 11125
XKS to SBZ: 9194
XKS to SMS: 16595
XKS to ELC: 16712
XKS to NRA: 15628
SMS to FDH: 8977
SMS to DAC: 6980
SMS to YEG: 16191
SMS to SPR: 16428
SMS to VCP: 10392
SMS to ATM: 12814
SMS to RAI: 9276
SMS to ASB: 7238
SMS to BMU: 8735
SMS to OMS: 9498
SMS to SLY: 10251
SMS to SBZ: 7945
SMS to ELC: 10013
SMS to NRA: 10563
BMU to FDH: 12396
BMU to DAC: 4913
BMU to YEG: 14187
BMU to SPR: 18277
BMU to VCP: 18633
BMU to ATM: 20398
BMU to RAI: 16135
BMU to ASB: 8216
BMU to OMS: 8795
BMU to SLY: 9743
BMU to SBZ: 11350
BMU to ELC: 2662
BMU to NRA: 5445
VCP to FDH: 9799
VCP to DAC: 15770
VCP to YEG: 10655
VCP to SPR: 6606
VCP to ATM: 2875
VCP to RAI: 4989
VCP to ASB: 13179
VCP to OMS: 14047
VCP to SLY: 13778
VCP to SBZ: 10808
VCP to ELC: 17838
VCP to NRA: 14609
ATM to FDH: 9073
ATM to DAC: 16060
ATM to YEG: 8920
ATM to SPR: 4871
ATM to RAI: 4263
ATM to ASB: 12715
ATM to OMS: 13085
ATM to SLY: 12828
ATM to SBZ: 10082
ATM to ELC: 20545
ATM to NRA: 17316
RAI to FDH: 4810
RAI to DAC: 11797
RAI to YEG: 8796
RAI to SPR: 8718
RAI to ASB: 8452
RAI to OMS: 9076
RAI to SLY: 8807
RAI to SBZ: 5819
RAI to ELC: 17957
RAI to NRA: 18820
ELC to FDH: 14184
ELC to DAC: 6748
ELC to YEG: 14937
ELC to SPR: 18451
ELC to ASB: 10035
ELC to OMS: 9899
ELC to SLY: 10847
ELC to SBZ: 13172
ELC to NRA: 4101
FDH to DAC: 7650
FDH to YEG: 7581
FDH to SPR: 9323
FDH to ASB: 4237
FDH to OMS: 4448
FDH to SLY: 4190
FDH to SBZ: 1516
FDH to NRA: 17093
OMS to DAC: 4555
OMS to YEG: 10250
OMS to SPR: 12469
OMS to ASB: 3118
OMS to SLY: 1691
OMS to SBZ: 3942
OMS to NRA: 12887
NRA to DAC: 9518
NRA to YEG: 13745
NRA to SPR: 16053
NRA to ASB: 12897
NRA to SLY: 13835
NRA to SBZ: 16045
SLY to DAC: 5843
SLY to YEG: 10256
SLY to SPR: 12475
SLY to ASB: 3871
SLY to SBZ: 4248
SPR to DAC: 16151
SPR to YEG: 4595
SPR to ASB: 12988
SPR to SBZ: 10297
SBZ to DAC: 6618
SBZ to YEG: 8543
SBZ to ASB: 3203
DAC to YEG: 12670
DAC to ASB: 3451
YEG to ASB: 10769
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test