4  Geospatial artificial intelligence (GeoAI) for remote sensing data

4.1 GeoAI for spatial prediction of future bushfire

4.1.1 Future climate data collection

Aim

We separately collected future climate datasets of temperature and precipitation for the time period 2021–2040 from WorldClim. The previous 2024 data will be used for model training, followed by predicting bushfire burn areas for the time period 2021–2040.

Description of steps

1. Download WorldClim future climate datasets of temperature and precipitation for the time period 2021–2040.
2. Preprocess the downloaded future climate data and organize it into vector format for subsequent predictions.

The data is downloaded from the WorldClim website and stored in the ./data/4. GeoAI Modeling/ directory, with period 2041-2060, GCM：ACCESS-CM2, scenarios:ssp585 (Links:https://www.worldclim.org/data/cmip6/cmip6_clim30s.html) .

4.1.2 GeoAI modelling

Aim

The step uses the gpboost model to fit temperature and precipitation data in 2024 for the next step of spatial prediction.

Description of steps

1. Load necessary libraries and data.
2. Build the GPBoost model using the data processed in Section 3.

See here for more details about the gpboost model on spatio-temporal data.

library(sf)

d24 = read_sf('./data/3. Spatial analysis/burnedarea_2024.shp')
names(d24) = c("pre","tem","burned","geometry")
d24
# Simple feature collection with 644 features and 3 fields
# Geometry type: POLYGON
# Dimension:     XY
# Bounding box:  xmin: 129 ymin: -14.9 xmax: 131 ymax: -13.3
# Geodetic CRS:  WGS 84
# # A tibble: 644 × 4
#     pre   tem burned                                        geometry
#   <dbl> <dbl>  <dbl>                                   <POLYGON [°]>
# 1  28.0 1893.   1250 ((130 -13.3, 130 -13.3, 130 -13.3, 130 -13.3, …
# 2  28.0 1856.   1529 ((130 -13.3, 130 -13.3, 130 -13.3, 130 -13.3, …
# 3  28.0 1888.   2203 ((130 -13.3, 130 -13.3, 130 -13.3, 130 -13.3, …
# 4  28.0 1884.   1289 ((131 -13.3, 131 -13.3, 131 -13.3, 131 -13.3, …
# 5  28.0 1865.   4247 ((131 -13.3, 131 -13.3, 131 -13.3, 131 -13.3, …
# 6  28.0 1873.   1991 ((131 -13.3, 131 -13.3, 131 -13.3, 131 -13.3, …
# # ℹ 638 more rows

library(gpboost)
gp_model = GPModel(gp_coords = sdsfun::sf_coordinates(d24), 
                   cov_function = "exponential")
# Training
bst = gpboost(data = as.matrix(sf::st_drop_geometry(d24)[,1:2]), 
              label = as.matrix(sf::st_drop_geometry(d24)[,3,drop = FALSE]), 
              gp_model = gp_model, objective = "regression_l2", verbose = 0)
bst
# <gpb.Booster>
#   Public:
#     add_valid: function (data, name, valid_set_gp = NULL, use_gp_model_for_validation = TRUE) 
#     best_iter: -1
#     best_score: NA
#     current_iter: function () 
#     dump_model: function (num_iteration = NULL, feature_importance_type = 0L) 
#     eval: function (data, name, feval = NULL) 
#     eval_train: function (feval = NULL) 
#     eval_valid: function (feval = NULL) 
#     finalize: function () 
#     initialize: function (params = list(), train_set = NULL, modelfile = NULL, 
#     lower_bound: function () 
#     params: list
#     predict: function (data, start_iteration = NULL, num_iteration = NULL, 
#     raw: NA
#     record_evals: list
#     reset_parameter: function (params, ...) 
#     rollback_one_iter: function () 
#     save: function () 
#     save_model: function (filename, start_iteration = NULL, num_iteration = NULL, 
#     save_model_to_string: function (start_iteration = NULL, num_iteration = NULL, feature_importance_type = 0L, 
#     set_train_data_name: function (name) 
#     to_predictor: function () 
#     update: function (train_set = NULL, fobj = NULL) 
#     upper_bound: function () 
#   Private:
#     eval_names: NULL
#     fixed_effect_train_loaded_from_file: NULL
#     get_eval_info: function () 
#     gp_model: GPModel, R6
#     gp_model_prediction_data_loaded_from_file: FALSE
#     handle: gpb.Booster.handle
#     has_gp_model: TRUE
#     higher_better_inner_eval: NULL
#     init_predictor: NULL
#     inner_eval: function (data_name, data_idx, feval = NULL) 
#     inner_predict: function (idx) 
#     is_predicted_cur_iter: list
#     label_loaded_from_file: NULL
#     name_train_set: training
#     name_valid_sets: list
#     num_class: 1
#     num_dataset: 1
#     predict_buffer: list
#     residual_loaded_from_file: NULL
#     set_objective_to_none: FALSE
#     train_set: gpb.Dataset, R6
#     train_set_version: 1
#     use_gp_model_for_validation: TRUE
#     valid_sets: list
#     valid_sets_gp: list

4.1.3 Spatial prediction

Aim

In this step, the gpboost model constructed in the previous step is used to predict the burned area of 2030.

Description of steps

1. Read the futural climate data.
2. Process the data to use the gpboost model to predict.
3. Do spatial prediction by the gpboost model.

library(terra)

pref = terra::rast('./data/4. GeoAI Modeling/future_prec.tif')
pref
# class       : SpatRaster 
# dimensions  : 193, 154, 12  (nrow, ncol, nlyr)
# resolution  : 0.00833, 0.00833  (x, y)
# extent      : 129, 131, -14.9, -13.3  (xmin, xmax, ymin, ymax)
# coord. ref. : lon/lat WGS 84 (EPSG:4326) 
# source      : future_prec.tif 
# names       : wc2.1~ec_01, wc2.1~ec_02, wc2.1~ec_03, wc2.1~ec_04, wc2.1~ec_05, wc2.1~ec_06, ...
pref = terra::app(pref,fun = "sum",na.rm = TRUE)
names(pref) = "pre"
pref
# class       : SpatRaster 
# dimensions  : 193, 154, 1  (nrow, ncol, nlyr)
# resolution  : 0.00833, 0.00833  (x, y)
# extent      : 129, 131, -14.9, -13.3  (xmin, xmax, ymin, ymax)
# coord. ref. : lon/lat WGS 84 (EPSG:4326) 
# source(s)   : memory
# name        :  pre 
# min value   : 1109 
# max value   : 1750

temf = terra::rast('./data/4. GeoAI Modeling/future_tmax.tif')
temf
# class       : SpatRaster 
# dimensions  : 193, 154, 12  (nrow, ncol, nlyr)
# resolution  : 0.00833, 0.00833  (x, y)
# extent      : 129, 131, -14.9, -13.3  (xmin, xmax, ymin, ymax)
# coord. ref. : lon/lat WGS 84 (EPSG:4326) 
# source      : future_tmax.tif 
# names       : wc2.1~ax_01, wc2.1~ax_02, wc2.1~ax_03, wc2.1~ax_04, wc2.1~ax_05, wc2.1~ax_06, ...
temf = terra::app(temf,fun = "mean",na.rm = TRUE)
names(temf) = "tem"
temf
# class       : SpatRaster 
# dimensions  : 193, 154, 1  (nrow, ncol, nlyr)
# resolution  : 0.00833, 0.00833  (x, y)
# extent      : 129, 131, -14.9, -13.3  (xmin, xmax, ymin, ymax)
# coord. ref. : lon/lat WGS 84 (EPSG:4326) 
# source(s)   : memory
# name        :  tem 
# min value   : 33.9 
# max value   : 37.4

d30 = c(pref,temf)
d30 = d30 |> 
  terra::as.polygons(aggregate = FALSE) |> 
  sf::st_as_sf() |> 
  dplyr::filter(dplyr::if_all(1:2,\(.x) !is.na(.x)))
d30
# Simple feature collection with 16430 features and 2 fields
# Geometry type: POLYGON
# Dimension:     XY
# Bounding box:  xmin: 129 ymin: -14.9 xmax: 131 ymax: -13.3
# Geodetic CRS:  WGS 84
# First 10 features:
#     pre  tem                       geometry
# 1  1739 34.6 POLYGON ((130 -13.3, 130 -1...
# 2  1735 34.6 POLYGON ((130 -13.3, 130 -1...
# 3  1745 34.6 POLYGON ((130 -13.3, 130 -1...
# 4  1733 34.6 POLYGON ((130 -13.3, 130 -1...
# 5  1732 34.6 POLYGON ((130 -13.3, 130 -1...
# 6  1731 34.7 POLYGON ((130 -13.3, 130 -1...
# 7  1725 34.8 POLYGON ((130 -13.3, 130 -1...
# 8  1750 34.8 POLYGON ((130 -13.3, 130 -1...
# 9  1741 34.8 POLYGON ((130 -13.3, 130 -1...
# 10 1725 34.7 POLYGON ((130 -13.3, 130 -1...

pred = predict(bst, data = as.matrix(sf::st_drop_geometry(d30)[,1:2]), 
               gp_coords_pred = sdsfun::sf_coordinates(d30), 
               predict_var = TRUE, pred_latent = FALSE)

pred
# $fixed_effect
# NULL
# 
# $random_effect_mean
# [1] NA
# 
# $random_effect_cov
# [1] NA
# 
# $response_mean
#     [1]  3307  3270  3095  3089  3078  3055  3017  2874  2905  2929
#    [11]  2940  2935  2916  2648  2723  2786  2831  2859  2872  2875
#    [21]  2182  2296  2428  2552  2654  2733  2789  2829  2862  1705
#    [31]  1836  2034  2234  2406  2544  2649  2727  2786  2839  1271
#    [41]  1254  1528  1833  2096  2306  2467  2587  2675  2741  2800
#    [51]  2867  1394   927   933  1388  1756  2046  2268  2433  2551
#    [61]  2634  2693  2744  2800  1774  1475  1213  1235  1529  1841
#    [71]  2101  2300  2445  2544  2606  2644  2670  2699  2037  1869
#    [81]  1716  1626  1671  1843  2055  2247  2398  2503  2566  2593
#    [91]  2595  2583  2136  2054  2007  1994  2022  2096  2207  2335
#   [101]  2454  2546  2600  2616  2596  2550  2041  2066  2141  2258
#   [111]  2399  2506  2572  2634  2692  2728  2729  2691  2616  2513
#   [121]  1886  1928  2060  2240  2471  2748  2893  2900  2921  2940
#   [131]  2934  2886  2792  2655  1789  1858  2043  2286  2578  2895
#   [141]  3086  3139  3176  3191  3163  3077  2928  1808  1731  1804
#   [151]  2003  2279  2595  2907  3151  3310  3412  3457  3430  3316
#   [161]  1828  1653  1596  1695  1926  2238  2584  2925  3231  3480
#   [171]  3662  3762  3758  3627  3362  1910  1651  1449  1383  1523
#   [181]  1820  2188  2577  2964  3340  3684  3960  4136  4178  4043
#   [191]  3714  3225  2632  5295  2057  1773  1490  1228  1090  1322
#   [201]  1729  2166  2602  3030  3485  3944  4327  4596  4713  4604
#   [211]  4192  3582  2838  2014  5216  5147  2219  1954  1680  1403
#   [221]  1126   893  1251  1727  2209  2691  3167  3708  4285  4780
#   [231]  5146  5339  5280  4785  4081  3221  2254  1251  5158  5065
#   [241]  4984  3224  3025  2362  2122  1878  1636  1409  1228  1191
#   [251]  1428  1844  2328  2850  3417  4050  4716  5328  5799  6042
#   [261]  5956  5492  4737  3804  2814  1958  1505  1388  1448  1531
#   [271]  1625  5013  4903  4807  3258  3073  2880  2678  2469  2253
#   [281]  2035  1821  1622  1459  1370  1417  1642  2018  2491  3039
#   [291]  3674  4409  5207  5974  6593  6935  6880  6390  5553  4524
#   [301]  3477  2599  2036  1777  1709  1740  1818  1920  5005  4863
#   [311]  4731  4615  3269  3094  2914  2728  2537  2341  2143  1949
#   [321]  1766  1609  1500  1474  1572  1817  2194  2666  3223  3899
#   [331]  4747  5730  6712  7547  8072  8088  7514  6509  5307  4106
#   [341]  3106  2459  2149  2052  2066  2139  2241  4880  4713  4552
#   [351]  4410  3261  3089  2917  2743  2567  2388  2207  2027  1855
#   [361]  1701  1579  1511  1524  1659  1950  2364  2857  3408  4069
#   [371]  5038  6278  7521  8626  9449  9618  8833  7550  6105  4666
#   [381]  3444  2751  2486  2407  2421  2486  2584  4570  4375  4197
#   [391]  3240  3065  2894  2726  2560  2394  2229  2063  1902  1750
#   [401]  1619  1525  1488  1532  1680  2060  2552  3106  3686  4258
#   [411]  5352  6916  8373  9689 10838 11479 10117  8554  6908  5247
#   [421]  3643  3031  2875  2809  2811  2863  2948  3056  3182  3325
#   [431]  3490  5684  4894  4680  4449  4211  3985  3419  3220  3030
#   [441]  2851  2681  2519  2363  2210  2059  1910  1765  1630  1517
#   [451]  1444  1435  1523  1755  2188  2772  3450  4188  5016  6219
#   [461]  7752  9251 10586 11624 11907 10931  9412  7723  6028  4547
#   [471]  3736  3420  3285  3247  3270  3333  3423  3530  3651  3786
#   [481]  5557  5416  5255  5073  4866  4631  4369  4084  3794  3539
#   [491]  3449  3216  2999  2799  2616  2449  2295  2151  2013  1879
#   [501]  1748  1620  1500  1398  1335  1341  1466  1768  2286  2997
#   [511]  3851  4818  5923  7233  8701 10152 11408 12242 12347 11578
#   [521] 10192  8531  6870  5469  4539  4046  3816  3724  3707  3740
#   [531]  3807  3890  3979  4071  5574  5435  5276  5095  4886  4643
#   [541]  4359  4030  3664  3305  3056  3057  3538  3255  2993  2756
#   [551]  2545  2360  2197  2054  1925  1806  1693  1582  1472  1366
#   [561]  1270  1204  1201  1326  1670  2297  3178  4237  5428  6736
#   [571]  8153  9631 11071 12312 13113 13188 12423 11020  9308  7590
#   [581]  6146  5168  4630  4366  4235  4175  4173  4215  4273  4322
#   [591]  4358  5613  5482  5332  5162  4967  4736  4456  4106  3674
#   [601]  3175  2736  2696  3203  4080  3722  3372  3043  2747  2487
#   [611]  2266  2080  1925  1796  1686  1591  1504  1418  1331  1241
#   [621]  1151  1074  1035  1102  1432  2197  3293  4568  5962  7444
#   [631]  8961 10476 11959 13302 14271 14432 13525 11929 10050  8157
#   [641]  6562  5597  5162  4949  4804  4685  4637  4667  4699  4696
#   [651]  4659  5557  5425  5278  5115  4925  4692  4381  3948  3345
#   [661]  2580  2332  3346  4322  5048  5528  5789  5861  5775  5565
#   [671]  5261  4891  4479  4046  3612  3194  2810  2474  2192  1963
#   [681]  1780  1636  1524  1439  1373  1317  1264  1206  1140  1066
#   [691]   988   915   873  1033  2037  3389  4843  6395  8039  9633
#   [701] 11156 12699 14200 15537 16073 14718 12830 10782  8674  6719
#   [711]  5923  5769  5656  5500  5280  5150  5208  5202  5121  4985
#   [721]  5661  5552  5439  5326  5211  5082  4900  4608  4134  3442
#   [731]  3207  4316  5285  5960  6366  6536  6502  6300  5970  5549
#   [741]  5069  4554  4024  3500  3002  2554  2175  1872  1641  1466
#   [751]  1335  1244  1187  1156  1141  1128  1108  1078  1037   989
#   [761]   944   922  1075  2156  3567  5076  6682  8383 10018 11573
#   [771] 13153 14706 16125 16787 15401 13546 11547  9482  7518  6792
#   [781]  6688  6587  6423  6163  5963  5939  5816  5603  5338  5792
#   [791]  5711  5635  5583  5570  5601  5647  5653  5570  5449  5598
#   [801]  6170  6791  7239  7471  7485  7295  6935  6451  5888  5281
#   [811]  4652  4017  3392  2801  2276  1849  1534  1312  1152  1037
#   [821]   965   938   950   983  1019  1045  1060  1067  1081  1128
#   [831]  1277  1697  2585  3826  5255  6810  8443 10083 11700 13292
#   [841] 14773 15915 16251 15483 14035 12326 10598  9134  8278  7913
#   [851]  7726  7563  7357  7122  6861  6526  6125  5696  5952  5898
#   [861]  5856  5858  5955  6184  6531  6936  7336  7701  8043  8363
#   [871]  8616  8764  8773  8597  8212  7651  6981  6258  5516  4772
#   [881]  4032  3302  2603  1981  1502  1193  1006   873   767   702
#   [891]   704   768   859   949  1023  1083  1142  1222  1364  1635
#   [901]  2136  2945  4038  5342  6800  8360  9972 11600 13198 14646
#   [911] 15701 16043 15537 14411 13014 11624 10450  9628  9150  8907
#   [921]  8774  8618  8322  7849  7257  6628  6017  6144  6119  6100
#   [931]  6128  6301  6740  7436  8280  9185 10019 10532 10621 10505
#   [941] 10351 10157  9812  9207  8400  7516  6625  5757  4914  4087
#   [951]  3264  2446  1691  1142   886   787   694   570   475   501
#   [961]   634   793   933  1047  1144  1242  1370  1569  1893  2403
#   [971]  3143  4114  5293  6644  8126  9689 11299 12923 14453 15647
#   [981] 16123 15699 14689 13496 12368 11416 10663 10152  9915  9885
#   [991]  9862  9531  8798  7899  7025  6239  6354  6377  6390  6394
#  [1001]  6409  6553  7196  8275  9522 10900 12312 13081 12726 12183
#  [1011] 11767 11461 11067 10199  9088  7986  6946  5979  5075  4208
#  [1021]  3339  2427  1481   783   716   785   730   536   312   361
#  [1031]   602   824   996  1127  1237  1350  1497  1713  2039  2516
#  [1041]  3173  4025  5074  6311  7715  9206 10763 12415 14106 15663
#  [1051] 16452 15834 14720 13623 12716 12010 11292 10722 10514 10661
#  [1061] 10982 10714  9534  8281  7198  6288  6570  6656  6736  6801
#  [1071]  6842  6859  7703  9069 10519 12128 13978 15267 14142 13320
#  [1081] 12754 12390 12179 10923  9563  8310  7171  6153  5246  4419
#  [1091]  3606  2726  1692   583  1022  1203  1134   847   379   474
#  [1101]   786  1006  1158  1267  1359  1459  1593  1792  2084  2496
#  [1111]  3053  3771  4668  5761  7068  8457  9918 11552 13318 15182
#  [1121] 16716 15410 14220 13219 12481 12083 11300 10658 10457 10699
#  [1131] 11384 11381  9604  8177  7033  6104  6805  6976  7158  7349
#  [1141]  7562  7906  8696  9877 11207 12629 14015 14729 14370 13745
#  [1151] 13188 12697 12087 11031  9731  8446  7267  6247  5406  4715
#  [1161]  4098  3464  2774  2247  2179  2165  1982  1643  1280  1172
#  [1171]  1262  1358  1425  1468  1506  1562  1658  1813  2047  2376
#  [1181]  2814  3376  4086  4974  6066  7324  8732 10287 11911 13427
#  [1191] 14259 13880 13047 12220 11538 10988 10386  9872  9651  9739
#  [1201]  9973  9685  8614  7472  6491  5673  6807  7039  7310  7621
#  [1211]  7974  8389  8928  9674 10611 11646 12682 13565 14036 13997
#  [1221] 13660 13210 12668 11938 10926  9703  8425  7229  6230  5509
#  [1231]  5055  4766  4526  4268  4018  3807  3550  3187  2749  2339
#  [1241]  2064  1924  1843  1776  1715  1670  1657  1693  1789  1955
#  [1251]  2192  2504  2894  3383  4016  4864  5972  7308  8761 10170
#  [1261] 11326 11951 11916 11442 10797 10140  9533  8990  8555  8275
#  [1271]  8129  7994  7651  7036  6326  5650  5042  6927  7241  7621
#  [1281]  8069  8588  9177  9828 10520 11235 11947 12600 13114 13422
#  [1291] 13503 13370 13058 12564 11839 10844  9633  8329  7078  6069
#  [1301]  5499  5381  5528  5757  5932  5919  5643  5167  4588  3981
#  [1311]  3424  2983  2657  2400  2178  1987  1835  1736  1702  1735
#  [1321]  1835  1991  2188  2409  2658  2985  3540  4499  5817  7225
#  [1331]  8478  9412  9936 10035  9764  9233  8568  7915  7389  6990
#  [1341]  6643  6294  5933  5600  5302  4996  4660  4302  6683  6990
#  [1351]  7381  7864  8444  9119  9876 10647 11284 11781 12205 12528
#  [1361] 12720 12874 13050 13081 12902 12509 11854 10867  9628  8265
#  [1371]  6890  5741  5321  5680  6339  7066  7727  8000  7597  6857
#  [1381]  6046  5239  4493  3892  3415  2991  2603  2261  1985  1789
#  [1391]  1682  1661  1714  1820  1943  2040  2070  2041  2163  3000
#  [1401]  4489  5965  7116  7859  8268  8446  8296  7800  7048  6259
#  [1411]  5763  5456  5071  4528  3911  3567  3618  3706  3686  3563
#  [1421]  6620  6969  7426  8001  8696  9507 10421 11398 11969 12252
#  [1431] 12477 12573 12465 12390 12777 12927 12830 12532 12033 11009
#  [1441]  9747  8372  6901  5390  5061  6121  7215  8323  9467 10304
#  [1451]  9441  8428  7453  6490  5524  4805  4208  3606  3028  2514
#  [1461]  2097  1800  1626  1568  1609  1716  1842  1919  1856  1557
#  [1471]   992  1759  3751  5306  6342  6849  7002  7341  7270  6766
#  [1481]  5879  4717  4387  4276  3875  3164  2155  1649  2258  2673
#  [1491]  2877  2922  6469  6842  7347  7997  8787  9699 10692 11671
#  [1501] 12288 12595 12790 12847 12734 12674 12906 12988 12858 12549
#  [1511] 12035 11127  9995  8766  7478  6271  6092  7064  8200  9358
#  [1521] 10493 11176 10601  9688  8744  7772  6771  5895  5081  4245
#  [1531]  3436  2719  2148  1749  1522  1453  1520  1693  1924  2135
#  [1541]  2225  2093  1809  2531  4178  5506  6347  6716  6821  6984
#  [1551]  6848  6331  5470  4447  3991  3756  3290  2553  1628  1206
#  [1561]  1650  2069  2327  2442  5975  6220  6591  7122  7831  8705
#  [1571]  9698 10732 11676 12379 12833 13128 13301 13360 13368 13355
#  [1581] 13234 12970 12571 12012 11257 10359  9410  8508  7857  7805
#  [1591]  8383  9257 10198 11023 11439 11245 10661  9916  9071  8131
#  [1601]  7113  6025  4894  3802  2845  2104  1614  1359  1305  1432
#  [1611]  1729  2166  2671  3147  3533  3932  4654  5652  6522  7079
#  [1621]  7325  7365  7282  7003  6476  5744  4969  4364  3868  3301
#  [1631]  2625  1967  1620  1674  1872  2041  2135  5673  5870  6202
#  [1641]  6730  7488  8448  9540 10663 11675 12454 13005 13426 13776
#  [1651] 14020 14070 13891 13546 13113 12627 12079 11459 10796 10152
#  [1661]  9614  9300  9325  9696 10295 10972 11559 11875 11829 11496
#  [1671] 10993 10348  9498  8369  6999  5524  4093  2851  1932  1382
#  [1681]  1136  1120  1320  1771  2491  3410  4407  5385  6276  7043
#  [1691]  7651  8073  8297  8337  8221  7968  7569  7024  6367  5670
#  [1701]  5002  4362  3709  3052  2471  2087  1931  1918  1949  1970
#  [1711]  5269  5317  5434  5674  6152  6957  8017  9231 10502 11662
#  [1721] 12490 13040 13547 14110 14627 14769 14384 13777 13178 12641
#  [1731] 12147 11668 11223 10857 10623 10555 10635 10860 11236 11701
#  [1741] 12139 12404 12412 12235 11963 11588 10925  9689  7975  6108
#  [1751]  4291  2701  1598  1069   898   931  1169  1746  2801  4215
#  [1761]  5793  7397  8800  9631  9873  9856  9743  9561  9281  8877
#  [1771]  8376  7804  7178  6510  5796  5058  4325  3630  3023  2560
#  [1781]  2255  2076  1971  1901  4962  4944  4962  5048  5373  6263
#  [1791]  7420  8722 10154 11596 12380 12741 13263 14049 15030 15445
#  [1801] 14615 13714 13012 12500 12123 11797 11554 11434 11462 11635
#  [1811] 11764 11823 12010 12317 12679 12945 12908 12795 12712 12666
#  [1821] 12447 11042  8852  6618  4448  2424  1086   791   767   844
#  [1831]  1039  1576  3050  4999  7115  9339 11475 12365 12025 11575
#  [1841] 11177 10826 10433  9873  9277  8681  8081  7454  6687  5848
#  [1851]  5028  4262  3582  3021  2589  2272  2045  1882  4664  4597
#  [1861]  4547  4528  4659  5589  6698  7931  9329 10898 11568 11793
#  [1871] 12318 13185 14406 15145 14007 13094 12471 12089 11896 11753
#  [1881] 11723 11824 12051 12397 12563 12502 12555 12720 12985 13252
#  [1891] 13127 13043 13051 13158 13293 11754  9365  7028  4748  2528
#  [1901]   999   902   920  1015  1217  1663  3505  5776  8198 10743
#  [1911] 13344 14279 13595 12948 12386 11915 11464 10788 10153  9556
#  [1921]  8975  8382  7565  6651  5751  4898  4123  3456  2907  2471
#  [1931]  2133  1880  4497  4389  4294  4229  4240  4466  5056  5886
#  [1941]  6850  7914  8949  9644 10102 10657 11401 12218 12612 12307
#  [1951] 11849 11522 11372 11377 11495 11717 12028 12391 12728 12899
#  [1961] 12896 12863 12874 12942 13000 12970 12936 12935 12894 12533
#  [1971] 11326  9436  7348  5273  3394  2099  1556  1405  1479  1825
#  [1981]  2679  4325  6535  8985 11439 13516 14502 14396 13882 13282
#  [1991] 12700 12125 11520 10934 10377  9810  9165  8365  7439  6469
#  [2001]  5518  4636  3859  3202  2659  2219  1878  4260  4132  4022
#  [2011]  3951  3963  4127  4483  4992  5591  6237  6876  7451  7980
#  [2021]  8525  9101  9643 10014 10163 10213 10284 10436 10703 11093
#  [2031] 11583 12118 12624 13009 13185 13153 13007 12842 12712 12631
#  [2041] 12590 12577 12544 12377 11878 10860  9371  7633  5863  4272
#  [2051]  3083  2380  2069  2074  2459  3401  5017  7176  9588 11919
#  [2061] 13774 14779 14921 14532 13925 13278 12668 12117 11621 11150
#  [2071] 10642 10016  9213  8246  7189  6122  5116  4229  3479  2846
#  [2081]  2307  1872  4030  3885  3758  3668  3640  3702  3856  4071
#  [2091]  4300  4524  4797  5219  5753  6265  6688  7047  7454  7961
#  [2101]  8478  8949  9404  9932 10610 11394 12179 12871 13361 13532
#  [2111] 13390 13068 12694 12357 12142 12083 12103 12085 11908 11443
#  [2121] 10598  9395  7955  6441  5035  3924  3188  2778  2661  2927
#  [2131]  3797  5429  7654 10126 12497 14371 15376 15498 15068 14398
#  [2141] 13687 13066 12593 12227 11894 11510 10964 10156  9110  7933
#  [2151]  6721  5566  4572  3764  3070  2433  1878  3805  3641  3493
#  [2161]  3372  3291  3255  3246  3224  3132  2935  2761  3068  3705
#  [2171]  4211  4473  4576  4962  5910  6907  7743  8432  9136 10124
#  [2181] 11238 12280 13183 13848 14004 13647 13094 12486 11906 11527
#  [2191] 11511 11625 11684 11584 11235 10564  9586  8382  7053  5737
#  [2201]  4674  3992  3534  3254  3238  3839  5575  8011 10640 13199
#  [2211] 15331 16317 16156 15532 14742 13933 13290 12953 12763 12604
#  [2221] 12410 12034 11209 10033  8721  7350  6002  4901  4122  3416
#  [2231]  2685  1952  3583  3399  3227  3074  2946  2839  2727  2563
#  [2241]  2275  1778   999  1344  2199  2685  2816  2603  2683  4372
#  [2251]  5777  6904  7773  8413  9836 11247 12464 13507 14392 14532
#  [2261] 13849 13087 12287 11480 10778 11012 11246 11404 11424 11244
#  [2271] 10747  9969  8975  7813  6536  5444  4938  4451  4022  3692
#  [2281]  3537  5758  8398 11096 13778 16369 17308 16637 15845 14982
#  [2291] 14094 13324 13267 13249 13245 13234 13186 12260 10950  9567
#  [2301]  8104  6557  5307  4706  4011  3217  2316  3161  2965  2784
#  [2311]  2624  2483  2340  2152  1857  1411   932  1042  1541  1876
#  [2321]  1983  1984  2451  3793  5263  6587  7723  8797 10145 11538
#  [2331] 12755 13748 14432 14473 13868 13039 12156 11333 10797 10797
#  [2341] 11022 11263 11413 11384 11091 10536  9766  8827  7785  6861
#  [2351]  6202  5620  5115  4804  5076  6658  8961 11445 13897 16010
#  [2361] 16910 16603 15926 15140 14371 13820 13675 13706 13779 13814
#  [2371] 13651 12926 11782 10477  9080  7663  6495  5691  4933  4137
#  [2381]  3329  2931  2711  2505  2326  2187  2079  1969  1815  1602
#  [2391]  1415  1409  1546  1672  1774  2007  2653  3817  5255  6726
#  [2401]  8126  9468 10807 12079 13180 14021 14479 14407 13831 12969
#  [2411] 12041 11237 10747 10668 10885 11224 11534 11689 11601 11263
#  [2421] 10726 10043  9262  8459  7690  6979  6409  6161  6530  7733
#  [2431]  9581 11708 13785 15439 16277 16289 15825 15191 14590 14185
#  [2441] 14051 14108 14229 14281 14095 13519 12587 11442 10201  8967
#  [2451]  7862  6928  6096  5329  4675  2716  2474  2241  2044  1923
#  [2461]  1897  1935  1990  2029  2030  1976  1883  1804  1827  2103
#  [2471]  2809  3995  5507  7145  8765 10274 11615 12774 13740 14451
#  [2481] 14778 14582 13887 12901 11860 10982 10467 10409 10717 11221
#  [2491] 11752 12140 12250 12089 11764 11340 10805 10105  9253  8380
#  [2501]  7668  7319  7563  8524 10075 11923 13743 15184 15948 16018
#  [2511] 15645 15109 14616 14316 14268 14413 14633 14784 14695 14237
#  [2521] 13437 12430 11338 10242  9188  8208  7329  6581  6009  2527
#  [2531]  2266  2002  1766  1651  1740  1963  2245  2549  2764  2670
#  [2541]  2341  2041  1917  2106  2825  4151  5848  7698  9551 11224
#  [2551] 12529 13537 14369 15015 15323 14998 14045 12821 11580 10518
#  [2561]  9910  9948 10439 11169 11994 12696 12969 12890 12734 12589
#  [2571] 12372 11804 10799  9693  8751  8157  8157  8958 10370 12076
#  [2581] 13809 15237 15921 15848 15412 14884 14431 14207 14296 14598
#  [2591] 14985 15332 15440 15071 14307 13378 12410 11441 10437  9411
#  [2601]  8479  7723  7190  2626  2379  2113  1826  1525  1329  1598
#  [2611]  1997  2454  2998  3580  3384  2720  2225  1963  1980  2626
#  [2621]  4270  6211  8275 10373 12326 13461 14238 14924 15532 16006
#  [2631] 15579 14171 12681 11236  9910  9031  9339 10045 10963 12080
#  [2641] 13283 13590 13431 13421 13576 13831 13541 12166 10802  9631
#  [2651]  8727  8297  9104 10490 12102 13823 15486 16083 15623 15060
#  [2661] 14518 14060 13850 14162 14655 15226 15820 16297 15918 15070
#  [2671] 14183 13321 12508 11573 10427  9420  8632  8108  2508  2282
#  [2681]  1776  1495  1319  1610  2031  2508  3066  3652  3444  2761
#  [2691]  2254  1999  2054  2772  4524  6593  8784 10977 12965 14056
#  [2701] 14718 15245 15685 16007 15459 13963 12413 10925  9562  8644
#  [2711]  8917  9592 10494 11629 12907 13353 13393 13619 14010 14465
#  [2721] 14308 12986 11604 10359  9336  8745  9359 10528 11918 13440
#  [2731] 14954 15471 15002 14487 14029 13673 13571 13993 14596 15276
#  [2741] 15977 16561 16282 15533 14740 13958 13199 12281 11113 10057
#  [2751]  9211  8632  2055  1858  1681  1621  1771  2058  2402  2750
#  [2761]  2972  2839  2444  2096  1986  2284  3225  4878  6970  9220
#  [2771] 11382 13170 14339 14985 15324 15448 15291 14605 13404 12016
#  [2781] 10656  9487  8770  8696  9085  9753 10616 11524 12215 12751
#  [2791] 13323 13909 14306 14140 13289 12121 10952 10001  9526  9744
#  [2801] 10497 11524 12640 13605 14049 13965 13692 13426 13279 13380
#  [2811] 13796 14423 15134 15799 16217 16149 15679 15033 14314 13516
#  [2821] 12561 11459 10370  9434  8732  2145  2024  1914  1872  1935
#  [2831]  2075  2233  2352  2367  2227  1986  1789  1809  2252  3326
#  [2841]  5073  7283  9652 11871 13628 14724 15214 15293 15090 14621
#  [2851] 13838 12772 11557 10348  9311  8622  8373  8489  8846  9376
#  [2861] 10053 10860 11773 12730 13596 14146 14131 13499 12479 11373
#  [2871] 10443  9913  9904 10333 11006 11737 12355 12722 12827 12781
#  [2881] 12711 12737 12969 13453 14129 14875 15544 15958 15984 15661
#  [2891] 15130 14481 13703 12733 11587 10403  9331  8481  2424  2337
#  [2901]  2326  2317  2265  2178  2110  2102  2117  2097  2012  1865
#  [2911]  1694  1529  1415  1465  1901  3054  5029  7507 10123 12555
#  [2921] 14404 15338 15507 15246 14735 14036 13180 12191 11107 10004
#  [2931]  9007  8287  7941  7862  7916  8075  8487  9377 10659 12039
#  [2941] 13293 14178 14371 13793 12766 11625 10614  9962  9815 10057
#  [2951] 10471 10898 11259 11549 11758 11871 11936 12058 12372 12954
#  [2961] 13722 14550 15304 15796 15853 15542 15057 14496 13809 12833
#  [2971] 11552 10188  8935  7911  2532  2354  2333  2490  2608  2620
#  [2981]  2520  2383  2336  2254  2070  1789  1460  1259  1171  1105
#  [2991]  1100  1314  2405  4828  7684 10595 13378 15560 16149 15796
#  [3001] 15162 14379 13492 12595 11705 10743  9716  8680  7861  7542
#  [3011]  7373  7161  6888  6805  7814  9578 11372 13040 14432 14909
#  [3021] 14136 12972 11747 10587  9727  9577  9786 10034 10215 10314
#  [3031] 10528 10848 11071 11200 11314 11623 12341 13227 14150 15043
#  [3041] 15724 15712 15251 14740 14276 13809 12879 11309  9709  8275
#  [3051]  7063  2711  2592  2427  2476  2841  3081  3166  3068  2790
#  [3061]  2767  2570  2218  1757  1230  1022  1017  1020  1038  1069
#  [3071]  1845  4886  7928 10932 13874 16691 16577 15805 14939 13998
#  [3081] 12997 12107 11356 10540  9637  8620  7575  7483  7250  6847
#  [3091]  6267  5515  6737  8832 10791 12645 14424 15317 14172 12997
#  [3101] 11815 10623  9436  9516  9712  9823  9818  9670  9808 10218
#  [3111] 10482 10633 10708 10861 11769 12687 13610 14540 15474 15237
#  [3121] 14591 14027 13589 13317 12535 10612  8901  7401  6100  2768
#  [3131]  2780  2810  2872  3082  3439  3759  3945  3945  3778  3518
#  [3141]  3108  2555  1946  1410  1130  1105  1225  1474  1970  3239
#  [3151]  5581  8312 11054 13589 15443 15874 15360 14521 13572 12631
#  [3161] 11819 11152 10523  9857  9125  8457  8025  7607  7093  6552
#  [3171]  6306  7067  8606 10303 11949 13357 13982 13578 12781 11883
#  [3181] 10982 10256  9988  9944  9888  9778  9660  9714  9935 10145
#  [3191] 10305 10459 10771 11389 12139 12902 13611 14088 13977 13453
#  [3201] 12857 12294 11710 10742  9268  7746  6368  5207  2639  2721
#  [3211]  2878  3093  3369  3731  4160  4580  4905  5041  4912  4491
#  [3221]  3823  3018  2221  1597  1284  1303  1598  2148  3040  4459
#  [3231]  6446  8757 11092 13151 14557 15033 14719 13970 13061 12189
#  [3241] 11491 10995 10628 10291  9904  9441  8910  8312  7704  7223
#  [3251]  7107  7588  8601  9866 11141 12193 12757 12761 12413 11923
#  [3261] 11407 10952 10618 10368 10145  9944  9802  9777  9862  9995
#  [3271] 10142 10327 10618 11051 11573 12097 12523 12710 12528 12029
#  [3281] 11366 10630  9807  8802  7606  6359  5197  4232  2383  2432
#  [3291]  2636  2951  3349  3813  4324  4866  5427  5945  6285  6222
#  [3301]  5625  4639  3511  2446  1655  1320  1459  1967  2786  3924
#  [3311]  5398  7177  9161 11164 12919 14099 14479 14149 13386 12457
#  [3321] 11601 11025 10779 10752 10809 10804 10544  9937  9141  8385
#  [3331]  7843  7656  7900  8536  9418 10366 11194 11741 11968 11973
#  [3341] 11883 11757 11556 11224 10823 10448 10149  9949  9859  9864
#  [3351]  9933 10044 10198 10409 10678 10982 11273 11467 11451 11135
#  [3361] 10539  9753  8852  7882  6888  5893  4900  3949  3139  2194
#  [3371]  2028  2149  2495  2961  3523  4164  4809  5443  6147  6912
#  [3381]  7597  7738  6860  5448  3949  2552  1486  1152  1501  2234
#  [3391]  3269  4593  6100  7698  9438 11241 12896 14034 14245 13727
#  [3401] 12840 11796 10836 10358 10443 10796 11279 11755 11784 10969
#  [3411]  9857  8891  8224  7913  7949  8300  8892  9604 10301 10842
#  [3421] 11185 11435 11694 11986 12113 11750 11166 10657 10284 10040
#  [3431]  9910  9870  9891  9957 10056 10167 10267 10367 10455 10477
#  [3441] 10327  9856  9100  8169  7113  5999  5026  4268  3529  2755
#  [3451]  2022  2300  1927  1586  1841  2328  2887  3553  4357  5112
#  [3461]  5747  6555  7530  8643  9494  7887  6046  4287  2620  1099
#  [3471]   858  1512  2389  3531  4993  6582  7915  9480 11180 12869
#  [3481] 14318 14155 13373 12369 11210  9982  9537 10057 10692 11472
#  [3491] 12442 13180 11642 10163  9023  8247  7848  7709  7841  8227
#  [3501]  8777  9405  9958 10307 10696 11198 11880 12651 11979 11199
#  [3511] 10644 10271 10033  9903  9848  9835  9850  9888  9914  9816
#  [3521]  9717  9618  9501  9327  8666  7740  6713  5564  4281  3284
#  [3531]  2912  2424  1813  1111  2212  1856  1602  1769  2193  2721
#  [3541]  3364  4135  4904  5638  6512  7520  8559  9053  7900  6215
#  [3551]  4517  2907  1562  1212  1683  2459  3506  4843  6295  7666
#  [3561]  9196 10835 12421 13608 13623 12942 11995 10907  9849  9449
#  [3571]  9824 10411 11133 11945 12284 11167  9799  8665  7844  7350
#  [3581]  7116  7134  7388  7810  8328  8819  9218  9668 10237 10945
#  [3591] 11548 11259 10721 10327 10077  9928  9843  9794  9754  9710
#  [3601]  9652  9535  9304  9026  8731  8421  8041  7346  6436  5443
#  [3611]  4368  3248  2427  2073  1727  1305   842  2207  1919  1754
#  [3621]  1811  2068  2459  2972  3607  4336  5149  6052  6978  7730
#  [3631]  7918  7257  6035  4637  3303  2275  1825  1944  2440  3228
#  [3641]  4290  5575  7028  8625 10259 11718 12689 12905 12483 11710
#  [3651] 10810 10020  9620  9666  9966 10361 10681 10594  9886  8865
#  [3661]  7871  7062  6510  6232  6209  6393  6717  7116  7530  7939
#  [3671]  8379  8876  9402  9799  9889  9808  9739  9724  9737  9743
#  [3681]  9719  9659  9557  9395  9141  8776  8324  7819  7281  6693
#  [3691]  6002  5217  4371  3493  2662  2041  1674  1421  1202  1063
#  [3701]  2230  1978  1819  1793  1897  2113  2442  2916  3577  4414
#  [3711]  5341  6225  6872  7047  6630  5751  4659  3583  2725  2233
#  [3721]  2125  2323  2783  3541  4672  6174  7900  9634 11131 12120
#  [3731] 12428 12136 11486 10716 10030  9585  9412  9411  9447  9382
#  [3741]  9082  8492  7693  6827  6034  5447  5157  5145  5312  5571
#  [3751]  5877  6216  6579  6955  7334  7706  8059  8386  8695  8997
#  [3761]  9281  9507  9632  9644  9569  9420  9183  8819  8306  7667
#  [3771]  6946  6189  5454  4782  4148  3498  2826  2207  1755  1506
#  [3781]  1389  1349  1433  2247  2004  1821  1715  1684  1719  1827
#  [3791]  2085  2654  3541  4535  5459  6156  6430  6162  5488  4622
#  [3801]  3733  2973  2470  2226  2166  2265  2630  3571  5199  7148
#  [3811]  9086 10778 11922 12248 11927 11291 10558  9882  9382  9066
#  [3821]  8836  8577  8210  7742  7209  6550  5754  4918  4240  3970
#  [3831]  4052  4256  4469  4677  4928  5240  5543  5793  6008  6314
#  [3841]  6860  7544  8219  8827  9306  9558  9586  9488  9312  9042
#  [3851]  8604  7944  7116  6181  5196  4306  3699  3287  2863  2366
#  [3861]  1873  1567  1510  1567  1667  1857  2249  1786  1613  1473
#  [3871]  1351  1234  1165  1604  2662  3750  4743  5578  6059  5823
#  [3881]  5260  4570  3828  3116  2646  2367  2119  1870  1678  2261
#  [3891]  4274  6505  8645 10607 12111 12275 11754 11069 10333  9621
#  [3901]  9081  8716  8347  7880  7247  6572  6176  5652  4890  3938
#  [3911]  2984  2806  3116  3380  3537  3599  3730  4045  4295  4424
#  [3921]  4440  4547  5405  6491  7499  8408  9186  9552  9522  9391
#  [3931]  9206  8962  8528  7704  6714  5615  4408  3233  2815  2762
#  [3941]  2580  2219  1731  1505  1748  1993  2181  2363  1520  1312
#  [3951]  1101   870   620   935  2027  3079  4047  4923  5577  5394
#  [3961]  5010  4541  3995  3391  2997  2715  2369  1949  1476  1736
#  [3971]  3914  6132  8245 10231 11944 11955 11400 10760 10079  9388
#  [3981]  8850  8474  8042  7488  6751  5942  5658  5192  4461  3493
#  [3991]  2378  2262  2622  2844  2921  2866  2875  3159  3343  3405
#  [4001]  3352  3318  4416  5705  6895  7980  8944  9398  9363  9235
#  [4011]  9045  8803  8401  7496  6476  5361  4133  2845  2627  2795
#  [4021]  2789  2578  2171  2008  2436  2758  2984  3164  1453  1222
#  [4031]  1000   805   730  1025  1723  2547  3354  4079  4593  4766
#  [4041]  4722  4563  4310  3987  3667  3344  2975  2604  2419  2903
#  [4051]  4295  6067  7862  9492 10667 11023 10801 10354  9822  9280
#  [4061]  8802  8387  7949  7431  6823  6227  5745  5216  4532  3723
#  [4071]  2983  2660  2664  2696  2664  2583  2558  2635  2718  2773
#  [4081]  2862  3201  4060  5230  6435  7547  8447  8966  9104  9028
#  [4091]  8823  8507  8016  7286  6405  5444  4467  3669  3371  3426
#  [4101]  3507  3491  3398  3419  3632  3867  4077  4327  1184   988
#  [4111]   856   858  1085  1538  2110  2704  3266  3758  4154  4456
#  [4121]  4658  4743  4689  4495  4187  3825  3521  3465  3889  4860
#  [4131]  6172  7564  8816  9719 10140 10145  9907  9553  9159  8771
#  [4141]  8396  8012  7594  7134  6650  6149  5594  4961  4289  3686
#  [4151]  3266  3017  2836  2664  2502  2387  2336  2333  2383  2562
#  [4161]  3012  3830  4927  6115  7229  8123  8682  8896  8848  8623
#  [4171]  8265  7788  7194  6505  5764  5055  4532  4329  4401  4587
#  [4181]  4766  4896  4995  5089  5184  5314  5548  1165   999   904
#  [4191]   920  1079  1369  1736  2124  2524  3001  3608  4259  4843
#  [4201]  5291  5524  5462  5157  4769  4453  4365  4656  5359  6335
#  [4211]  7388  8343  9059  9460  9571  9481  9281  9026  8741  8442
#  [4221]  8149  7860  7553  7182  6713  6166  5577  4983  4424  3927
#  [4231]  3502  3133  2808  2529  2312  2165  2090  2102  2271  2729
#  [4241]  3567  4691  5916  7080  8028  8619  8835  8772  8516  8133
#  [4251]  7699  7259  6779  6246  5730  5372  5307  5511  5854  6229
#  [4261]  6540  6677  6633  6546  6536  6670  1139   995   919   930
#  [4271]  1036  1220  1442  1654  1856  2252  3133  4165  5121  5944
#  [4281]  6525  6559  6169  5702  5307  5093  5224  5768  6523  7326
#  [4291]  8060  8627  8970  9107  9100  9013  8889  8702  8471  8277
#  [4301]  8133  8013  7798  7348  6805  6255  5717  5185  4614  4032
#  [4311]  3493  3015  2610  2294  2071  1936  1891  1969  2338  3262
#  [4321]  4505  5816  7079  8163  8787  8934  8831  8550  8129  7726
#  [4331]  7502  7255  6901  6487  6174  6262  6663  7175  7740  8273
#  [4341]  8439  8134  7796  7607  7614  1091   963   897   904   984
#  [4351]  1118  1271  1396  1445  1443  2899  4248  5466  6570  7579
#  [4361]  7611  7072  6546  6083  5727  5648  6163  6757  7367  7924
#  [4371]  8374  8630  8742  8756  8725  8709  8605  8413  8319  8313
#  [4381]  8385  8465  7914  7398  6906  6423  5943  5283  4551  3854
#  [4391]  3226  2697  2294  2021  1865  1800  1802  1857  3073  4436
#  [4401]  5790  7116  8397  9058  9096  9019  8792  8378  7874  8047
#  [4411]  8013  7802  7454  7009  7303  7873  8458  9099  9840 10104
#  [4421]  9341  8771  8414  8290  1015   900   845   857   938  1076
#  [4431]  1248  1430  1641  2120  3230  4560  5844  6994  7862  8061
#  [4441]  7727  7259  6807  6465  6385  6650  7058  7496  7898  8212
#  [4451]  8396  8460  8440  8383  8334  8269  8208  8230  8331  8465
#  [4461]  8490  8234  7869  7480  7053  6537  5846  5023  4180  3397
#  [4471]  2744  2270  1987  1869  1881  2012  2396  3333  4553  5819
#  [4481]  7060  8183  8898  9191  9307  9287  9135  9000  9069  9098
#  [4491]  8996  8792  8614  8780  9188  9644 10122 10554 10555  9989
#  [4501]  9371  8895  8618   914   812   767   790   895  1081  1333
#  [4511]  1650  2083  2764  3780  5004  6250  7355  8130  8404  8234
#  [4521]  7848  7439  7137  7035  7151  7403  7699  7973  8177  8282
#  [4531]  8277  8177  8027  7896  7840  7888  8033  8230  8412  8492
#  [4541]  8417  8233  7983  7644  7140  6405  5471  4457  3495  2704
#  [4551]  2174  1927  1917  2082  2405  2948  3773  4800  5898  6979
#  [4561]  7955  8724  9275  9676  9964 10150 10274 10371 10413 10391
#  [4571] 10331 10297 10365 10526 10725 10914 10990 10791 10289  9664
#  [4581]  9084  8652   798   713   672   702   841  1101  1458  1906
#  [4591]  2483  3257  4259  5435  6664  7785  8581  8871  8706  8320
#  [4601]  7922  7638  7526  7584  7755  7965  8150  8274  8315  8239
#  [4611]  8027  7722  7450  7369  7516  7793  8096  8355  8516  8557
#  [4621]  8516  8424  8238  7819  7034  5927  4685  3494  2527  1951
#  [4631]  1807  1977  2331  2818  3445  4218  5102  6033  6956  7835
#  [4641]  8652  9404 10094 10717 11238 11587 11742 11787 11817 11867
#  [4651] 11902 11868 11783 11699 11610 11434 11072 10497  9793  9077
#  [4661]  8469   783   696   636   587   591   760  1121  1586  2129
#  [4671]  2780  3589  4588  5749  7006  8242  9192  9447  9112  8622
#  [4681]  8201  7936  7852  7927  8102  8297  8440  8514  8539  8428
#  [4691]  8094  7563  7018  6865  7169  7596  7993  8325  8548  8636
#  [4701]  8683  8754  8807  8607  7758  6378  4858  3397  2178  1549
#  [4711]  1633  2071  2634  3259  3940  4674  5446  6228  6999  7773
#  [4721]  8620  9546 10497 11449 12339 12929 13056 13026 13079 13257
#  [4731] 13409 13249 12873 12518 12216 11887 11402 10707  9875  8986
#  [4741]  8140   775   666   663   634   573   494   662  1176  1725
#  [4751]  2313  2973  3756  4730  5856  7117  8495  9866  9965  9245
#  [4761]  8632  8208  7999  7999  8172  8446  8724  8898  8917  9039
#  [4771]  8964  8541  7766  6718  6417  7049  7564  7957  8299  8570
#  [4781]  8573  8629  8821  9149  9476  8460  6689  4961  3307  1749
#  [4791]   962  1567  2314  3056  3780  4488  5179  5851  6499  7120
#  [4801]  7732  8575  9662 10797 12001 13290 14285 14084 13888 13938
#  [4811] 14267 14770 14370 13631 13076 12661 12298 11771 10940 10000
#  [4821]  8964  7840   852   750   765   763   730   684   870  1370
#  [4831]  1907  2471  3092  3811  4688  5698  6834  8089  9327  9421
#  [4841]  8761  8215  7883  7792  7944  8302  8788  9284  9658  9840
#  [4851] 10028  9964  9516  8691  7588  7146  7532  7812  7981  8129
#  [4861]  8252  8198  8240  8449  8807  9134  8232  6594  4981  3445
#  [4871]  2028  1382  2029  2854  3666  4431  5135  5769  6341  6866
#  [4881]  7368  7897  8689  9760 10921 12165 13477 14453 14325 14140
#  [4891] 14175 14472 14907 14530 13815 13266 12853 12488 11965 11154
#  [4901] 10225  9185  8042  1415  1140  1010   991  1012  1048  1126
#  [4911]  1333  1691  2125  2606  3143  3761  4477  5285  6163  7048
#  [4921]  7744  7920  7673  7373  7217  7297  7657  8283  9095  9955
#  [4931] 10706 11228 11477 11397 10979 10286  9482  8893  8583  8316
#  [4941]  8033  7788  7608  7498  7510  7648  7823  7790  7189  6117
#  [4951]  4921  3793  2916  2610  2978  3682  4471  5234  5909  6469
#  [4961]  6927  7322  7717  8204  8899  9815 10863 11958 12977 13655
#  [4971] 13836 13801 13802 13907 13991 13811 13445 13099 12802 12480
#  [4981] 12017 11359 10556  9658  8730  1608  1384  1271  1260  1317
#  [4991]  1421  1567  1767  2026  2337  2700  3118  3594  4126  4697
#  [5001]  5274  5799  6182  6343  6318  6244  6264  6511  7101  8061
#  [5011]  9299 10649 11896 12790 13165 13072 12684 12131 11458 10679
#  [5021]  9816  8918  8062  7339  6837  6589  6548  6613  6663  6552
#  [5031]  6165  5533  4804  4136  3692  3633  3992  4641  5414  6176
#  [5041]  6822  7290  7603  7834  8074  8430  8995  9775 10680 11594
#  [5051] 12387 12913 13121 13117 13044 12981 12928 12857 12772 12695
#  [5061] 12606 12438 12112 11600 10955 10240  9506  2880  2642  2347
#  [5071]  2042  1768  1569  1483  1506  1611  1778  1978  2160  2319
#  [5081]  2502  2737  3023  3349  3695  4035  4330  4545  4684  4805
#  [5091]  4913  4993  5118  5449  6230  7569  9305 11238 13126 14510
#  [5101] 14949 14710 14294 13893 13388 12439 11015  9456  7985  6732
#  [5111]  5879  5529  5488  5533  5537  5444  5254  4979  4660  4391
#  [5121]  4287  4451  4910  5598  6412  7227  7878  8235  8358  8380
#  [5131]  8404  8551  8970  9657 10453 11224 11863 12266 12392 12311
#  [5141] 12119 11897 11747 11783 11966 12179 12352 12412 12253 11856
#  [5151] 11341 10803 10256  3566  3071  3003  2751  2450  2153  1884
#  [5161]  1681  1629  1696  1842  2065  2344  2512  2530  2584  2704
#  [5171]  2872  3064  3250  3395  3456  3397  3258  3355  3611  3793
#  [5181]  3934  4174  5001  6792  9009 11489 14146 16371 16559 15869
#  [5191] 15364 15193 15155 14127 11957  9766  7756  5953  4676  4416
#  [5201]  4491  4559  4545  4459  4459  4507  4529  4580  4739  5098
#  [5211]  5698  6477  7374  8314  9085  9268  9149  8959  8741  8581
#  [5221]  8853  9544 10266 10916 11443 11747 11726 11517 11192 10792
#  [5231] 10457 10645 11145 11636 12072 12414 12432 12046 11598 11210
#  [5241] 10901  3222  3105  2779  2841  2930  3038  3074  2789  2507
#  [5251]  2236  1982  1758  1744  1829  1975  2203  2527  2690  2574
#  [5261]  2550  2595  2679  2773  2842  2851  2762  2532  2137  2247
#  [5271]  2601  2820  2958  3086  3748  5941  8355 11038 14069 17404
#  [5281] 16863 15886 15403 15403 15859 14892 12132  9673  7441  5348
#  [5291]  3551  3636  3765  3824  3800  3693  3874  4176  4455  4754
#  [5301]  5121  5637  6375  7233  8187  9208 10224 10148  9885  9589
#  [5311]  9234  8802  8940  9619 10200 10683 11073 11307 11105 10799
#  [5321] 10403  9916  9351  9749 10474 11125 11715 12262 12448 11998
#  [5331] 11592 11282 11113  2850  2723  2466  2519  2613  2728  2831
#  [5341]  2844  2709  2511  2299  2097  1940  1884  1915  2005  2150
#  [5351]  2326  2418  2401  2393  2420  2465  2501  2502  2440  2294
#  [5361]  2064  1828  1817  1984  2153  2328  2657  3541  5223  7351
#  [5371]  9731 12214 14219 14733 14455 14231 14207 14129 13170 11233
#  [5381]  9114  7099  5294  4001  3516  3407  3373  3353  3395  3626
#  [5391]  4014  4462  4953  5507  6173  6972  7865  8807  9724 10419
#  [5401] 10623 10510 10279  9986  9717  9721  9994 10284 10516 10668
#  [5411] 10676 10486 10177  9810  9438  9221  9469 10047 10675 11253
#  [5421] 11702 11837 11615 11277 10945 10621  4498  3785  2591  2444
#  [5431]  2301  2185  2121  2132  2214  2341  2480  2593  2639  2598
#  [5441]  2493  2353  2204  2078  1998  1964  1963  1989  2034  2078
#  [5451]  2115  2160  2212  2254  2269  2241  2155  2011  1826  1663
#  [5461]  1599  1633  1722  1893  2279  3087  4398  6065  7889  9659
#  [5471] 11058 11825 12110 12205 12194 11927 11136  9808  8230  6651
#  [5481]  5249  4200  3586  3280  3129  3082  3179  3479  3961  4546
#  [5491]  5186  5878  6647  7501  8409  9317 10137 10743 11043 11090
#  [5501] 11000 10846 10684 10572 10515 10468 10406 10311 10157  9928
#  [5511]  9645  9352  9117  9060  9286  9747 10291 10792 11141 11242
#  [5521] 11084 10760 10351  9867  4155  3535  3395  2342  2170  1992
#  [5531]  1832  1737  1756  1882  2059  2237  2384  2480  2515  2491
#  [5541]  2416  2310  2197  2096  2004  1906  1803  1725  1724  1805
#  [5551]  1916  2012  2074  2091  2058  1974  1847  1698  1561  1470
#  [5561]  1429  1433  1516  1789  2409  3419  4657  5919  7061  8035
#  [5571]  8852  9473  9849  9953  9742  9176  8289  7203  6071  5038
#  [5581]  4208  3619  3235  2997  2888  2977  3355  3978  4710  5470
#  [5591]  6252  7087  7988  8915  9808 10594 11182 11523 11664 11701
#  [5601] 11691 11612 11392 11044 10663 10310  9993  9706  9437  9182
#  [5611]  8954  8802  8812  9053  9481  9974 10414 10701 10755 10563
#  [5621] 10182  9678  9086  4117  3944  3771  3598  3429  3268  3118
#  [5631]  2123  1928  1707  1482  1317  1350  1560  1810  2040  2228
#  [5641]  2377  2488  2539  2523  2446  2333  2220  2088  1901  1660
#  [5651]  1419  1364  1530  1724  1869  1953  1978  1949  1873  1764
#  [5661]  1640  1521  1421  1338  1264  1207  1244  1622  2447  3369
#  [5671]  4139  4670  5156  6028  6966  7587  7825  7709  7358  6839
#  [5681]  6159  5410  4703  4098  3603  3229  2954  2759  2759  3251
#  [5691]  4105  5005  5855  6665  7524  8474  9426 10319 11108 11711
#  [5701] 12034 12185 12299 12433 12507 12184 11484 10769 10156  9652
#  [5711]  9262  8984  8771  8598  8480  8494  8777  9247  9734 10146
#  [5721] 10405 10406 10119  9640  9031  8336  3533  3345  3160  2983
#  [5731]  2120  1956  1748  1498  1213   911   981  1326  1646  1926
#  [5741]  2154  2344  2546  2672  2714  2665  2528  2434  2285  2033
#  [5751]  1674  1212  1064  1405  1660  1825  1915  1939  1909  1839
#  [5761]  1743  1639  1542  1458  1375  1268  1106   860   876  1782
#  [5771]  2489  2876  2855  2462  3714  4971  5737  6050  5956  5757
#  [5781]  5565  5185  4725  4292  3938  3555  3278  3065  2845  2587
#  [5791]  3326  4498  5531  6426  7196  7998  9025  9972 10837 11621
#  [5801] 12300 12477 12550 12661 12877 13240 12812 11641 10663  9872
#  [5811]  9242  8776  8552  8412  8315  8231  8153  8550  9106  9589
#  [5821]  9970 10226 10195  9752  9174  8483  7696  3286  3081  2879
#  [5831]  2685  2507  2169  2167  2111  2016  1865  1660  1409  1137
#  [5841]   909   968  1274  1610  1926  2208  2469  2723  2917  3024
#  [5851]  3030  2946  2832  2650  2364  1982  1561  1403  1589  1779
#  [5861]  1908  1971  1977  1935  1861  1770  1684  1619  1581  1554
#  [5871]  1503  1390  1215  1274  1801  2235  2385  2227  2055  2807
#  [5881]  3803  4482  4793  4790  4689  4570  4336  4047  3789  3600
#  [5891]  3454  3399  3407  3425  3529  4252  5346  6367  7258  8038
#  [5901]  8832  9727 10571 11333 12000 12502 12665 12674 12684 12755
#  [5911] 12826 12316 11255 10253  9417  8767  8336  8152  8114  8148
#  [5921]  8202  8300  8661  9143  9554  9852  9998  9866  9408  8789
#  [5931]  8078  7327  3033  2812  2593  2380  2182  1879  1920  1991
#  [5941]  2055  1996  1868  1675  1440  1210  1072  1128  1371  1698
#  [5951]  2042  2377  2704  3017  3283  3466  3545  3518  3397  3184
#  [5961]  2883  2527  2194  2012  2004  2061  2108  2118  2087  2021
#  [5971]  1931  1835  1761  1736  1776  1864  1957  2018  2059  2180
#  [5981]  2403  2572  2582  2474  2470  2816  3350  3788  4017  4051
#  [5991]  3970  3825  3620  3397  3235  3199  3318  3582  3944  4367
#  [6001]  4896  5646  6555  7465  8307  9078  9814 10532 11205 11805
#  [6011] 12298 12610 12688 12590 12415 12205 11890 11305 10467  9584
#  [6021]  8795  8185  7827  7739  7856  8083  8349  8639  8980  9332
#  [6031]  9621  9798  9808  9581  9107  8473  7774  7106  2545  2314
#  [6041]  2082  1557  1693  1877  2028  2102  2085  1982  1802  1570
#  [6051]  1345  1222  1289  1540  1889  2263  2637  3021  3414  3771
#  [6061]  4041  4194  4211  4090  3851  3529  3174  2849  2618  2495
#  [6071]  2436  2393  2338  2260  2160  2044  1931  1853  1864  2009
#  [6081]  2267  2567  2848  3077  3239  3320  3302  3191  3048  2985
#  [6091]  3085  3294  3489  3584  3563  3447  3260  3025  2791  2656
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#  [7481]  6837  7999 10109 12385 14767 17190 18916 18672 18259 17913
#  [7491] 17654 17330 15521 13192 10928  8745  6659  5204  4546  3925
#  [7501]  3255  2506  1800  1690  1596  1404  1126   830  1262  2133
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#  [7571]  4657  4693  4927  4489  3898  3141  2486  2396  2311  2150
#  [7581]  1990  1941  2239  2774  3390  4006  4561  5167  5860  6375
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#  [7601] 12628 14869 17113 18636 18528 18153 17823 17551 17104 15397
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#  [7641]  2126  1754  2443  3056  3526  3916  4205  4240  4255  4304
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#  [7711]  7557  7717  7851  8031  8460  9434 10938 12697 14517 16172
#  [7721] 17257 17560 17433 17149 16728 15958 14554 12676 10659  8702
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#  [7761]  3925  3908  3872  3821  3747  3700  3706  3764  3886  4100
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#  [7791]  4225  4023  3963  3836  3638  3461  3411  3507  3714  3995
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#  [8051]  8060  8450  8847  8758  7576  6141  4764  3512  2617  2872
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#  [8071]  9931  9911 10003 10222 10569 11030 11589 12210 12844 13426
#  [8081] 13862 14075 14125 14029 13768 13271 12379 11189  9837  8397
#  [8091]  7014  6251  6249  6394  6535  6616  6426  5601  4555  3517
#  [8101]  2566  1842  1773  2252  2942  3773  4736  5833  7068  8436
#  [8111]  9928 11497 12794 12832 12347 11986 11852 11807 10854  8876
#  [8121]  6917  5145  3569  2417  2067  2006  2006  2034  2110  2350
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#  [8141]  5095  5929  6916  8010  9083  9632  9639  9547  9423  9241
#  [8151]  8759  7664  6361  5008  3651  2447  1912  1794  1708  1571
#  [8161]  1382  1353  1583  1783  1898  1941  7551  7877  8247  8679
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#  [8181]  5333  6688  8234  9189  8981  9004  9273  9775 10417 10346
#  [8191] 10336 10462 10685 10967 11270 11581 11900 12225 12555 12835
#  [8201] 12937 12991 12976 12860 12605 11879 10908  9798  8565  7233
#  [8211]  6585  6955  7270  7518  7705  7714  6600  5378  4188  3076
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#  [8231] 12391 14277 13982 13363 13014 12969 13233 12236  9699  7416
#  [8241]  5363  3485  1922  1714  1649  1619  1614  1633  1900  2284
#  [8251]  2644  2964  3235  3410  3444  3484  3577  3781  4154  4884
#  [8261]  5843  6989  8293  9714 10443 10476 10528 10570 10557 10255
#  [8271]  8835  7268  5631  3958  2302  1712  1552  1366  1119   785
#  [8281]   656   993  1227  1363  1417  7821  8191  8587  9013  9450
#  [8291]  9788  9625  8644  7326  5995  4784  3946  3937  4560  5437
#  [8301]  6457  7504  8195  8423  8625  8976  9468  9956 10245 10470
#  [8311] 10739 11031 11284 11451 11523 11537 11544 11585 11660 11746
#  [8321] 11846 11928 11935 11784 11375 10747  9984  9141  8349  7969
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#  [8361]  3713  2408  1767  1500  1382  1354  1426  1656  1997  2350
#  [8371]  2663  2905  3047  3094  3116  3185  3384  3809  4543  5560
#  [8381]  6789  8146  9460 10385 10888 11227 11447 11437 10930  9737
#  [8391]  8130  6360  4598  3078  2135  1639  1294   987   716   619
#  [8401]   737   890  1004  1088  8022  8404  8780  9136  9428  9540
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#  [8431] 11316 11599 11646 11461 11140 10799 10541 10441 10512 10699
#  [8441] 10913 11072 11110 10984 10709 10334  9917  9550  9350  9337
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#  [8501]  7749  9080 10190 11043 11705 12166 12277 11803 10645  8982
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#  [8731]  2712  2575  2290  1906  1548  1541  2322  3620  5107  6671
#  [8741]  8224  9623 10868 12085 13280 14262 14293 12751 10516  8198
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#  [8801]  8542  9233  9847 10415 10946 11467 12021 12645 12814 12316
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#  [8861]  6003  7668  9113 10360 11721 13213 14844 15918 13357 10787
#  [8871]  8362  6076  3940  2889  2331  1870  1494  1201   984   835
#  [8881]   733   654   575  7486  8186  8731  9056  9148  9051  8840
#  [8891]  8586  8258  7776  7345  7043  6869  6726  6264  5629  5016
#  [8901]  4418  3880  3881  4593  5365  6037  6616  7238  8166  9205
#  [8911] 10241 11250 12044 11759 10550  9202  7874  6670  6077  6555
#  [8921]  7343  8153  8927  9652 10337 10990 11622 12239 12782 12891
#  [8931] 12500 12063 11707 11424 10857  9361  7635  6051  4687  3635
#  [8941]  3169  3209  3508  3998  4648  5432  6318  7260  8200  9072
#  [8951]  9764 10075 10087  9881  9459  8820  7959  6903  5713  4464
#  [8961]  3253  2280  1777  1521  1384  1327  1398  1877  2594  3236
#  [8971]  3684  3859  3759  3412  2798  2001  1171   684  1259  2408
#  [8981]  3739  5182  6692  8095  9400 10778 12236 13636 14097 12529
#  [8991] 10369  8211  6162  4362  3244  2591  2083  1669  1345  1111
#  [9001]   961   878   844   859  6591  7571  8467  9124  9431  9375
#  [9011]  9040  8550  8025  7537  7119  6805  6589  6428  6242  5934
#  [9021]  5527  5100  4707  4448  4512  4929  5498  6077  6645  7266
#  [9031]  8005  8813  9601 10272 10628 10391  9603  8572  7528  6684
#  [9041]  6322  6567  7191  7960  8759  9540 10287 10995 11657 12232
#  [9051] 12617 12649 12316 11787 11188 10521  9633  8398  6990  5628
#  [9061]  4441  3557  3096  3038  3259  3675  4249  4965  5796  6689
#  [9071]  7573  8372  8994  9361  9467  9339  8986  8414  7632  6667
#  [9081]  5569  4418  3339  2501  2007  1795  1767  1882  2177  2717
#  [9091]  3430  4145  4706  4976  4863  4352  3526  2548  1656  1170
#  [9101]  1344  2061  3078  4254  5512  6789  8066  9351 10572 11501
#  [9111] 11679 10851  9406  7773  6171  4762  3689  2913  2313  1833
#  [9121]  1467  1221  1090  1060  1118  1284  4367  5225  6406  7703
#  [9131]  8892  9739 10035  9767  9109  8259  7410  6752  6376  6194
#  [9141]  6080  5961  5817  5651  5465  5268  5096  5019  5117  5404
#  [9151]  5814  6277  6766  7288  7849  8418  8934  9309  9436  9227
#  [9161]  8698  7969  7205  6603  6370  6589  7149  7885  8686  9487
#  [9171] 10254 10975 11638 12187 12505 12462 12037 11337 10475  9509
#  [9181]  8464  7357  6213  5083  4060  3281  2865  2804  2988  3332
#  [9191]  3818  4468  5271  6151  7013  7781  8394  8811  9005  8967
#  [9201]  8697  8203  7502  6618  5583  4472  3427  2639  2222  2118
#  [9211]  2219  2479  2915  3552  4350  5203  5956  6395  6290  5581
#  [9221]  4465  3214  2101  1407  1304  1711  2422  3295  4280  5374
#  [9231]  6541  7691  8694  9374  9534  9102  8226  7129  5991  4921
#  [9241]  3979  3177  2506  1956  1540  1285  1194  1236  1390  1672
#  [9251]  3202  3540  4615  6183  7879  9473 10654 10949 10353  9293
#  [9261]  8023  6753  5876  5633  5668  5681  5599  5484  5458  5495
#  [9271]  5519  5532  5577  5698  5912  6202  6546  6925  7321  7706
#  [9281]  8060  8343  8493  8470  8297  7968  7476  6906  6418  6255
#  [9291]  6546  7135  7870  8671  9475 10227 10930 11594 12168 12516
#  [9301] 12413 11809 10882  9754  8512  7331  6371  5490  4566  3641
#  [9311]  2882  2534  2565  2763  3033  3394  3964  4787  5703  6578
#  [9321]  7345  7975  8455  8746  8809  8628  8214  7599  6798  5806
#  [9331]  4669  3530  2699  2416  2486  2715  3067  3579  4300  5217
#  [9341]  6261  7308  8085  8054  7021  5494  3873  2399  1383  1100
#  [9351]  1348  1819  2376  3033  3916  4987  6026  6878  7432  7627
#  [9361]  7469  7012  6370  5658  4920  4130  3340  2630  2019  1538
#  [9371]  1277  1258  1385  1613  1963  2453  3963  6001  8057 10064
#  [9381] 11857 12150 11010  9589  7978  6200  4886  5126  5466  5582
#  [9391]  5480  5266  5402  5680  5884  6030  6151  6276  6424  6606
#  [9401]  6828  7092  7375  7589  7767  7884  7876  7710  7599  7486
#  [9411]  7188  6743  6240  6023  6513  7171  7891  8671  9485 10172
#  [9421] 10822 11488 12126 12641 12537 11650 10510  9175  7656  6218
#  [9431]  5591  5022  4280  3388  2472  2239  2488  2722  2903  3060
#  [9441]  3476  4435  5425  6327  7102  7740  8313  8722  8898  8818
#  [9451]  8476  7958  7276  6336  5154  3791  2681  2726  3003  3294
#  [9461]  3647  4141  4900  5911  7117  8476  9858 10133  8414  6442
#  [9471]  4498  2628  1095   873  1129  1405  1635  1841  2503  3579
#  [9481]  4534  5265  5722  5926  5986  5835  5539  5195  4833  4163
#  [9491]  3382  2682  2051  1480  1193  1323  1529  1789  2144  2285
#  [9501]  3921  6037  8155 10241 12182 12521 11350  9958  8377  6582
#  [9511]  5173  5529  5868  5950  5814  5563  5754  6111  6398  6615
#  [9521]  6769  6872  6940  6999  7081  7208  7370  7462  7541  7583
#  [9531]  7533  7360  7322  7343  7193  6886  6464  6246  6751  7331
#  [9541]  7937  8606  9344  9965 10587 11253 11906 12457 12361 11418
#  [9551] 10249  8894  7363  5904  5444  5024  4423  3641  2754  2571
#  [9561]  2834  3012  3106  3156  3472  4424  5401  6306  7103  7782
#  [9571]  8438  8953  9253  9308  9093  8696  8125  7270  6142  4779
#  [9581]  3572  3643  3842  4014  4248  4642  5347  6346  7574  8990
#  [9591] 10496 10901  9084  7105  5152  3224  1516  1224  1306  1343
#  [9601]  1306  1219  1647  2551  3338  3937  4318  4524  4696  4720
#  [9611]  4638  4521  4395  3892  3254  2679  2145  1627  1364  1526
#  [9621]  1716  1939  2246  3420  4590  6297  8152  9934 11325 11781
#  [9631] 11302 10374  9236  8045  7187  6935  6888  6777  6593  6454
#  [9641]  6528  6771  7047  7286  7446  7501  7459  7367  7281  7244
#  [9651]  7260  7305  7368  7426  7449  7444  7480  7529  7499  7368
#  [9661]  7188  7131  7320  7629  7998  8444  8978  9568 10213 10889
#  [9671] 11502 11885 11774 11109 10108  8924  7685  6634  5982  5517
#  [9681]  5027  4466  3940  3683  3657  3662  3661  3737  4079  4769
#  [9691]  5626  6505  7338  8106  8813  9413  9852 10083 10074  9824
#  [9701]  9335  8598  7650  6592  5708  5254  5022  4871  4849  5068
#  [9711]  5622  6499  7604  8790  9759  9891  8935  7467  5858  4282
#  [9721]  2995  2283  1929  1661  1417  1284  1464  1935  2456  2896
#  [9731]  3214  3435  3593  3676  3687  3650  3546  3301  2969  2641
#  [9741]  2330  2053  1899  1900  1962  2070  2276  4267  5233  6582
#  [9751]  8095  9544 10668 11226 11211 10829 10273  9664  9102  8636
#  [9761]  8229  7854  7538  7348  7342  7502  7755  8014  8183  8174
#  [9771]  7981  7691  7409  7205  7112  7129  7226  7361  7500  7636
#  [9781]  7779  7914  8013  8058  8053  8025  8001  8000  8054  8217
#  [9791]  8549  9074  9750 10471 11099 11465 11411 10910 10093  9122
#  [9801]  8149  7323  6726  6299  5938  5589  5259  4982  4757  4560
#  [9811]  4414  4410  4670  5234  6004  6860  7721  8549  9325 10027
#  [9821] 10622 11061 11269 11178 10791 10181  9436  8623  7813  7059
#  [9831]  6369  5776  5373  5301  5663  6413  7376  8330  9014  9151
#  [9841]  8656  7719  6572  5388  4322  3469  2796  2224  1744  1426
#  [9851]  1362  1531  1807  2078  2298  2472  2612  2705  2743  2736
#  [9861]  2703  2658  2615  2582  2547  2496  2424  2332  2233  2165
#  [9871]  2197  2416  2873  3536  4323  5136  5845  6317  6552  6665
#  [9881]  6725  6741  6701  6599  6440  6242  6014  5752  5447  5117
#  [9891]  4798  4533  4367  4327  4411  4596  4837  5085  5291  4361
#  [9901]  4861  5678  6765  7999  9217 10231 10879 11165 11246 11262
#  [9911] 11220 10944 10327  9587  8930  8433  8134  8050  8161  8415
#  [9921]  8733  8966  8895  8480  7932  7428  7056  6876  6906  7088
#  [9931]  7341  7615  7887  8146  8390  8621  8834  8985  8962  8717
#  [9941]  8383  8086  7918  8012  8491  9252 10081 10811 11275 11301
#  [9951] 10875 10171  9365  8590  7945  7477  7171  6977  6836  6669
#  [9961]  6384  5992  5583  5236  5055  5192  5700  6451  7305  8189
#  [9971]  9060  9893 10691 11454 12138 12611 12677 12337 11812 11255
#  [9981] 10671  9918  8889  7738  6650  5765  5299  5481  6197  7102
#  [9991]  7931  8506  8713  8530  8018  7293  6461  5578  4659  3749
# [10001]  2894  2134  1554  1256  1222  1316  1429  1524  1621  1737
# [10011]  1830  1865  1853  1868  2001  2240  2513  2772  2958  2970
# [10021]  2787  2508  2223  2017  2016  2310  2796  3317  3791  4247
# [10031]  4803  5456  6096  6673  7126  7299  7122  6766  6386  6021
# [10041]  5629  5154  4608  4045  3519  3132  3051  3296  3692  4105
# [10051]  4479  4788  4516  4773  5239  5920  6801  7824  8899  9900
# [10061] 10603 11037 11453 11979 12602 12751 11811 10686  9778  9123
# [10071]  8713  8562  8637  8897  9308  9744  9656  8859  7998  7282
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# [10091]  9575  9938  9981  9419  8730  8101  7570  7323  7841  8793
# [10101]  9767 10644 11308 11424 10941 10264  9569  8948  8464  8148
# [10111]  8002  7998  8094  8165  7866  7270  6655  6088  5640  5601
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# [10181]  2147  2451  2585  2671  3288  4391  5491  6527  7472  7927
# [10191]  7520  6904  6361  5913  5474  4842  4086  3308  2523  1819
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# [10211]  6670  7505  8442  9460 10161 10612 11220 12061 13223 14264
# [10221] 12540 11211 10224  9515  9032  8837  8853  9054  9461 10101
# [10231] 10114  8801  7746  6932  6338  5945  6304  6808  7377  7955
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# [10271]  7733  7036  6354  6017  6764  7527  8320  9160 10063 10842
# [10281] 11683 12644 13748 15022 15375 14629 14126 13889 13941 14095
# [10291] 11981 10088  8344  6651  4914  5191  6307  7220  7908  8348
# [10301]  8628  8902  8950  8813  8536  8155  6968  5659  4342  3045
# [10311]  1787  1093   937   796   642   446   251   467   585   598
# [10321]   501   296   840  1621  2357  3081  3823  4139  3587  3042
# [10331]  2462  1794   994  1477  1835  1963  1838  1442  2104  3579
# [10341]  4898  6155  7447  8420  7456  6664  6037  5559  5211  4423
# [10351]  3546  2683  1780   784   525  1476  2281  2954  3513  3971
# [10361]  4939  5136  5441  5853  6375  7005  7730  8502  9165  9746
# [10371] 10431 11277 12194 12598 11927 10992 10200  9593  9159  8900
# [10381]  8793  8822  8983  9171  8899  8013  7096  6364  5883  5752
# [10391]  6081  6703  7440  8179  8831  9335  9698  9979 10242 10482
# [10401] 10409  9783  9028  8327  7722  7398  7786  8597  9448 10230
# [10411] 10840 10981 10616 10110  9629  9258  9055  9047  9224  9540
# [10421]  9916 10186 10008  9449  8792  8139  7573  7363  7682  8214
# [10431]  8834  9523 10260 11002 11798 12696 13683 14612 14952 14670
# [10441] 14344 14158 14067 13643 12380 10827  9302  7870  6759  6650
# [10451]  7244  7889  8418  8813  9136  9419  9582  9584  9384  8865
# [10461]  7853  6531  5108  3699  2433  1573  1115   807   554   331
# [10471]   205   246   315   341   330   402   839  1531  2264  2980
# [10481]  3608  3871  3661  3281  2823  2311  1909  1905  2003  1971
# [10491]  1802  1676  2157  3207  4343  5448  6444  6927  6565  5946
# [10501]  5360  4853  4363  3717  2974  2225  1481   841   755  1324
# [10511]  2023  2669  3229  3704  5015  5144  5344  5613  5951  6358
# [10521]  6833  7365  7932  8538  9206  9911 10533 10823 10653 10236
# [10531]  9792  9399  9058  8760  8501  8286  8104  7879  7460  6825
# [10541]  6147  5589  5272  5320  5788  6582  7531  8469  9252  9782
# [10551] 10059 10161 10168 10096  9873  9465  8983  8535  8200  8099
# [10561]  8344  8850  9437  9975 10346 10425 10210  9842  9462  9182
# [10571]  9091  9232  9575 10037 10491 10766 10705 10331  9807  9275
# [10581]  8844  8627  8674  8917  9295  9778 10341 10961 11646 12401
# [10591] 13178 13832 14161 14156 14012 13854 13645 13194 12374 11335
# [10601] 10275  9325  8651  8428  8575  8866  9173  9467  9761 10052
# [10611] 10286 10389 10252  9729  8738  7383  5867  4371  3057  2059
# [10621]  1384   925   595   360   228   200   229   277   359   556
# [10631]   956  1529  2169  2790  3304  3598  3642  3523  3316  3061
# [10641]  2828  2669  2529  2349  2167  2127  2425  3051  3819  4575
# [10651]  5182  5454  5310  4912  4429  3937  3445  2934  2411  1900
# [10661]  1438  1129  1140  1493  2014  2563  3076  3533  5033  5312
# [10671]  5464  5639  5850  6145  6588  7163  7780  8349  8802  9099
# [10681]  9237  9243  9166  9032  8822  8498  8075  7598  7092  6566
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# [10741] 11281 11875 12480 12993 13306 13402 13363 13255 13071 12753
# [10751] 12279 11710 11153 10688 10344 10105  9967  9939 10005 10153
# [10761] 10386 10688 11002 11236 11241 10792  9742  8237  6556  4922
# [10771]  3496  2385  1595  1050   671   417   272   223   241   306
# [10781]   431   661  1037  1535  2085  2617  3073  3417  3645  3780
# [10791]  3849  3857  3762  3530  3208  2877  2612  2498  2602  2907
# [10801]  3316  3714  4006  4128  4054  3801  3414  2958  2518  2166
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# [10901] 11952 11853 11863 11887 11646 11238 10926 10767 10757 10915
# [10911] 11235 11637 12042 12314 12068 10842  9018  7092  5276  3700
# [10921]  2505  1689  1123   727   462   314   270   297   374   504
# [10931]   722  1080  1542  2030  2489  2898  3283  3663  4015  4347
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# [10951]  2938  2954  2936  2924  2791  2481  2030  1598  1436  1454
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# [10971]  3666  3894  4666  5259  5619  5724  5828  6629  7298  7791
# [10981]  8159  8398  7947  7160  6279  5278  4139  3412  3450  3359
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# [11001] 10573  9783  8913  8288  8578  8873  9130  9395  9686  9713
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# [11051] 12696 13279 12932 12193 11677 11361 11207 11270 11624 12073
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# [11071]  1133   746   485   338   327   380   471   593   753  1121
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# [11091]  5117  4350  3719  3234  2888  2667  2536  2439  2306  2073
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# [11121]  4554  4862  4981  5189  5913  6616  7170  7584  7797  7428
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# [11171] 12078 12889 12870 12289 11771 11430 11276 10987 10241  9607
# [11181]  9196  9001  8976  8976  9069  9292  9620 10013 10313 10485
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# [11201] 12604 12091 11745 11556 11579 11848 12223 12663 13114 13179
# [11211] 11597  9421  7300  5343  3629  2393  1627  1095   732   500
# [11221]   391   405   488   610   756   942  1278  1692  2091  2456
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# [11261]  2496  2777  3087  3405  3522  3591  3907  4260  4544  4778
# [11271]  5103  6168  6642  6968  7056  6803  6260  5554  4770  4028
# [11281]  3538  3355  3300  3285  3383  3847  4907  6360  7927  9422
# [11291] 10600 11125 11027 10621 10099  9591  9290  9296  9462  9663
# [11301]  9853  9983 10006  9953  9887  9830  9782  9736  9677  9594
# [11311]  9484  9397  9491  9908 10516 11160 11750 12135 12097 11711
# [11321] 11241 10823 10461 10027  9459  8900  8455  8153  7985  7925
# [11331]  7973  8127  8368  8670  8983  9291  9615  9952 10296 10660
# [11341] 11067 11522 12020 12522 12874 12851 12533 12177 11905 11758
# [11351] 11759 11893 12097 12289 12324 11874 10625  8836  6913  5084
# [11361]  3506  2315  1517  1002   679   501   445   495   619   786
# [11371]   983  1220  1524  1871  2221  2557  2889  3256  3675  4114
# [11381]  4543  4900  5019  4747  4240  3699  3208  2787  2435  2135
# [11391]  1868  1623  1422  1345  1423  1537  1581  1527  1460  1525
# [11401]  1674  1803  1906  2015  2151  2327  2555  2825  3119  3422
# [11411]  3811  3990  4233  4485  4747  5462  5879  6471  6515  6330
# [11421]  5942  5419  4846  4324  3954  3772  3736  3822  4082  4627
# [11431]  5522  6683  7945  9137 10077 10759 10631 10372 10100  9914
# [11441]  9860  9905  9993 10078 10123 10102 10033  9951  9884  9850
# [11451]  9857  9901  9967 10045 10147 10302 10529 10811 11105 11347
# [11461] 11437 11287 10921 10448  9953  9467  8983  8495  8011  7558
# [11471]  7170  6900  6785  6802  6903  7064  7299  7633  8064  8552
# [11481]  9058  9559 10049 10536 11029 11527 11984 12293 12358 12221
# [11491] 12017 11850 11759 11739 11763 11784 11725 11453 10789  9626
# [11501]  8064  6322  4613  3127  2010  1281   841   588   470   472
# [11511]   581   764   987  1231  1494  1781  2082  2385  2682  2979
# [11521]  3289  3614  3937  4223  4414  4430  4225  3855  3419  2987
# [11531]  2589  2236  1923  1649  1422  1277  1266  1402  1626  1861
# [11541]  2054  2175  2217  2196  2143  2097  2097  2177  2345  2580
# [11551]  2854  3146  3441  4051  4164  4340  4552  4793  5071  5383
# [11561]  5696  5959  6124  6020  5749  5383  4985  4625  4367  4242
# [11571]  4253  4407  4732  5275  6046  6994  8014  8983  9782 10570
# [11581] 10477 10398 10353 10339 10334 10305 10226 10113 10004  9927
# [11591]  9907  9978 10141 10365 10623 10885 11066 11097 11052 11003
# [11601] 10938 10795 10508 10078  9559  8991  8415  7916  7521  7124
# [11611]  6663  6171  5780  5638  5669  5731  5795  5930  6278  6853
# [11621]  7520  8191  8832  9419  9945 10441 10928 11385 11723 11839
# [11631] 11777 11675 11612 11596 11579 11514 11384 11140 10686  9915
# [11641]  8772  7310  5663  3996  2523  1496   935   642   486   425
# [11651]   480   667   928  1209  1493  1772  2043  2305  2561  2809
# [11661]  3050  3287  3514  3719  3875  3947  3896  3709  3413  3056
# [11671]  2685  2326  1995  1695  1431  1218  1095  1137  1379  1759
# [11681]  2204  2649  2955  2957  2740  2481  2261  2128  2148  2325
# [11691]  2585  2875  3171  3463  4676  4880  5110  5355  5591  5785
# [11701]  5927  5841  5660  5415  5151  4918  4758  4701  4763  4958
# [11711]  5304  5815  6488  7282  9658 11023 11016 10897 10773 10672
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# [11731] 11142 11576 11845 11588 11186 10815 10488 10173  9753  9239
# [11741]  8688  8080  7405  6880  6695  6428  5968  5326  4688  4615
# [11751]  4736  4759  4686  4608  4941  5739  6586  7399  8158  8822
# [11761]  9328  9781 10238 10716 11160 11275 11195 11162 11208 11309
# [11771] 11338 11190 10955 10602 10058  9247  8102  6681  5072  3375
# [11781]  1765   833   589   498   447   415   486   789  1138  1468
# [11791]  1777  2065  2312  2532  2739  2933  3111  3268  3399  3494
# [11801]  3538  3514  3408  3218  2960  2658  2339  2024  1727  1454
# [11811]  1210  1005   863   914  1302  1839  2472  3185  3807  3678
# [11821]  3186  2737  2366  2082  2044  2291  2596  2903  3203  3492
# [11831]  4825  4990  5175  5367  5547  5693  5786  5810  5760  5648
# [11841]  5494  5332  5196  5117  5122  5228  5448  5794  6269  6864
# [11851] 10656 11426 10959 10799 10668 10439 10218 10058  9968  9957
# [11861] 10137 10546 11014 11516 12021 12386 11810 11129 10482  9913
# [11871]  9448  8929  8397  7905  7381  6749  6234  6282  6115  5686
# [11881]  4991  4104  4127  4225  4145  3940  3679  3965  4905  5837
# [11891]  6724  7541  8247  8686  9060  9430  9850 10355 10441 10387
# [11901] 10459 10627 10849 10963 10783 10521 10133  9561  8754  7615
# [11911]  6232  4674  3013  1333   496   495   534   572   587   648
# [11921]  1057  1441  1780  2084  2363  2577  2756  2919  3060  3174
# [11931]  3253  3292  3284  3226  3115  2956  2753  2514  2251  1976
# [11941]  1703  1446  1211  1002   825   688   717  1217  1819  2518
# [11951]  3336  4228  3943  3337  2844  2438  2091  2021  2330  2647
# [11961]  2955  3250  3530  4980  5113  5409  5549  5664  5740  5768
# [11971]  5748  5688  5603  5517  5455  5441  5496  5635  5870  6208
# [11981]  6650  7184  8438 10923 10418 10192 10035  9971 10033 10279
# [11991] 10705 12121 12167 11679 10873  9987  9160  8474  7931  7526
# [12001]  7230  6962  6679  6480  6413  6257  5902  5357  4784  4453
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# [12031] 10349 10305 10103  9744  9188  8384  7299  5978  4511  3018
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# [12051]  2413  2640  2826  2979  3105  3199  3254  3261  3213  3108
# [12061]  2949  2751  2535  2314  2089  1856  1616  1380  1164   976
# [12071]   818   700   657   788  1161  1686  2296  2938  3425  3431
# [12081]  3122  2782  2492  2294  2287  2483  2753  3035  3312  3577
# [12091]  5679  5745  5780  5783  5762  5729  5700  5693  5728  5821
# [12101] 10397 10946 11742 10991 10645 10348 10115  9963  9918 11900
# [12111] 12229 12146 11545 10547  9378  8255  7364  6824  6621  6636
# [12121]  6734  6827  6882  6876  6759  6501  6110  5634  5132  4602
# [12131]  4049  3561  3317  3503  4122  4985  5883  6669  7245  7569
# [12141]  7669  7622  7541  7559  7763  8155  8653  9150  9557  9803
# [12151]  9861  9744  9456  8964  8212  7171  5896  4506  3158  2052
# [12161]  1381  1153  1205  1385  1609  1855  2112  2360  2580  2772
# [12171]  2940  3087  3212  3307  3362  3367  3311  3185  2984  2720
# [12181]  2422  2140  1904  1700  1496  1281  1071   893   756   656
# [12191]   597   612   755  1052  1459  1914  2347  2661  2772  2717
# [12201]  2599  2490  2439  2494  2656  2883  3133  3385  3630  5785
# [12211]  5826  5848  5857  5861  5874  5909  6100  6279  7230  9912
# [12221] 10511 11104 12447 12012 11505 11008 10573 10237  9998  9844
# [12231]  9790  9894 10228 11461 12392 10276  8733  7227  6070  5566
# [12241]  5675  6102  6626  7110  7426  7521  7464  7314  7067  6656
# [12251]  6018  5208  4345  3573  3111  3216  3887  4840  5808  6620
# [12261]  7159  7365  7250  6883  6411  6127  6349  7013  7803  8513
# [12271]  9054  9386  9510  9462  9266  8889  8232  7217  5937  4566
# [12281]  3268  2234  1650  1520  1670  1946  2254  2531  2746  2910
# [12291]  3043  3153  3255  3361  3462  3535  3562  3530  3425  3233
# [12301]  2945  2567  2142  1772  1539  1383  1212  1001   790   642
# [12311]   566   525   505   529   651   890  1195  1497  1755  1961
# [12321]  2136  2273  2365  2432  2512  2633  2803  3009  3232  3459
# [12331]  3683  5895  5931  5962  5994  6037  6336  6771  7442 10591
# [12341] 13255 11582 10967 10440 10089  9868  9709  9615 12979 10106
# [12351]  8147  6165  4539  4135  4761  5659  6611  7522  8116  8231
# [12361]  8203  8175  8125  7866  7081  5968  4787  3653  2795  2821
# [12371]  3759  4932  6034  6921  7463  7556  7228  6521  5530  4685
# [12381]  4986  6117  7234  8125  8766  9137  9257  9231  9117  8912
# [12391]  8436  7389  6031  4638  3322  2238  1750  1848  2166  2557
# [12401]  2956  3269  3414  3482  3523  3546  3571  3644  3736  3797
# [12411]  3808  3754  3621  3391  3040  2553  1955  1432  1266  1216
# [12421]  1075   831   557   426   439   463   461   449   520   739
# [12431]   976  1149  1235  1306  1550  1876  2148  2364  2550  2731
# [12441]  2921  3119  3323  3527  3729  5976  6023  6069  6121  6185
# [12451]  7608  8003 11241 12304 11577 10893 10247  9956  9777  9621
# [12461]  9686 10558  9961  7767  5456  3021  2921  4193  5399  6606
# [12471]  7883  8873  8765  8778  8894  9070  9248  8155  6790  5407
# [12481]  4012  2612  2539  4004  5388  6611  7594  8226  8207  7752
# [12491]  6839  5434  3531  4219  5920  7186  8093  8723  9063  9061
# [12501]  8979  8878  8813  8791  7468  6047  4715  3443  2210  1835
# [12511]  2280  2734  3194  3661  4066  4055  4034  4005  3958  3884
# [12521]  3954  4051  4101  4101  4042  3910  3681  3323  2797  2058
# [12531]  1126  1292  1343  1186   869   440   324   457   533   544
# [12541]   477   421   715   904   972   909   714  1119  1619  2013
# [12551]  2329  2590  2816  3021  3213  3399  3581  3762  6117  6175
# [12561]  6240  7733  8102  9458  9985 12151 10848  9971  9774  9625
# [12571]  9520  9820 10511 11299  9727  7710  5644  3859  3524  4348
# [12581]  5387  6493  7629  8480  8798  9048  9339  9598  9580  8802
# [12591]  7576  6241  4928  3863  3850  4950  6280  7540  8571  9204
# [12601]  9289  8885  8043  6826  5626  5806  6878  7805  8452  8844
# [12611]  8974  8863  8653  8427  8222  7881  6974  5860  4802  3819
# [12621]  2982  2719  3011  3413  3827  4224  4505  4559  4529  4477
# [12631]  4413  4353  4367  4414  4439  4431  4383  4282  4105  3821
# [12641]  3393  2800  2210  2023  1886  1602  1206   804   637   693
# [12651]   776   821   810   824   957  1044  1032   938   875  1140
# [12661]  1579  1994  2354  2657  2907  3115  3294  3457  3616  3775
# [12671]  6275  6349  6437  6544  6833  9416  9901 10415  9721 11730
# [12681]  9480  7906  6364  5174  4722  4962  5557  6311  7129  7881
# [12691]  8503  9069  9586  9940  9921  9363  8377  7220  6144  5450
# [12701]  5488  6279  7476  8755  9863 10580 10787 10533  9944  9182
# [12711]  8546  8408  8672  8978  9159  9174  9011  8691  8273  7815
# [12721]  7348  6829  6192  5514  4885  4339  3936  3796  3913  4159
# [12731]  4448  4723  4913  4978  4961  4915  4864  4822  4801  4793
# [12741]  4784  4770  4746  4700  4619  4482  4259  3933  3550  3174
# [12751]  2754  2256  1736  1307  1085  1069  1157  1262  1336  1381
# [12761]  1401  1368  1280  1182  1173  1353  1684  2067  2436  2758
# [12771]  3014  3208  3360  3493  3624  3763  6783  6940  9335 11888
# [12781] 10686  9773 11097 10306  9330  8208  7129  6274  5774  5637
# [12791]  5782  6123  6624  7293  8109  8986  9797 10381 10531 10121
# [12801]  9262  8224  7290  6742  6814  7537  8724 10116 11416 12299
# [12811] 12597 12457 12126 11764 11420 11085 10754 10429 10085  9684
# [12821]  9193  8599  7914  7170  6431  5803  5369  5105  4945  4850
# [12831]  4800  4776  4790  4874  5027  5203  5327  5357  5327  5288
# [12841]  5261  5235  5192  5136  5092  5073  5081  5106  5143  5191
# [12851]  5226  5184  4953  4460  3767  3004  2290  1746  1472  1459
# [12861]  1601  1792  1951  2011  1949  1797  1611  1457  1415  1541
# [12871]  1818  2178  2554  2891  3140  3298  3403  3495  3596  3715
# [12881]  7203  7407  8857 11343  9861 10446  9956  9275  8517  7810
# [12891]  7212  6674  6238  5990  5926  6077  6638  7680  8903 10068
# [12901] 11006 11443 11101 10208  9157  8221  7652  7724  8493  9780
# [12911] 11395 13071 14240 14482 14294 14160 14201 14202 13696 12793
# [12921] 11883 11058 10276  9479  8618  7664  6614  5544  4733  4520
# [12931]  4700  4994  5324  5615  5676  5540  5446  5482  5611  5703
# [12941]  5664  5586  5551  5566  5581  5515  5397  5309  5284  5328
# [12951]  5423  5568  5800  6121  6439  6440  5790  4767  3709  2756
# [12961]  2035  1725  1797  2047  2355  2629  2722  2551  2253  1944
# [12971]  1689  1564  1649  1913  2272  2670  3043  3282  3366  3400
# [12981]  3445  3518  3622  8769 10643  9963 10214 10389 10327 10111
# [12991]  9741  9263  8763  8343  8045  7446  6718  6175  5786  5522
# [13001]  5853  7322  8898 10388 11730 12687 12190 11092  9955  8931
# [13011]  8175  8181  9064 10423 12228 14433 16285 15956 15538 15567
# [13021] 16066 16810 16034 14442 13072 11907 10854  9832  8774  7618
# [13031]  6318  4864  3555  3775  4431  5057  5702  6387  6473  6020
# [13041]  5739  5686  5837  5997  5800  5656  5636  5720  5849  5731
# [13051]  5515  5374  5338  5421  5573  5769  6138  6707  7466  8032
# [13061]  6959  5541  4257  3111  2132  1833  2105  2471  2879  3308
# [13071]  3515  3117  2654  2230  1861  1594  1674  1952  2306  2720
# [13081]  3175  3418  3354  3309  3317  3375  3476  9539  9817 10067
# [13091] 10237 10124 10131 10185 10182 10093  9898  9604  9246  8884
# [13101]  8588  8375  7783  6996  6360  5870  5527  5830  7370  9052
# [13111] 10670 12142 13229 12787 11720 10586  9528  8691  8575  9310
# [13121] 10500 12156 14283 16177 15897 15651 15909 16638 17580 16858
# [13131] 15230 13779 12510 11349 10227  9081  7851  6492  4988  3622
# [13141]  3860  4525  5152  5790  6463  6504  5977  5623  5500  5600
# [13151]  5745  5551  5446  5478  5612  5776  5657  5418  5242  5171
# [13161]  5237  5397  5627  6057  6706  7556  8233  7193  5821  4582
# [13171]  3474  2514  2232  2513  2870  3262  3673  3861  3418  2915
# [13181]  2451  2038  1717  1743  1960  2247  2602  3013  3225  3136
# [13191]  3083  3092  3157  3272 10151 10093 10033  9984 10040  9954
# [13201]  9773  9520  9215  8890  8570  8215  7707  7100  6555  6172
# [13211]  6091  6604  7814  9359 10917 12244 13005 12880 12099 11065
# [13221] 10038  9250  8961  9251 10002 11133 12508 13663 14200 14584
# [13231] 15171 15914 16431 16135 15152 13987 12839 11731 10635  9515
# [13241]  8344  7122  5925  5037  4806  4995  5292  5597  5818  5750
# [13251]  5425  5109  4924  4883  4901  4902  4956  5092  5261  5368
# [13261]  5308  5119  4916  4778  4757  4869  5126  5548  6107  6680
# [13271]  6917  6456  5590  4675  3846  3212  2946  3018  3235  3490
# [13281]  3700  3710  3435  3022  2597  2219  1950  1864  1933  2090
# [13291]  2305  2532  2673  2704  2721  2772  2867  3011  9975  9976
# [13301]  9964  9949 10015 10065  9895  9723  9488  9196  8861  8493
# [13311]  8087  7636  7170  6756  6498  6561  7139  8267  9733 11238
# [13321] 12484 13171 13120 12447 11445 10389  9509  8981  8858  9078
# [13331]  9559 10236 11027 11872 12791 13767 14664 15225 15216 14680
# [13341] 13862 12946 12000 11026 10014  8983  7970  7044  6315  5862
# [13351]  5625  5482  5353  5190  4956  4663  4364  4114  3960  3939
# [13361]  4059  4292  4574  4827  4963  4920  4722  4455  4212  4078
# [13371]  4120  4356  4737  5178  5557  5707  5528  5100  4582  4091
# [13381]  3714  3511  3476  3543  3640  3690  3613  3377  3036  2665
# [13391]  2325  2061  1902  1842  1853  1913  2000  2093  2183  2278
# [13401]  2387  2522  2703  9737  9790  9826  9853  9903 10013 10091
# [13411] 10073 10015  9909  9746  9523  9234  8879  8466  8031  7638
# [13421]  7296  6989  6779  6837  7418  8599 10124 11685 13000 13738
# [13431] 13647 12882 11777 10589  9517  8731  8254  7972  7798  7789
# [13441]  8228  9310 10731 12143 13342 14137 14371 14107 13560 12893
# [13451] 12171 11373 10501  9632  8831  8128  7497  6883  6292  5727
# [13461]  5162  4624  4206  3899  3590  3247  2948  2874  3129  3571
# [13471]  4035  4421  4632  4586  4318  3937  3541  3243  3194  3427
# [13481]  3794  4159  4434  4583  4613  4528  4369  4196  4048  3923
# [13491]  3827  3777  3747  3689  3550  3310  2998  2662  2345  2072
# [13501]  1854  1689  1568  1481  1442  1496  1644  1819  1986  2152
# [13511]  2363  8068  8241  8418  8595  8770  8937  9093  9467  9557
# [13521]  9633  9699  9759 10149 10160 10141 10087  9991  9846  9643
# [13531]  9369  9011  8558  8061  7748  7566  7347  7108  6979  7451
# [13541]  8852 10537 12214 13728 14706 14420 13366 12077 10707  9375
# [13551]  8358  7666  6989  6210  5379  5230  6787  8801 10630 12161
# [13561] 13274 13667 13507 13136 12695 12237 11653 10883 10160  9565
# [13571]  9102  8637  7864  6963  6050  5090  4121  3538  3311  2999
# [13581]  2527  1970  1723  2224  2923  3566  4101  4441  4354  3957
# [13591]  3441  2865  2315  2142  2482  2892  3213  3404  3526  3754
# [13601]  3961  4093  4194  4278  4223  4060  3919  3802  3677  3497
# [13611]  3230  2919  2597  2291  2013  1746  1498  1273  1057   868
# [13621]   885  1147  1419  1636  1803  2008  7430  7557  7693  7837
# [13631]  7988  8144  8303  8463  8621  8775  8921  9058  9184  9299
# [13641]  9404  9501 10052 10205 10250 10268 10256 10213 10137 10022
# [13651]  9859  9632  9318  8889  8321  8133  8115  7970  7725  7403
# [13661]  7554  9314 11030 12688 14276 15756 14981 13698 12328 10876
# [13671]  9336  8156  7389  6454  5296  3852  2481  5107  7446  9443
# [13681] 11131 12541 12950 12811 12563 12288 12064 11731 11010 10449
# [13691] 10047  9796  9665  8663  7589  6502  5322  3972  3273  3167
# [13701]  2811  2225  1433   732  1688  2520  3224  3819  4319  4128
# [13711]  3627  3044  2372  1604  1250  1787  2201  2478  2604  2586
# [13721]  3064  3468  3788  4072  4362  4357  4135  3950  3785  3621
# [13731]  3424  3116  2794  2472  2167  1895  1587  1292  1015   733
# [13741]   425   396   814  1159  1422  1597  1702  7404  7520  7644
# [13751]  7911  8052  8197  8343  8489  8632  8771  8905  9033  9155
# [13761]  9273  9865  9993 10118 10233 10325 10386 10413 10410 10381
# [13771] 10332 10262 10163 10023  9821  9543  9235  9071  9011  8913
# [13781]  8776  8710  9121 10254 11629 13001 14237 14993 14703 13728
# [13791] 12518 11196  9838  8640  7606  6517  5330  4196  3848  5077
# [13801]  6902  8667 10196 11355 11902 11965 11830 11634 11433 11155
# [13811] 10770 10446 10226 10056  9760  9073  8138  7104  5994  4886
# [13821]  4109  3638  3119  2481  1816  1495  1853  2455  3033  3510
# [13831]  3794  3700  3313  2792  2196  1619  1368  1547  1810  2018
# [13841]  2159  2329  2673  3085  3471  3815  4079  4145  4033  3869
# [13851]  3688  3488  3246  2949  2624  2293  1974  1670  1370  1082
# [13861]   816   573   392   436   731  1077  1389  1654  1938  7376
# [13871]  7482  7595  7714  7838  7967  8099  8234  8369  8505  8639
# [13881]  8771  8901  9159  9566  9715  9872 10036 10200 10352 10476
# [13891] 10555 10589 10590 10575 10556 10540 10525 10503 10459 10382
# [13901] 10282 10192 10120 10062 10054 10181 10586 11317 12242 13200
# [13911] 14017 14440 14269 13599 12656 11584 10450  9307  8168  7028
# [13921]  5953  5152  4993  5676  6898  8254  9488 10425 10949 11098
# [13931] 11014 10824 10614 10426 10283 10211 10188 10130  9901  9396
# [13941]  8661  7803  6895  6001  5203  4494  3796  3105  2521  2228
# [13951]  2314  2635  3001  3295  3434  3357  3084  2682  2223  1809
# [13961]  1575  1557  1649  1765  1895  2089  2393  2773  3163  3514
# [13971]  3771  3880  3845  3718  3537  3316  3055  2754  2423  2078
# [13981]  1738  1418  1129   875   659   492   421   513   772  1120
# [13991]  1486  1840  2188  7347  7444  7547  7656  7770  7888  8010
# [14001]  8135  8262  8391  8521  8652  9354  9517  9692  9880 10080
# [14011] 10287 10488 10655 10755 10784 10778 10769 10780 10821 10898
# [14021] 11008 11141 11274 11357 11340 11262 11223 11300 11516 11838
# [14031] 12240 12744 13315 13826 14079 13930 13431 12736 11949 11068
# [14041] 10034  8869  7709  6710  6041  5875  6271  7086  8084  9047
# [14051]  9799 10230 10341 10219  9970  9716  9593  9657  9841 10050
# [14061] 10185 10114  9752  9170  8499  7817  7117  6340  5486  4630
# [14071]  3849  3228  2872  2811  2942  3119  3243  3268  3185  2992
# [14081]  2698  2346  2010  1767  1645  1609  1624  1690  1846  2120
# [14091]  2483  2875  3238  3513  3651  3650  3545  3368  3136  2863
# [14101]  2556  2216  1851  1481  1144   874   670   514   413   405
# [14111]   540   824  1208  1637  2068  2456  7406  7501  7600  7705
# [14121]  7814  7928  8045  8165  9663  9878 10112 10364 10623 10857
# [14131] 10979 10977 10945 10936 10969 11061 11226 11464 11769 12124
# [14141] 12425 12444 12272 12192 12320 12634 12881 12910 13002 13259
# [14151] 13595 13798 13619 13177 12680 12201 11666 10776  9534  8322
# [14161]  7340  6703  6490  6714  7279  8029  8804  9433  9751  9754
# [14171]  9534  9165  8770  8654  8961  9416  9870 10253 10401 10111
# [14181]  9583  9061  8626  8198  7473  6455  5447  4564  3855  3416
# [14191]  3300  3340  3385  3358  3260  3172  3053  2838  2544  2228
# [14201]  1959  1768  1633  1541  1503  1578  1832  2202  2607  2998
# [14211]  3316  3479  3481  3383  3208  2968  2686  2382  2035  1641
# [14221]  1224   848   609   474   380   321   334   500   841  1283
# [14231]  1782  2302  2743  7369  7456  7548  7645  7746  7852  7962
# [14241]  8874  9409  9857 10116 10400 10711 11044 11202 11112 11053
# [14251] 11044 11094 11220 11462 11797 12228 12769 13405 13348 12941
# [14261] 12762 12881 13342 13681 13112 12831 12855 13116 13485 13136
# [14271] 12669 12327 12138 12102 11399  9919  8666  7709  7086  6831
# [14281]  6968  7389  7988  8651  9266  9461  9337  9037  8561  7923
# [14291]  7653  8361  9026  9636 10232 10756 10303  9728  9310  9101
# [14301]  9109  8464  7185  6101  5194  4417  3851  3840  3864  3826
# [14311]  3676  3393  3343  3302  3122  2837  2494  2174  1933  1712
# [14321]  1513  1350  1268  1555  1941  2353  2770  3168  3346  3326
# [14331]  3244  3088  2845  2542  2269  1917  1492  1018   535   372
# [14341]   327   286   253   241   407   835  1314  1850  2455  3053
# [14351]  7413  7498  7588  7682  7781  7993  8353  8954  9340  9563
# [14361]  9809 10079 10373 10687 10996 11147 11107 11066 11072 11144
# [14371] 11305 11582 11959 12427 12968 13479 13444 13055 12787 12754
# [14381] 12967 13005 12471 12073 11952 12069 12258 12047 11731 11540
# [14391] 11484 11476 10902  9713  8614  7756  7189  6947  7036  7380
# [14401]  7888  8459  8966  9152  9051  8776  8345  7817  7649  8165
# [14411]  8749  9297  9817 10175  9895  9434  9100  8949  8919  8399
# [14421]  7397  6495  5741  5103  4665  4582  4556  4469  4284  4021
# [14431]  3893  3785  3565  3248  2871  2499  2170  1853  1559  1317
# [14441]  1208  1393  1724  2107  2507  2883  3097  3150  3132  3036
# [14451]  2841  2572  2273  1892  1441   956   514   321   275   262
# [14461]   266   299   481   856  1293  1779  2317  2798  8141  8398
# [14471]  8541  9258  9484  9733 10002 10286 10570 10813 10953 10986
# [14481] 10986 11012 11102 11283 11569 11949 12386 12811 13083 13026
# [14491] 12697 12318 12023 11816 11546 11143 10783 10581 10532 10538
# [14501] 10479 10394 10357 10346 10230  9787  9022  8196  7495  7020
# [14511]  6825  6917  7244  7717  8230  8658  8884  8889  8727  8457
# [14521]  8179  8093  8278  8577  8878  9124  9214  9050  8748  8468
# [14531]  8263  8066  7697  7161  6634  6190  5835  5590  5461  5374
# [14541]  5265  5106  4905  4696  4454  4140  3759  3336  2902  2474
# [14551]  2055  1666  1359  1218  1298  1548  1879  2229  2553  2805
# [14561]  2972  3063  3064  2953  2725  2390  1961  1474   992   600
# [14571]   374   296   299   348   445   625   897  1224  1585  1964
# [14581]  2305  7652  7744  7842  7947  8059  8604  8772  8957  9161
# [14591]  9385  9630  9892 10163 10423 10638 10771 10823 10837 10868
# [14601] 10956 11137 11424 11795 12199 12544 12698 12547 12117 11546
# [14611] 10957 10412  9929  9515  9177  8924  8761  8696  8730  8834
# [14621]  8958  9033  8964  8665  8152  7549  6996  6607  6470  6615
# [14631]  6989  7494  8024  8471  8751  8850  8816  8705  8576  8484
# [14641]  8450  8449  8444  8403  8296  8109  7864  7598  7340  7101
# [14651]  6889  6715  6593  6524  6484  6427  6328  6210  6099  5984
# [14661]  5821  5562  5205  4784  4324  3842  3344  2832  2312  1809
# [14671]  1392  1165  1190  1406  1699  1998  2285  2569  2838  3054
# [14681]  3176  3161  2969  2595  2094  1544  1025   622   394   326
# [14691]   361   455   585   745   929  1128  1337  1561  1812  7872
# [14701]  7980  8507  9050  9268  9504  9756 10018 10272 10486 10612
# [14711] 10646 10643 10653 10714 10873 11159 11532 11929 12264 12387
# [14721] 12115 11476 10648  9748  8877  8199  7782  7476  7178  6900
# [14731]  6761  6900  7213  7521  7729  7773  7610  7261  6806  6349
# [14741]  6002  5908  6154  6641  7240  7855  8384  8726  8890  8957
# [14751]  8980  8965  8851  8615  8329  8026  7707  7406  7172  6950
# [14761]  6677  6354  6069  6000  6167  6437  6748  7051  7200  7105
# [14771]  6936  6834  6805  6728  6429  5946  5416  4890  4363  3822
# [14781]  3251  2641  2004  1413  1051  1078  1340  1629  1867  2086
# [14791]  2391  2772  3121  3373  3476  3324  2875  2260  1610  1010
# [14801]   558   345   333   428   572   730   868   970  1043  1094
# [14811]  1150  1301  7535  7799  7901  8926  9133  9357  9597  9850
# [14821] 10108 10351 10474 10452 10412 10388 10397 10497 10798 11181
# [14831] 11579 11952 12180 11760 10821  9738  8558  7320  6133  5901
# [14841]  5560  5121  4767  5693  6189  6537  6711  6668  6424  6067
# [14851]  5665  5292  5161  5600  6250  6965  7697  8374  8755  8927
# [14861]  9061  9196  9326  9229  8741  8195  7641  7062  6527  6312
# [14871]  6151  5878  5473  5012  5053  5615  6212  6832  7498  7931
# [14881]  7667  7384  7296  7410  7582  7208  6547  5946  5403  4880
# [14891]  4340  3753  3090  2340  1519   877  1068  1479  1780  1929
# [14901]  1978  2288  2821  3274  3627  3875  3813  3177  2411  1655
# [14911]   952   388   238   337   506   704   904  1029  1048  1015
# [14921]   927   788   756  7556  7639  7728  8043  8613  8790  8982
# [14931]  9190  9412  9647  9891 10138 10257 10200 10144 10103 10082
# [14941] 10120 10417 10762 11109 11442 11709 11171 10078  8887  7592
# [14951]  6185  4670  4288  3780  3251  3760  4477  5069  5510  5784
# [14961]  5836  5677  5404  5070  4726  4556  5155  5888  6664  7460
# [14971]  8242  8651  8853  9044  9238  9435  9359  8704  8018  7322
# [14981]  6604  5904  5733  5606  5359  4964  4430  4529  5269  5964
# [14991]  6666  7452  8082  7659  7355  7300  7492  7868  7471  6814
# [15001]  6281  5822  5379  4901  4358  3718  2964  2084  1227  1578
# [15011]  2014  2277  2358  2273  2548  3098  3525  3850  4108  4098
# [15021]  3311  2481  1686   949   317   237   401   617   850  1076
# [15031]  1200  1172  1087   934   707   518  7575  8068  8482  8644
# [15041]  8819  9006  9204  9408  9611  9787  9879  9878  9845  9816
# [15051]  9813  9882 10061 10295 10523 10682 10637 10140  9232  8128
# [15061]  5730  4798  4262  3852  3428  3016  2808  3072  3625  4989
# [15071]  5107  5040  4849  4611  4427  4479  4912  5578  6336  7108
# [15081]  7804  8302  8629  8882  9079  9166  8982  8465  7789  7070
# [15091]  6378  5822  5519  5349  5164  4921  4707  4800  5217  5717
# [15101]  6231  6724  7010  6940  6804  6797  6936  7083  6971  6676
# [15111]  6391  6133  5856  5508  5064  4521  3901  3261  2808  2795
# [15121]  2984  3136  3195  3216  3367  3637  3869  4013  4033  3790
# [15131]  3197  2454  1709  1044   575   436   553   777  1022  1232
# [15141]  1347  1350  1273  1144  1009  1014  8210  8346  8491  8647
# [15151]  8811  8980  9150  9308  9437  9514  9536  9529  9518  9527
# [15161]  9578  9679  9800  9892  9885  9684  9195  8426  7472  5415
# [15171]  4545  3871  3324  2846  2478  2342  2538  2991  4382  4548
# [15181]  4530  4392  4223  4136  4258  4655  5268  5991  6728  7395
# [15191]  7926  8323  8622  8827  8875  8670  8192  7538  6833  6184
# [15201]  5691  5407  5275  5198  5125  5079  5130  5283  5477  5668
# [15211]  5828  5914  5913  5898  5937  6041  6164  6243  6284  6323
# [15221]  6351  6312  6141  5826  5415  4979  4583  4304  4189  4186
# [15231]  4217  4242  4258  4284  4308  4286  4187  3977  3605  3058
# [15241]  2399  1720  1121   723   612   743   994  1259  1470  1588
# [15251]  1609  1557  1473  1413  1456  7522  8207  8335  8471  8610
# [15261]  8752  8889  9013  9112  9175  9204  9210  9208  9214  9237
# [15271]  9274  9303  9285  9167  8890  8412  7738  6019  5125  4301
# [15281]  3580  2949  2402  1986  1820  2000  2452  3012  3550  3961
# [15291]  4159  4144  4006  3845  3769  3901  4306  4919  5634  6363
# [15301]  7027  7564  7978  8308  8555  8646  8457  7958  7278  6563
# [15311]  5926  5478  5281  5275  5351  5437  5490  5475  5390  5257
# [15321]  5089  4912  4794  4783  4835  4909  5002  5151  5408  5755
# [15331]  6134  6496  6756  6785  6570  6263  6001  5828  5694  5537
# [15341]  5397  5331  5326  5319  5225  5024  4749  4412  4006  3532
# [15351]  2995  2392  1751  1158   768   726   960  1290  1596  1819
# [15361]  1935  1953  1906  1842  1809  1846  8179  8294  8411  8527
# [15371]  8637  8733  8810  8861  8897  8894  8882  8869  8830  8735
# [15381]  8550  8238  7777  6453  4861  4082  3352  2673  2047  1510
# [15391]  1217  1435  1975  3201  3708  3929  3850  3667  3470  3331
# [15401]  3413  3877  4540  5269  6009  6694  7206  7582  7922  8240
# [15411]  8470  8345  7740  6985  6243  5586  5146  5109  5308  5566
# [15421]  5813  5975  5888  5546  5090  4563  4009  3637  3652  3782
# [15431]  3880  3937  4053  4488  5147  5844  6544  7178  7418  7172
# [15441]  6892  6778  6862  6953  6716  6429  6300  6316  6362  6170
# [15451]  5731  5224  4682  4103  3543  3047  2512  1894  1231   733
# [15461]   827  1277  1724  2073  2299  2391  2369  2289  2207  2167
# [15471]  2184  7840  8025  8121  8218  8311  8472  8530  8570  8534
# [15481]  8483  8396  8254  8031  7705  6073  5369  1825  1177   556
# [15491]   983  2889  3516  3762  3559  3351  3142  2935  2806  3485
# [15501]  4187  4898  5620  6356  6782  7075  7397  7757  8167  8233
# [15511]  7379  6595  5884  5245  4684  4976  5400  5822  6203  6508
# [15521]  6351  5735  5012  4191  3279  2454  2714  2905  3013  3032
# [15531]  2957  3629  4548  5441  6360  7360  7874  7370  7093  7089
# [15541]  7406  8047  7449  7064  6951  7040  7265  7001  6327  5665
# [15551]  4993  4292  3626  3281  2848  2299  1606   747  1194  1881
# [15561]  2385  2723  2915  2949  2838  2682  2535  2451  2469  7508
# [15571]  7797  7876  7955  8032  8172  8272  8300  8206  8128  7841
# [15581]  7599  6351  5769  3774  3092  2424  1196   818  1973  2514
# [15591]  3001  3225  3166  3040  2908  2807  2883  3327  3913  4524
# [15601]  5135  5708  6115  6408  6692  6987  7248  7192  6666  6060
# [15611]  5509  5064  4853  5101  5595  6117  6557  6791  6580  5924
# [15621]  5043  4051  3061  2358  2227  2305  2404  2491  2658  3224
# [15631]  4053  4922  5800  6628  7032  6888  6740  6787  7064  7371
# [15641]  7282  7151  7191  7355  7496  7280  6710  6040  5345  4671
# [15651]  4119  3762  3445  3073  2623  2251  2458  2943  3331  3563
# [15661]  3640  3558  3344  3070  2802  2601  2493  7482  7732  7796
# [15671]  7856  8003  7903  7809  6535  6067  5534  4950  4330  3693
# [15681]  3056  2436  1861  1374  1732  2114  2449  2655  2726  2733
# [15691]  2734  2782  2948  3277  3707  4165  4615  5028  5372  5646
# [15701]  5871  6044  6129  6043  5769  5422  5105  4907  4940  5280
# [15711]  5841  6457  6959  7164  6908  6193  5179  4057  3021  2284
# [15721]  1953  1908  2003  2177  2472  2963  3615  4321  5005  5577
# [15731]  5896  5956  5935  5984  6149  6373  6571  6796  7093  7396
# [15741]  7559  7421  6977  6357  5692  5086  4637  4376  4236  4133
# [15751]  4033  3998  4127  4348  4520  4578  4495  4263  3899  3459
# [15761]  3015  2648  2425  7494  7766  7793  7705  7631  7528  7388
# [15771]  6961  1223  1317  1511  1743  1966  2155  2305  2434  2568
# [15781]  2737  2958  3232  3538  3845  4132  4402  4670  4907  5062
# [15791]  5112  5070  4983  4883  4771  4672  4664  4867  5355  6064
# [15801]  6840  7492  7782  7487  6612  5389  4072  2890  2052  1649
# [15811]  1581  1702  1931  2255  2681  3182  3699  4172  4545  4780
# [15821]  4881  4900  4908  4982  5205  5625  6195  6812  7359  7683
# [15831]  7645  7250  6645  5987  5417  5065  4981  5097  5314  5557
# [15841]  5761  5875  5897  5847  5717  5472  5073  4522  3872  3201
# [15851]  2618  2260  7190  7228  7267  7430  7504  7536  7561  7522
# [15861]  7466  7389  6966  1254  1236  1299  1402  1526  1695  1910
# [15871]  2140  2388  2666  2948  3192  3411  3598  4067  4308  4412
# [15881]  4330  4128  4017  4101  4208  4273  4360  4642  5299  6221
# [15891]  7217  8130  8670  8340  7149  5609  4025  2598  1614  1251
# [15901]  1269  1452  1717  2036  2394  2766  3114  3395  3587  3726
# [15911]  3826  3838  3767  3698  3871  4543  5499  6477  7348  7945
# [15921]  8006  7569  6912  6214  5617  5336  5496  5928  6490  7093
# [15931]  7563  7647  7452  7189  6898  6532  5984  5225  4342  3410
# [15941]  2533  1977  7162  7195  7227  7260  7291  7399  7307  7251
# [15951]  7177  7078  1417  1223  1126  1095  1098  1113  1256  1543
# [15961]  1845  2175  2559  2947  3156  3341  3867  3871  4036  4273
# [15971]  5171  6312  7481  8658  9730  9359  7587  5733  3921  2201
# [15981]   930   849  1027  1271  1551  1850  2140  2405  2618  2741
# [15991]  2748  2778  2926  2934  2787  2509  2371  3495  4872  6161
# [16001]  7342  8355  8480  7858  7141  6410  5722  5393  5938  6689
# [16011]  7544  8496  9414  9326  8841  8403  8008  7610  6972  5987
# [16021]  4913  3761  2539  1548  7151  7176  7199  7219  7236  7246
# [16031]  7232  7211  7109  7057  6990   865   844   963  3566  3893
# [16041]  4097  5284  6385  7505  8625  9621  9228  7486  5646  3850
# [16051]  2152   913   802   966  1195  1452  1711  1940  2125  2250
# [16061]  2287  2226  2211  2326  2326  2190  1949  1896  3054  4507
# [16071]  5887  7157  8239  8453  7931  7302  6663  6080  5876  6516
# [16081]  7386  8362  9411 10370 10329  9842  9364  8912  8451  7754
# [16091]  6725  5607  4418  3168  2169  7114  7126  7108  7087  7062
# [16101]  7034  6966  6926  6880  6825  4254  4996  5624  6441  7290
# [16111]  8047  8452  8051  6859  5346  3801  2415  1456  1083  1077
# [16121]  1223  1425  1631  1807  1938  2013  2029  2004  2000  2029
# [16131]  2028  1987  1996  2315  3193  4413  5680  6829  7679  7989
# [16141]  7801  7395  6959  6651  6689  7194  7999  8936  9863 10543
# [16151] 10704 10457 10055  9592  9049  8332  7420  6403  5355  4372
# [16161]  3692  6938  6902  6864  5153  5471  5909  6431  6953  7348
# [16171]  7432  7023  6125  4938  3682  2556  1747  1334  1235  1310
# [16181]  1459  1618  1747  1833  1878  1891  1889  1896  1916  1942
# [16191]  1992  2157  2590  3383  4438  5563  6581  7327  7680  7666
# [16201]  7444  7192  7070  7226  7718  8472  9352 10193 10794 11010
# [16211] 10880 10552 10122  9592  8918  8103  7222  6364  5612  6099
# [16221]  6348  6579  6708  6616  6206  5475  4519  3483  2526  1822
# [16231]  1459  1362  1414  1534  1660  1746  1788  1807  1819  1835
# [16241]  1864  1910  1974  2077  2290  2739  3508  4499  5542  6489
# [16251]  7201  7562  7599  7464  7312  7281  7498  8018  8775 10506
# [16261] 11129 11341 11205 10902 10079  9477  6186  6174  6182  6140
# [16271]  5960  5566  4946  4154  3267  2387  1724  1489  1458  1516
# [16281]  1627  1747  1782  1767  1761  1776  1815  1882  1973  2085
# [16291]  2219  2403  2778  3592  4598  5601  6523  7269  7603  7578
# [16301]  7300  7521  8103  8898 11533  5851  5735  5612  5411  5059
# [16311]  4540  3888  3138  2330  1616  1576  1580  1617  1695  1816
# [16321]  1785  1725  1708  1735  1808  1927  2087  2273  2468  2655
# [16331]  2854  3809  4796  5722  6575  7348  7622  7504  7368  7224
# [16341]  7386  8049  8845  5223  5100  4922  4642  4243  3739  3157
# [16351]  2553  2076  1859  1767  1719  1704  1705  1671  1629  1626
# [16361]  1677  1792  1980  2234  2536  2860  3200  5886  6561  7094
# [16371]  7331  7310  7217  4608  4499  4313  4040  3688  3280  2858
# [16381]  2486  2205  1995  1825  1690  1591  1526  1500  1519  1595
# [16391]  1751  2389  2843  3341  3856  6090  6550  6887  7053  4063
# [16401]  3914  3706  3453  3173  2871  2551  2234  1935  1670  1473
# [16411]  1377  1368  1409  1496  3157  3847  6578  6758  3846  3762
# [16421]  3645  3497  3265  2896  2477  2058  1657  1338  1346  3694
# 
# $response_var
#     [1] 19975046 20033177 19175362 19384741 19483421 19416930
#     [7] 19142071 18223737 18638782 18913308 18988901 18825423
#    [13] 18391468 17125220 17810290 18300076 18540279 18500873
#    [19] 18160934 17500303 13541989 14717688 15924485 16942087
#    [25] 17675243 18090698 18178329 17932472 17344462  9677309
#    [31] 11096835 12991294 14733562 16111769 17085713 17665674
#    [37] 17869502 17708602 17184318  5833936  5875127  8652938
#    [43] 11481088 13741514 15419790 16581617 17288228 17583024
#    [49] 17490718 17018706 16158945  7113856  2758206  2868036
#    [55]  7334383 10663220 13138611 14941943 16191438 16966106
#    [61] 17317396 17274367 16846121 16022895  9910172  7604024
#    [67]  5261720  5359740  7958519 10683339 12937745 14664822
#    [73] 15897419 16681209 17054996 17043394 16654235 15878413
#    [79] 10824424  9802120  8477766  7419771  7558248  9011526
#    [85] 10999234 12906316 14474867 15634893 16389564 16760991
#    [91] 16767183 16413712  9687406  9685908  9316064  8479404
#    [97]  7733475  7909452  9190124 10996133 12765915 14233009
#   [103] 15321252 16032401 16387434 16402550  7205389  8266596
#   [109]  8434661  7499405  6195013  6372389  8308301 10530261
#   [115] 12416073 13859574 14887295 15547882 15878284 15897236
#   [121]  2273885  4736218  7174039  7705997  6344356  3259663
#   [127]  3417297  7140300  9960213 11956331 13341585 14278683
#   [133] 14872050 15171335  3300966  5053605  7207688  7726402
#   [139]  6503182  3950014  4088473  7219461  9752233 11498096
#   [145] 12655748 13424746 13929353  7884590  6591612  7010311
#   [151]  7998837  8295799  7632695  6653299  6780801  8209136
#   [157]  9788253 10948379 11687218 12203327 10523744  8709193
#   [163]  7765695  7894348  8459539  8649494  8237105  7705748
#   [169]  7801744  8618288  9538249 10070218 10237326 10427747
#   [175] 10864842 12491504 10217953  8092042  6908774  7241481
#   [181]  8113693  8382227  7786829  6932922  6991016  7987366
#   [187]  8793500  8782075  8127221  7843681  8607500  9470658
#   [193]  9543107 23069461 14453034 12222224  9532935  6400505
#   [199]  3956627  5360958  7304035  7787480  6654053  4437694
#   [205]  4488329  6748249  7921865  7466362  5510129  4107885
#   [211]  6172247  7935588  8067193  6525473 22816756 22710684
#   [217] 16246089 14399905 12127799  9294109  5672428  1449311
#   [223]  4477206  7021004  7590846  6224636  2887480  2962376
#   [229]  6273898  7614947  7010919  4417947  1480336  5236415
#   [235]  7379850  7530139  5692351  1983590 22569478 22403105
#   [241] 22257768 21266731 20651022 17707212 16233345 14444444
#   [247] 12307590  9831443  7227032  5568135  6302787  7672717
#   [253]  8052733  7188142  5753940  5771655  7207138  8050703
#   [259]  7650327  6273121  5485371  6637069  7864458  7961397
#   [265]  6866280  5589263  6343348 10840222 12603204 13905104
#   [271] 14822743 22114208 21888331 21687921 21605196 21135320
#   [277] 20537625 19782272 18835231 17659913 16221721 14499936
#   [283] 12517392 10408857  8543003  7549461  7724218  8364097
#   [289]  8575298  8117618  7494583  7499930  8123984  8571704
#   [295]  8353166  7701026  7399113  7858019  8466490  8518472
#   [301]  7965497  7494989  7986846  9450589 11234411 12863555
#   [307] 14167510 15134143 21872622 21559574 21252484 20974373
#   [313] 21769070 21419710 20970659 20396064 19665151 18742695
#   [319] 17590706 16173004 14466899 12492225 10378981  8493330
#   [325]  7483657  7673586  8336490  8553592  8081804  7435413
#   [331]  7441515  8089529  8551120  8326038  7650025  7335103
#   [337]  7814592  8444197  8497752  7925854  7430945  7929772
#   [343]  9420974 11225155 12870444 14196509 15198451 21306700
#   [349] 20892652 20475403 20087183 21762423 21509733 21182838
#   [355] 20760281 20215233 19515261 18622480 17494226 16084475
#   [361] 14346675 12241127  9764149  7104384  5365799  6171917
#   [367]  7616224  8010853  7108676  5581537  5601912  7129721
#   [373]  8008684  7593563  6141084  5288247  6530322  7813717
#   [379]  7913924  6772393  5396698  6188474  8552464 10816929
#   [385] 12618667 13983834 15007196 20104985 19540415 18996074
#   [391] 21587553 21407914 21176824 20877777 20488844 19981992
#   [397] 19322683 18469876 17376139 15986916 14236581 12036289
#   [403]  9245321  5623265  1135072  4425629  7005151  7579274
#   [409]  6200919  2776678  2855060  6238568  7577038  6968010
#   [415]  4356589  1182588  5170194  7294177  7442063  5625855
#   [421]  1789860  3950946  7728486 10370805 12217772 13537619
#   [427] 14533575 15336121 15997844 16512585 16848105 22644856
#   [433] 20515850 19894672 19197563 18441641 17677772 21352433
#   [439] 21246837 21116192 20953731 20748187 20483335 20136964
#   [445] 19679756 19074751 18277768 17238654 15902733 14211550
#   [451] 12102417  9515257  6499741  4213392  5494806  7350609
#   [457]  7819723  6724630  4637026  4669019  6751634  7816543
#   [463]  7320508  5452150  4167857  5979166  7584271  7705306
#   [469]  6298188  4305958  5294676  7993790 10185377 11724354
#   [475] 12819245 13708576 14545588 15355853 16080153 16642639
#   [481] 21964629 21528956 21031866 20464234 19812511 19059010
#   [487] 18187202 17196761 16132968 15127278 20837850 20744930
#   [493] 20637920 20515749 20372052 20196149 19972703 19679856
#   [499] 19287063 18754196 18032865 17070060 15814544 14228618
#   [505] 12313511 10170531  8147798  7022389  7327844  8155587
#   [511]  8413452  7843392  7026015  7034556  7853650  8409602
#   [517]  8139059  7299589  6889781  7507962  8280835  8346700
#   [523]  7644595  6950465  7363598  8702405 10048627 11010419
#   [529] 11693752 12399667 13313330 14373275 15401276 16250821
#   [535] 21553436 21038006 20453675 19791700 19035200 18155126
#   [541] 17111072 15865073 14421880 12915333 11729272 11430289
#   [547] 20196490 20093120 19980680 19867575 19752798 19629163
#   [553] 19486598 19312100 19085866 18776528 18339178 17717830
#   [559] 16851662 15684849 14183590 12371333 10401226  8662796
#   [565]  7745625  7881416  8449625  8640720  8225888  7673939
#   [571]  7679126  8232678  8637904  8437500  7851456  7586032
#   [577]  7991694  8541130  8589732  8086736  7634840  7906818
#   [583]  8771625  9552893  9874710  9955989 10411759 11553191
#   [589] 13066342 14532877 15731555 21085708 20476089 19791699
#   [595] 19029300 18175243 17194264 16020309 14559740 12723664
#   [601] 10534488  8453980  7847968  9356096 19527668 19451403
#   [607] 19317941 19164633 19019971 18895893 18788295 18685710
#   [613] 18578416 18459230 18314666 18113913 17804492 17317001
#   [619] 16574790 15504237 14046405 12178483  9968987  7743125
#   [625]  6439267  6902245  7942810  8251955  7560672  6510657
#   [631]  6523765  7576720  8250769  7925841  6873760  6327872
#   [637]  7140846  8094207  8173049  7314298  6389541  6782517
#   [643]  7986045  8653475  8321464  7427151  7509414  9301477
#   [649] 11600252 13624609 15189762 19832019 19025856 18148380
#   [655] 17202375 16162222 14949027 13417499 11366525  8578649
#   [661]  5020754  3386697  6778074  9990037 12373401 14098755
#   [667] 15371449 16353460 17141454 17771124 18240937 18539160
#   [673] 18662735 18626871 18468101 18241159 18007171 17813575
#   [679] 17676183 17579599 17498969 17423892 17361409 17314668
#   [685] 17256782 17122387 16819774 16248938 15312436 13916454
#   [691] 11965214  9355522  6028407  3009738  4932282  7165381
#   [697]  7694070  6439972  3747681  3796801  6469133  7682023
#   [703]  7123687  4877668  2995131  5541832  7417614  7552361
#   [709]  5928877  3220395  4450495  6946842  7826547  6902675
#   [715]  4342263  3577269  7157169 10423568 12920138 14753633
#   [721] 19097783 18132979 17104597 16052474 14991069 13858507
#   [727] 12486247 10625245  8011181  4517480  2760091  6275230
#   [733]  9351782 11552727 13101156 14247584 15187747 16014569
#   [739] 16725241 17271489 17606930 17710520 17594128 17305524
#   [745] 16927690 16564035 16299705 16156202 16086696 16029778
#   [751] 15971306 15953010 16019272 16153381 16263754 16220181
#   [757] 15893258 15169034 13942613 12102115  9512918  6049043
#   [763]  2594099  4844367  7209394  7726831  6388926  3442222
#   [769]  3490949  6385232  7643455  7067021  4696050  2521703
#   [775]  5408967  7370909  7510403  5819825  2804279  4211372
#   [781]  6832895  7697063  6710442  3985985  3050443  6799704
#   [787] 10086227 12616565 14504798 18278126 17098881 15846968
#   [793] 14625215 13540542 12595810 11609469 10309154  8568337
#   [799]  6760034  6209542  7568464  9438537 10957844 12040430
#   [805] 12896655 13748969 14654877 15515310 16193704 16594268
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# [16279]  7596621  7715703  6327094  4383657  5322978  7858741
# [16285]  9780938 10916620 11436895 11502952 11141458 10225156
# [16291]  8566650  6146102  4247514  5647909  7421815  7806613
# [16297]  6653912  4615907  4828292  6862714  5388393  4281732
# [16303]  6119880  7638461  4324358  6993522  7569011  6191195
# [16309]  2746393  2826701  6233783  7575803  6965204  4343049
# [16315]  1088836  5160164  7289849  7437698  5617293  1734996
# [16321]  3886023  7467696  9722462 11006993 11600196 11676491
# [16327] 11262102 10225943  8318455  5204792   897161  4591710
# [16333]  7072092  7548893  6069174  2518342  3049104  6349758
# [16339]  7591505  4154033  1285785  5316887  7341943  7993638
# [16345]  7081027  5524018  5546250  7107164  7998455  7577385
# [16351]  6098234  5221968  6494652  7798340  7900544  6742193
# [16357]  5317599  6018688  8101969  9818791 10851905 11319254
# [16363] 11377738 11054992 10223022  8725511  6661945  7979342
# [16369]  7007265  5465041  5611602  7179068  8009602  8070045
# [16375]  7418727  7426616  8082701  8548147  8320090  7635570
# [16381]  7315734  7801404  8437953  8493305  7912733  7371049
# [16387]  7700133  8753308  9762996 10322364 10489999 10407611
# [16393]  9996472  9113213  7996845  8537311  8034905  7398251
# [16399]  7450133  7525722  8139727  8581187  8364322  7720134
# [16405]  7422990  7875070  8475967  8528775  7980413  7471870
# [16411]  7738341  8583884  9226703  9256698  9305090  8844654
# [16417]  8094463  7499367  7234448  8068037  7671812  6317637
# [16423]  5551854  6673624  7878289  7974459  6899667  5631630
# [16429]  8338140  1583364

d30$burned = pred$response_mean
d30
# Simple feature collection with 16430 features and 3 fields
# Geometry type: POLYGON
# Dimension:     XY
# Bounding box:  xmin: 129 ymin: -14.9 xmax: 131 ymax: -13.3
# Geodetic CRS:  WGS 84
# First 10 features:
#     pre  tem                       geometry burned
# 1  1739 34.6 POLYGON ((130 -13.3, 130 -1...   3307
# 2  1735 34.6 POLYGON ((130 -13.3, 130 -1...   3270
# 3  1745 34.6 POLYGON ((130 -13.3, 130 -1...   3095
# 4  1733 34.6 POLYGON ((130 -13.3, 130 -1...   3089
# 5  1732 34.6 POLYGON ((130 -13.3, 130 -1...   3078
# 6  1731 34.7 POLYGON ((130 -13.3, 130 -1...   3055
# 7  1725 34.8 POLYGON ((130 -13.3, 130 -1...   3017
# 8  1750 34.8 POLYGON ((130 -13.3, 130 -1...   2874
# 9  1741 34.8 POLYGON ((130 -13.3, 130 -1...   2905
# 10 1725 34.7 POLYGON ((130 -13.3, 130 -1...   2929

4.2 Analysing future bushfire patterns

Aim

In this step, the predicted burned area of 2030 is used to analyse the future bushfire patterns.

Description of steps

1. Visualise the predicted burned area of 2030.
2. Analyse the future bushfire patterns.