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: ERZ, YHM, PAV, OZC, OLB, MUK, TET, AIN, TQA, YKQ, EXT, DOY, PKB, KEJ, GGW, JZH, RAK, TEE
- Travel distances (in kilometers) between each pair of airports:
ERZ to OZC: 10411
ERZ to OLB: 2668
ERZ to JZH: 7542
ERZ to RAK: 4556
ERZ to AIN: 14403
ERZ to GGW: 11419
ERZ to PAV: 11021
ERZ to EXT: 3747
ERZ to TEE: 3773
ERZ to DOY: 7975
ERZ to TQA: 7219
ERZ to MUK: 19888
ERZ to KEJ: 5725
ERZ to TET: 7575
ERZ to PKB: 9763
ERZ to YHM: 9451
ERZ to YKQ: 9541
YHM to OZC: 14156
YHM to OLB: 7308
YHM to JZH: 13310
YHM to RAK: 7827
YHM to AIN: 6826
YHM to GGW: 4781
YHM to PAV: 10009
YHM to EXT: 6451
YHM to TEE: 8038
YHM to DOY: 12207
YHM to TQA: 8322
YHM to MUK: 12453
YHM to KEJ: 11410
YHM to TET: 14918
YHM to PKB: 2996
YHM to YKQ: 2759
PAV to OZC: 19740
PAV to OLB: 8583
PAV to JZH: 16791
PAV to RAK: 6550
PAV to AIN: 14403
PAV to GGW: 10429
PAV to EXT: 8530
PAV to TEE: 8175
PAV to DOY: 16860
PAV to TQA: 12631
PAV to MUK: 13807
PAV to KEJ: 13734
PAV to TET: 10527
PAV to PKB: 8619
PAV to YKQ: 9234
OZC to OLB: 11444
OZC to JZH: 3454
OZC to RAK: 13370
OZC to AIN: 14575
OZC to GGW: 12539
OZC to EXT: 11775
OZC to TEE: 12619
OZC to DOY: 3384
OZC to TQA: 14626
OZC to MUK: 11295
OZC to KEJ: 12007
OZC to TET: 12347
OZC to PKB: 14172
OZC to YKQ: 14273
OLB to JZH: 8651
OLB to RAK: 2220
OLB to AIN: 12506
OLB to GGW: 9330
OLB to EXT: 1521
OLB to TEE: 1668
OLB to DOY: 8729
OLB to TQA: 5753
OLB to MUK: 17970
OLB to KEJ: 5629
OLB to TET: 8061
OLB to PKB: 7507
OLB to YKQ: 7264
MUK to JZH: 14003
MUK to RAK: 17661
MUK to AIN: 11610
MUK to GGW: 9691
MUK to EXT: 16662
MUK to TEE: 18387
MUK to DOY: 12880
MUK to TQA: 17383
MUK to KEJ: 20566
MUK to TET: 17537
MUK to PKB: 11343
MUK to YKQ: 11924
TET to JZH: 10325
TET to RAK: 9067
TET to AIN: 20087
TET to GGW: 16940
TET to EXT: 9131
TET to TEE: 8880
TET to DOY: 11600
TET to TQA: 13084
TET to KEJ: 11520
TET to PKB: 14991
TET to YKQ: 14986
AIN to JZH: 13520
AIN to RAK: 12739
AIN to GGW: 4774
AIN to EXT: 11138
AIN to TEE: 13195
AIN to DOY: 12417
AIN to TQA: 11676
AIN to KEJ: 15527
AIN to PKB: 6571
AIN to YKQ: 6943
TQA to JZH: 11764
TQA to RAK: 6518
TQA to GGW: 9221
TQA to EXT: 4382
TQA to TEE: 6439
TQA to DOY: 11545
TQA to KEJ: 8707
TQA to PKB: 7172
TQA to YKQ: 7548
YKQ to JZH: 12993
YKQ to RAK: 6680
YKQ to GGW: 3587
YKQ to EXT: 6372
YKQ to TEE: 7543
YKQ to DOY: 11890
YKQ to KEJ: 11399
YKQ to PKB: 1538
EXT to JZH: 8785
EXT to RAK: 2226
EXT to GGW: 8207
EXT to TEE: 2112
EXT to DOY: 8741
EXT to KEJ: 5729
EXT to PKB: 6158
DOY to JZH: 1769
DOY to RAK: 10548
DOY to GGW: 10381
DOY to TEE: 9899
DOY to KEJ: 9104
DOY to PKB: 11365
PKB to JZH: 12468
PKB to RAK: 6908
PKB to GGW: 2733
PKB to TEE: 7786
PKB to KEJ: 11002
KEJ to JZH: 9045
KEJ to RAK: 7413
KEJ to GGW: 13051
KEJ to TEE: 6787
GGW to JZH: 11484
GGW to RAK: 8901
GGW to TEE: 9764
JZH to RAK: 10470
JZH to TEE: 9756
RAK to TEE: 1710
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": "ERZ", "id": 0}, {"name": "YHM", "id": 1}, {"name": "PAV", "id": 2}, {"name": "OZC", "id": 3}, {"name": "OLB", "id": 4}, {"name": "MUK", "id": 5}, {"name": "TET", "id": 6}, {"name": "AIN", "id": 7}, {"name": "TQA", "id": 8}, {"name": "YKQ", "id": 9}, {"name": "EXT", "id": 10}, {"name": "DOY", "id": 11}, {"name": "PKB", "id": 12}, {"name": "KEJ", "id": 13}, {"name": "GGW", "id": 14}, {"name": "JZH", "id": 15}, {"name": "RAK", "id": 16}, {"name": "TEE", "id": 17}], "links": [{"weight": 10411, "source": 0, "target": 3}, {"weight": 2668, "source": 0, "target": 4}, {"weight": 7542, "source": 0, "target": 15}, {"weight": 4556, "source": 0, "target": 16}, {"weight": 14403, "source": 0, "target": 7}, {"weight": 11419, "source": 0, "target": 14}, {"weight": 11021, "source": 0, "target": 2}, {"weight": 3747, "source": 0, "target": 10}, {"weight": 3773, "source": 0, "target": 17}, {"weight": 7975, "source": 0, "target": 11}, {"weight": 7219, "source": 0, "target": 8}, {"weight": 19888, "source": 0, "target": 5}, {"weight": 5725, "source": 0, "target": 13}, {"weight": 7575, "source": 0, "target": 6}, {"weight": 9763, "source": 0, "target": 12}, {"weight": 9451, "source": 0, "target": 1}, {"weight": 9541, "source": 0, "target": 9}, {"weight": 14156, "source": 1, "target": 3}, {"weight": 7308, "source": 1, "target": 4}, {"weight": 13310, "source": 1, "target": 15}, {"weight": 7827, "source": 1, "target": 16}, {"weight": 6826, "source": 1, "target": 7}, {"weight": 4781, "source": 1, "target": 14}, {"weight": 10009, "source": 1, "target": 2}, {"weight": 6451, "source": 1, "target": 10}, {"weight": 8038, "source": 1, "target": 17}, {"weight": 12207, "source": 1, "target": 11}, {"weight": 8322, "source": 1, "target": 8}, {"weight": 12453, "source": 1, "target": 5}, {"weight": 11410, "source": 1, "target": 13}, {"weight": 14918, "source": 1, "target": 6}, {"weight": 2996, "source": 1, "target": 12}, {"weight": 2759, "source": 1, "target": 9}, {"weight": 19740, "source": 2, "target": 3}, {"weight": 8583, "source": 2, "target": 4}, {"weight": 16791, "source": 2, "target": 15}, {"weight": 6550, "source": 2, "target": 16}, {"weight": 14403, "source": 2, "target": 7}, {"weight": 10429, "source": 2, "target": 14}, {"weight": 8530, "source": 2, "target": 10}, {"weight": 8175, "source": 2, "target": 17}, {"weight": 16860, "source": 2, "target": 11}, {"weight": 12631, "source": 2, "target": 8}, {"weight": 13807, "source": 2, "target": 5}, {"weight": 13734, "source": 2, "target": 13}, {"weight": 10527, "source": 2, "target": 6}, {"weight": 8619, "source": 2, "target": 12}, {"weight": 9234, "source": 2, "target": 9}, {"weight": 11444, "source": 3, "target": 4}, {"weight": 3454, "source": 3, "target": 15}, {"weight": 13370, "source": 3, "target": 16}, {"weight": 14575, "source": 3, "target": 7}, {"weight": 12539, "source": 3, "target": 14}, {"weight": 11775, "source": 3, "target": 10}, {"weight": 12619, "source": 3, "target": 17}, {"weight": 3384, "source": 3, "target": 11}, {"weight": 14626, "source": 3, "target": 8}, {"weight": 11295, "source": 3, "target": 5}, {"weight": 12007, "source": 3, "target": 13}, {"weight": 12347, "source": 3, "target": 6}, {"weight": 14172, "source": 3, "target": 12}, {"weight": 14273, "source": 3, "target": 9}, {"weight": 8651, "source": 4, "target": 15}, {"weight": 2220, "source": 4, "target": 16}, {"weight": 12506, "source": 4, "target": 7}, {"weight": 9330, "source": 4, "target": 14}, {"weight": 1521, "source": 4, "target": 10}, {"weight": 1668, "source": 4, "target": 17}, {"weight": 8729, "source": 4, "target": 11}, {"weight": 5753, "source": 4, "target": 8}, {"weight": 17970, "source": 4, "target": 5}, {"weight": 5629, "source": 4, "target": 13}, {"weight": 8061, "source": 4, "target": 6}, {"weight": 7507, "source": 4, "target": 12}, {"weight": 7264, "source": 4, "target": 9}, {"weight": 14003, "source": 5, "target": 15}, {"weight": 17661, "source": 5, "target": 16}, {"weight": 11610, "source": 5, "target": 7}, {"weight": 9691, "source": 5, "target": 14}, {"weight": 16662, "source": 5, "target": 10}, {"weight": 18387, "source": 5, "target": 17}, {"weight": 12880, "source": 5, "target": 11}, {"weight": 17383, "source": 5, "target": 8}, {"weight": 20566, "source": 5, "target": 13}, {"weight": 17537, "source": 5, "target": 6}, {"weight": 11343, "source": 5, "target": 12}, {"weight": 11924, "source": 5, "target": 9}, {"weight": 10325, "source": 6, "target": 15}, {"weight": 9067, "source": 6, "target": 16}, {"weight": 20087, "source": 6, "target": 7}, {"weight": 16940, "source": 6, "target": 14}, {"weight": 9131, "source": 6, "target": 10}, {"weight": 8880, "source": 6, "target": 17}, {"weight": 11600, "source": 6, "target": 11}, {"weight": 13084, "source": 6, "target": 8}, {"weight": 11520, "source": 6, "target": 13}, {"weight": 14991, "source": 6, "target": 12}, {"weight": 14986, "source": 6, "target": 9}, {"weight": 13520, "source": 7, "target": 15}, {"weight": 12739, "source": 7, "target": 16}, {"weight": 4774, "source": 7, "target": 14}, {"weight": 11138, "source": 7, "target": 10}, {"weight": 13195, "source": 7, "target": 17}, {"weight": 12417, "source": 7, "target": 11}, {"weight": 11676, "source": 7, "target": 8}, {"weight": 15527, "source": 7, "target": 13}, {"weight": 6571, "source": 7, "target": 12}, {"weight": 6943, "source": 7, "target": 9}, {"weight": 11764, "source": 8, "target": 15}, {"weight": 6518, "source": 8, "target": 16}, {"weight": 9221, "source": 8, "target": 14}, {"weight": 4382, "source": 8, "target": 10}, {"weight": 6439, "source": 8, "target": 17}, {"weight": 11545, "source": 8, "target": 11}, {"weight": 8707, "source": 8, "target": 13}, {"weight": 7172, "source": 8, "target": 12}, {"weight": 7548, "source": 8, "target": 9}, {"weight": 12993, "source": 9, "target": 15}, {"weight": 6680, "source": 9, "target": 16}, {"weight": 3587, "source": 9, "target": 14}, {"weight": 6372, "source": 9, "target": 10}, {"weight": 7543, "source": 9, "target": 17}, {"weight": 11890, "source": 9, "target": 11}, {"weight": 11399, "source": 9, "target": 13}, {"weight": 1538, "source": 9, "target": 12}, {"weight": 8785, "source": 10, "target": 15}, {"weight": 2226, "source": 10, "target": 16}, {"weight": 8207, "source": 10, "target": 14}, {"weight": 2112, "source": 10, "target": 17}, {"weight": 8741, "source": 10, "target": 11}, {"weight": 5729, "source": 10, "target": 13}, {"weight": 6158, "source": 10, "target": 12}, {"weight": 1769, "source": 11, "target": 15}, {"weight": 10548, "source": 11, "target": 16}, {"weight": 10381, "source": 11, "target": 14}, {"weight": 9899, "source": 11, "target": 17}, {"weight": 9104, "source": 11, "target": 13}, {"weight": 11365, "source": 11, "target": 12}, {"weight": 12468, "source": 12, "target": 15}, {"weight": 6908, "source": 12, "target": 16}, {"weight": 2733, "source": 12, "target": 14}, {"weight": 7786, "source": 12, "target": 17}, {"weight": 11002, "source": 12, "target": 13}, {"weight": 9045, "source": 13, "target": 15}, {"weight": 7413, "source": 13, "target": 16}, {"weight": 13051, "source": 13, "target": 14}, {"weight": 6787, "source": 13, "target": 17}, {"weight": 11484, "source": 14, "target": 15}, {"weight": 8901, "source": 14, "target": 16}, {"weight": 9764, "source": 14, "target": 17}, {"weight": 10470, "source": 15, "target": 16}, {"weight": 9756, "source": 15, "target": 17}, {"weight": 1710, "source": 16, "target": 17}]}
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: ERZ, YHM, PAV, OZC, OLB, MUK, TET, AIN, TQA, YKQ, EXT, DOY, PKB, KEJ, GGW, JZH, RAK, TEE
- Travel distances (in kilometers) between each pair of airports:
ERZ to OZC: 10411
ERZ to OLB: 2668
ERZ to JZH: 7542
ERZ to RAK: 4556
ERZ to AIN: 14403
ERZ to GGW: 11419
ERZ to PAV: 11021
ERZ to EXT: 3747
ERZ to TEE: 3773
ERZ to DOY: 7975
ERZ to TQA: 7219
ERZ to MUK: 19888
ERZ to KEJ: 5725
ERZ to TET: 7575
ERZ to PKB: 9763
ERZ to YHM: 9451
ERZ to YKQ: 9541
YHM to OZC: 14156
YHM to OLB: 7308
YHM to JZH: 13310
YHM to RAK: 7827
YHM to AIN: 6826
YHM to GGW: 4781
YHM to PAV: 10009
YHM to EXT: 6451
YHM to TEE: 8038
YHM to DOY: 12207
YHM to TQA: 8322
YHM to MUK: 12453
YHM to KEJ: 11410
YHM to TET: 14918
YHM to PKB: 2996
YHM to YKQ: 2759
PAV to OZC: 19740
PAV to OLB: 8583
PAV to JZH: 16791
PAV to RAK: 6550
PAV to AIN: 14403
PAV to GGW: 10429
PAV to EXT: 8530
PAV to TEE: 8175
PAV to DOY: 16860
PAV to TQA: 12631
PAV to MUK: 13807
PAV to KEJ: 13734
PAV to TET: 10527
PAV to PKB: 8619
PAV to YKQ: 9234
OZC to OLB: 11444
OZC to JZH: 3454
OZC to RAK: 13370
OZC to AIN: 14575
OZC to GGW: 12539
OZC to EXT: 11775
OZC to TEE: 12619
OZC to DOY: 3384
OZC to TQA: 14626
OZC to MUK: 11295
OZC to KEJ: 12007
OZC to TET: 12347
OZC to PKB: 14172
OZC to YKQ: 14273
OLB to JZH: 8651
OLB to RAK: 2220
OLB to AIN: 12506
OLB to GGW: 9330
OLB to EXT: 1521
OLB to TEE: 1668
OLB to DOY: 8729
OLB to TQA: 5753
OLB to MUK: 17970
OLB to KEJ: 5629
OLB to TET: 8061
OLB to PKB: 7507
OLB to YKQ: 7264
MUK to JZH: 14003
MUK to RAK: 17661
MUK to AIN: 11610
MUK to GGW: 9691
MUK to EXT: 16662
MUK to TEE: 18387
MUK to DOY: 12880
MUK to TQA: 17383
MUK to KEJ: 20566
MUK to TET: 17537
MUK to PKB: 11343
MUK to YKQ: 11924
TET to JZH: 10325
TET to RAK: 9067
TET to AIN: 20087
TET to GGW: 16940
TET to EXT: 9131
TET to TEE: 8880
TET to DOY: 11600
TET to TQA: 13084
TET to KEJ: 11520
TET to PKB: 14991
TET to YKQ: 14986
AIN to JZH: 13520
AIN to RAK: 12739
AIN to GGW: 4774
AIN to EXT: 11138
AIN to TEE: 13195
AIN to DOY: 12417
AIN to TQA: 11676
AIN to KEJ: 15527
AIN to PKB: 6571
AIN to YKQ: 6943
TQA to JZH: 11764
TQA to RAK: 6518
TQA to GGW: 9221
TQA to EXT: 4382
TQA to TEE: 6439
TQA to DOY: 11545
TQA to KEJ: 8707
TQA to PKB: 7172
TQA to YKQ: 7548
YKQ to JZH: 12993
YKQ to RAK: 6680
YKQ to GGW: 3587
YKQ to EXT: 6372
YKQ to TEE: 7543
YKQ to DOY: 11890
YKQ to KEJ: 11399
YKQ to PKB: 1538
EXT to JZH: 8785
EXT to RAK: 2226
EXT to GGW: 8207
EXT to TEE: 2112
EXT to DOY: 8741
EXT to KEJ: 5729
EXT to PKB: 6158
DOY to JZH: 1769
DOY to RAK: 10548
DOY to GGW: 10381
DOY to TEE: 9899
DOY to KEJ: 9104
DOY to PKB: 11365
PKB to JZH: 12468
PKB to RAK: 6908
PKB to GGW: 2733
PKB to TEE: 7786
PKB to KEJ: 11002
KEJ to JZH: 9045
KEJ to RAK: 7413
KEJ to GGW: 13051
KEJ to TEE: 6787
GGW to JZH: 11484
GGW to RAK: 8901
GGW to TEE: 9764
JZH to RAK: 10470
JZH to TEE: 9756
RAK to TEE: 1710
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test