# draw.laplace: Generates variates from Laplace distribution In UnivRNG: Univariate Pseudo-Random Number Generation

## Description

This function implements pseudo-random number generation for a Laplace (double exponential) distribution with pdf

f(x|λ,α)=\frac{λ}{2}e^{-λ|x-α|}

for lambda>0 where alpha and lambda are the location and scale parameters, respectively.

## Usage

 1 draw.laplace(nrep, alpha, lambda) 

## Arguments

 nrep Number of data points to generate. alpha Location parameter for the desired Laplace distribution. lambda Scale parameter for the desired Laplace distribution.

## Value

A list of length five containing generated data, the theoretical mean, the empirical mean, the theoretical variance, and the empirical variance with names y, theo.mean, emp.mean, theo.var, and emp.var, respectively.

## Examples

 1 2 3 draw.laplace(nrep=100000, alpha=4, lambda=2) draw.laplace(nrep=100000, alpha=-5, lambda=4) 

### Example output

\$y
[1]  4.079356128  3.826856463  4.564202816  4.203304980  3.783472216
[6]  4.019088983  4.149464291  4.109154847  2.940419336  5.418032858
[11]  2.228270267  4.228422619  4.464127399  4.240859706  4.304646409
[16]  3.712135374  3.811951379  4.745816707  3.838060748  4.000409278
[21]  3.671362621  4.866263110  3.818297376  3.955370912  3.926177889
[26]  3.385178154  4.228365984  3.859236771  4.439381434  3.900613570
[31]  6.513094363  4.565728462  4.659060533  3.579808926  2.783610496
[36]  4.577302168  3.919676848  3.748633179  4.224202768  3.806704909
[41]  4.428457691  4.152468458  0.203494081  3.552866258  4.085677060
[46]  4.063590946  3.697995867  3.839528751  3.407535391  4.063938232
[51]  4.058069480  4.403967187  3.383782113  3.366153283  3.193968664
[56]  3.823689963  3.759742428  3.045784476  2.980110414  3.501045673
[61]  4.450564667  4.980422945  3.040873783  2.723052635  4.246121808
[66]  4.711555443  4.234625672  4.083818699  4.712233504  3.593349127
[71]  4.543308634  4.334703628  3.361369641  4.254383721  3.309358988
[76]  4.170643633  3.981548473  4.644383088  3.651687366  3.861100471
[81]  4.130802876  3.772321110  4.112451051  4.044486300  3.675749871
[86]  3.877137928  3.911489348  3.698073150  6.684958749  3.350858383
[91]  3.070213388  4.151542894  3.853569729  4.016806878  4.270865510
[96]  3.776003278  3.066541799  4.466749687  3.886800514  4.757787933
[101]  5.191463367  4.960867660  3.593503712  3.970599860  3.751907830
[106]  4.014968604  3.920533770  4.214000657  4.158222202  3.569666395
[111]  3.229062802  2.454041833  3.760615075  3.847222578  4.452139277
[116]  4.072477276  4.228474827  3.956605225  3.165408940  5.133938128
[121]  4.109854561  3.802985619  4.043180857  3.677999816  3.862877753
[126]  3.983073469  5.467309344  5.056483965  4.359792336  4.909169871
[131]  3.914741846  3.789608893  4.128543460  4.238676479  3.423196888
[136]  4.433186844  4.234746550  4.572938746  4.472704694  3.397298152
[141]  3.146059628  4.578203626  3.869564024  3.764159631  3.712134000
[146]  3.950084385  3.377444655  3.613756165  3.828758606  4.794500344
[151]  3.682020351  2.400237813  3.460928246  5.314309035  4.042799931
[156]  4.625714354  3.293708385  1.693884930  4.265639013  3.430211260
[161]  3.546885561  4.176041301  3.528424718  4.138311147  3.510777982
[166]  4.244647496  3.912081099  2.519748803  3.396409806  4.805836055
[171]  4.050347712  3.575061388  3.972184058  4.296768705  3.337833229
[176]  3.643443257  3.744485232  3.698586985  5.205940642  3.945226870
[181]  4.720112324  4.094993070  4.067694807  4.551962844  3.403356207
[186]  3.603058738  4.042137048  4.306857137  4.193909139  4.115886152
[191]  4.782731694  4.515392894  4.151515448  4.726836040  5.240142480
[196]  3.463249169  2.660377537  5.618636288  4.097779768  5.326861304
[201]  3.747963327  3.314403952  3.966343011  4.704949156  4.014373186
[206]  2.643023358  3.849116736  5.451539479  4.479894074  3.911324748
[211]  5.112987501  3.447202681  4.479647940  3.694284842  4.331958744
[216]  3.543350058  4.472468999  3.632621455  3.819008601  4.821977413
[221]  3.952086095  2.138362249  4.736407417  3.677682676  4.668192621
[226]  3.849773507  4.957258721  3.986191814  3.808630314  4.071278492
[231]  3.658152989  5.908004767  4.118454586  6.239031473  3.876994259
[236]  3.828408845  4.192786035  5.693013165  4.381681410  4.014556003
[241]  3.934719545  4.984838697  4.637097528  3.670020461  3.933597910
[246]  3.765863441  3.518576792  4.314658780  5.403555596  3.631126036
[251]  3.857954800  4.115467507  4.028623627  4.193728848  3.974310641
[256]  3.896591135  3.685924549  4.126230900  4.844346358  5.610962269
[261]  1.830338761  3.965177611  4.624218618  3.673798764  3.950210525
[266]  4.146693819  4.084543135  4.152493260  4.021234662  3.248064091
[271]  4.125176393  4.669920936  3.868195353  3.934972374  4.160697839
[276]  3.167210461  4.284889324  4.102894512  3.456409596  4.293749535
[281]  4.064825559  4.400885249  3.539294654  4.203851492  4.330802381
[286]  4.259701088  4.632510285  3.362767021  4.454431384  4.823903987
[291]  3.588800721  4.367426918  4.176674715  3.396735751  4.097981842
[296]  4.038379862  4.748427073  4.265512820  3.201012779  5.352657170
[301]  3.851056395  3.989048522  3.809546940  4.271950952  3.596417678
[306]  3.776385164  3.748719985  3.758852017  3.733760066  4.096315689
[311]  2.388581589  3.853787676  3.020850532  3.662023450  2.755317762
[316]  3.437487530  5.276620224  3.594131568  3.811637796  3.883458809
[321]  4.669657985  3.777905216  2.555397421  3.958883350  3.324132478
[326]  2.945494028  4.053823969  4.855330859  4.169393771  3.919273318
[331]  3.911288941  3.697992578  4.033936385  3.026519197  4.506005619
[336]  4.861143763  3.601751005  4.406364839  3.794202426  5.204726270
[341]  3.308290128  3.753428310  4.386970804  4.524091726  4.171027524
[346]  4.154122426  4.037392185  4.529091336  2.585665664  4.726348046
[351]  4.480337860  4.450573637  3.341106621  4.393212002  4.146949494
[356]  3.410182887  3.637612096  4.151565928  3.426977752  3.993824365
[361]  4.147641050  3.028253779  3.481376257  4.101870088  3.929209095
[366]  3.676233916  4.155663482  4.010402079  3.765817920  3.759173798
[371]  3.433117196  3.426857427  3.764339618  3.783226314  4.515890764
[376]  4.121698267  4.797595039  3.441666173  3.990391389  4.182352051
[381]  4.337876049  4.382650207  4.191295360  4.094591025  4.336010049
[386]  6.271014655  4.009548678  3.911901611  4.361352405  4.235537310
[391]  4.102684531  2.944685713  4.191459606  4.217623977  3.429526459
[396]  4.500402827  3.585978538  3.755342058  4.103835110  2.820102501
[401]  5.266435443  4.070531722  3.848838381  4.330324339  4.935227329
[406]  3.742400137  4.180495637  3.951435621  4.150907536  4.156263333
[411]  4.748660558  3.546711798  3.288078356  3.834627890  3.825169567
[416]  1.853981501  3.705998535  3.996366127  3.755184141  3.844866004
[421]  3.970340741  4.561350300  4.242398361  3.568222977  3.361845831
[426]  3.646279703  4.037645951  3.556877998  3.372294457  1.498836959
[431]  2.849918758  5.343651420  5.058357942  4.109660855  5.094395769
[436]  3.475486253  4.246541986  3.936191533  3.852993005  4.838235608
[441]  4.271871576  4.053516135  3.076377183  3.426678226  4.348773940
[446]  4.685705371  3.633173280  3.597811779  3.595177321  3.770334436
[451]  3.552298406  3.514493395  4.716939571  4.367998888  5.112174964
[456]  3.899990440  3.946320223  4.216650509  3.252048492  3.974487818
[461]  3.969761014  3.697487599  4.395858306  3.958289116  4.602924613
[466]  4.588393040  4.091143093  3.877038079  3.710990512  3.949211511
[471]  4.268626399  3.969754275  3.451504501  4.321768155  6.107891563
[476]  3.542491827  4.062430694  3.394998099  2.982810644  4.195101339
[481]  4.294968659  4.108577325  3.640947414  4.702885974  3.869956285
[486]  3.493189938  3.979493100  3.620445289  2.780524892  3.655861300
[491]  4.365676365  2.499430660  3.958001608  2.364520989  3.887902367
[496]  3.830223537  4.428966621  4.110587955  2.970295601  3.968794625
[501]  4.062345774  4.613519254  3.421555009  4.014001453  2.863903171
[506]  5.834915998  4.094762313  5.270320580  5.012342270  3.939629006
[511]  4.199620307  4.139824427  2.156741907  4.065275682  3.163561382
[516]  3.942655925  5.376626351  3.984350833  4.303982556  3.946725594
[521]  4.023730818  5.108036640  3.830191193  3.731829380  3.910495381
[526]  3.956410548  4.274938716  3.666294925  3.394622040  1.533903069
[531]  4.016980161  4.194666750  3.638924121  4.150210972  3.950078818
[536]  3.951942085  3.833598627  5.805862510  3.278504403  3.841485249
[541]  4.750894984  5.382503760  5.275536309  3.739289059  4.446899347
[546]  4.838649324  3.572678148  4.000582928  5.061975255  4.117726002
[551]  4.269530552  4.142813838  4.294208761  3.693567842  3.852576246
[556]  4.419889606  4.430836739  3.515888461  4.374320009  2.932376769
[561]  3.322734476  4.282356730  3.822358283  3.065457672  3.311638176
[566]  3.896543445  3.680941819  4.483782360  5.270047153  4.589333289
[571]  2.990786474  3.114290552  4.658393898  4.414768372  4.512588123
[576]  3.580809437  2.247338844  3.021055158  2.151672855  3.773738819
[581]  4.190825308  3.645317835  1.429363058  4.394157965  5.073349914
[586]  3.996277982  4.020318453  3.520278570  3.893142591  5.371683103
[591]  4.608132245  4.306142993  2.583904773  3.453887574  3.931860049
[596]  4.787138850  3.086445856  4.008146869  4.284092396  4.001405817
[601]  4.270016173  3.789582573  4.681864782  4.991181729  4.021304541
[606]  4.240205890  4.013512436  3.846078465  4.342773130  3.686415399
[611]  4.454023586  4.060225878  4.248962582  3.686479435  4.702712376
[616]  5.268662288  4.419232703  3.755078976  4.458452128  3.496495142
[621]  3.480113817  4.179923955  3.681737604  4.170359001  3.503679035
[626]  4.148669736  3.840179771  3.023903439  3.684905470  3.563638797
[631]  4.767571508  4.115937216  4.349883069  3.891146627  4.298633196
[636]  3.297879563  4.553233278  3.991860710  3.529043147  3.543275159
[641]  4.634175568  4.323781769  4.010416142  3.886059696  4.178193752
[646]  3.251572046  3.955733013  3.994414276  4.133491895  4.592529610
[651]  3.734188101  3.757969107  2.723539648  3.813049036  3.892992049
[656]  3.814920839  3.086025224  3.350960223  4.652129199  4.519063173
[661]  3.647110630  4.603750227  3.807354136  5.296635159  4.397588438
[666]  4.526241077  4.695063927  5.243964421  3.652484393  3.909957926
[671]  5.302215795  3.114906399  2.602306265  3.523642071  4.786327736
[676]  4.066337546  4.301622954  3.989059472  3.892950083  3.860098946
[681]  3.922038670  3.802717523  6.509814494  3.777864264  4.087045106
[686]  2.938724852  4.434773194  3.887370627  3.164854939  5.250482642
[691]  4.580233821  3.752069495  3.797979880  3.639058704  3.733228065
[696]  4.680758225  3.785746391  4.166037672  4.590247318  3.733940091
[701]  3.759224963  4.211911381  4.419093655  4.597666938  4.408936710
[706]  3.172344498  3.921020133  5.701741803  2.456820265  4.225346396
[711]  3.946455175  4.284731129  4.028191250  3.359254863  2.825265462
[716]  5.439300815  3.816846556  2.417261779  3.858311383  3.083120596
[721]  3.850038919  3.819422049  3.754521117  3.853820173  4.665652578
[726]  5.142842646  3.125104658  4.979681511  3.971260665  3.630363195
[731]  2.259195698  3.524987036  4.267398405  5.296235538  4.091104176
[736]  3.189390697  3.663066782  3.991601065  4.238048747  4.317491921
[741]  3.814906657  3.921138563  3.953336591  5.048074913  4.513599708
[746]  4.165376587  2.880214389  4.665344577  2.628875275  4.123011183
[751]  3.651123335  3.701801092  4.330280877  4.046784913  4.061043562
[756]  4.504964871  1.568378503  3.355156457  4.254758089  4.937068789
[761]  5.946031223  5.138086523  3.921512555  3.808372442  4.666614517
[766]  5.516616475  3.862789751  4.465752810  5.350873920  3.664024719
[771]  4.053680914  4.361030347  4.002776411  3.650383099  5.118371849
[776]  2.916354641  4.072946280  3.290923189  4.014977558  3.955574693
[781]  4.208431639  3.346797057  2.703921859  4.579156769  3.684517581
[786]  3.742520856  3.637750576  4.987509480  3.878763579  4.096536871
[791]  4.423644532  0.537257918  3.879898994  4.267691477  4.334790811
[796]  4.043174220  4.402142852  2.828533602  3.957625742  3.957030809
[801]  3.651382877  4.039335485  3.873539721  4.222235429  3.767323570
[806]  4.411147882  2.628329213  4.103877955  4.904170142  4.108702782
[811]  4.235258086  3.979191917  2.968334126  4.199093519  3.848597117
[816]  3.619837787  4.027567490  4.420498983  4.232332269  3.934637484
[821]  3.856718942  4.023409059  2.306079045  4.033725218  4.265541216
[826]  3.487713480  3.835358345  5.541548546  4.643225483  3.750162564
[831]  4.098531176  3.932475492  6.020866307  4.225600872  2.977559051
[836]  4.239425018  4.328935991  2.749858742  3.794588393  4.576616183
[841]  4.282048725  4.361041356  3.012022321  3.083081047  4.217550120
[846]  3.689752847  4.134207416  3.901036655  4.024657246  3.817725619
[851]  2.489113700  3.979679384  4.054518641  4.522207574  3.884732551
[856]  3.027340509  4.876140676  3.237280324  3.668689911  5.526441143
[861]  4.948640036  5.078341545  6.357888574  4.560216328  4.251687845
[866]  3.825253494  4.574048540  4.092779056  4.209964432  3.209967748
[871]  3.808517955  4.020190967  3.477685924  3.483604334  4.199577447
[876]  4.529632212  2.448022597  3.705599135  4.505088966  3.533213306
[881]  3.749425968  3.874596511  3.140120797  4.671662427  3.427227360
[886]  3.707101699  1.614303088  3.859480852  2.935001819  3.921761384
[891]  3.943560470  5.178582400  3.802683644  3.596154414  3.745188995
[896]  3.942965888  4.127093698  2.822968539  3.325810600  4.145477387
[901]  4.881975204  4.247111357  4.139888865  3.466873675  2.705204994
[906]  4.467361208  5.917656290  3.751550021  3.530333213  4.068986089
[911]  4.530697720  3.737439885  3.771678285  4.402283885  1.909224963
[916]  3.719547443  3.689644036  4.274875842  3.946855496  3.757428285
[921]  3.734200300  4.655299420  4.190094387  4.057180632  4.721164451
[926]  4.277126257  5.393281221  3.588921781  4.210413577  5.902008781
[931]  3.443408779  4.021586034  4.551477710  4.252568980  3.960249701
[936]  3.846917303  3.831248597  5.625061426  3.839039322  3.850123352
[941]  3.359958771  4.131512961  2.608709391  2.670366707  3.802017918
[946]  4.410602113  4.538743213  3.439808926  3.693115779  3.946803542
[951]  4.782067834  4.435983476  4.606711503  4.576276137  4.977860269
[956]  3.259543733  3.956455813  4.231484735  6.010825734  3.253073860
[961]  3.682852448  3.612226440  3.982916256  4.392726850  3.125411911
[966]  4.077549939  5.811118285  3.247142030  4.616940250  4.525017532
[971]  4.205230226  4.522834597  4.086266021  4.330896551  3.798172383
[976]  3.996300077  4.087869341  3.556243592  3.455284699  3.719838869
[981]  4.286681062  3.246626374  3.575041153  4.262135137  4.013370916
[986]  3.637054634  3.986059402  3.512000398  3.593201546  3.083742095
[991]  4.458511155  3.719760096  4.466450663  5.019882329  3.439542587
[996]  4.201436746  4.011514316  3.827216434  4.285601483  3.390063472
[1001]  5.152107284  4.287127919  4.730997236  3.991223583  4.514703997
[1006]  4.350803033  3.573183709  4.403465285  3.705971438  3.827884678
[1011]  3.999731868  3.236259257  4.033758728  4.003543589  3.923369895
[1016]  3.500394297  5.199060284  4.995922610  4.231060446  4.665398556
[1021]  3.551052076  4.195587940  4.854547095  4.121295068  4.630959169
[1026]  3.907583624  3.615492406  3.201513499  3.160819468  3.799494577
[1031]  3.987669514  3.615723970  5.230357042  5.160848531  4.094552468
[1036]  3.827223873  3.925579810  3.665340239  4.278961408  4.194696445
[1041]  3.617906016  5.260184369  4.073354058  3.439343810  3.695507795
[1046]  4.125586482  3.885374451  3.134245987  4.436940995  3.336073568
[1051]  4.757482261  3.901729449  3.585599258  4.632700207  5.064601417
[1056]  3.750595347  3.141524556  3.791180200  3.604760042  3.712210745
[1061]  3.687131279  3.889704443  3.826000647  3.346038630  5.138085790
[1066]  3.746414210  3.702224317  2.186583405  2.996588474  4.052529092
[1071]  5.162298852  4.084500735  5.878291200  3.411568479  5.587890292
[1076]  5.543431058  4.056006733  5.097201907  4.086083154  3.929310889
[1081]  3.866000538  2.653128232  3.826125066  6.310313189  4.901058318
[1086]  4.425692148  4.112488180  4.761734181  5.804511103  4.275147036
[1091]  4.167880694  5.492977172  3.877722742  3.670446465  4.253415136
[1096]  3.432581193  3.905522960  4.181678485  4.568491986  4.601110527
[1101]  3.440836099  4.057734902  4.393600190  3.905300648  4.010767800
[1106]  4.506673815  4.127789189  4.120728106  4.012938678  6.365872512
[1111]  4.482559509  4.584212543  3.613059487  4.572350401  3.818931737
[1116]  3.933412529  4.099740809  4.005971188  5.224301034  5.549224367
[1121]  4.125377442  3.802727077  4.383698090  3.999532304  3.264546810
[1126]  3.660543658  3.642038950  3.896655761  3.741765543  3.333315189
[1131]  3.590299976  2.670620044  3.811976572  3.237504813  3.885929828
[1136]  4.727039969  4.415809485  4.407071764  4.659270084  4.112464023
[1141]  4.826484767  4.198158798  4.063429715  3.685025108  1.696498772
[1146]  3.962083626  3.992320545  3.471078182  3.840718479  3.784860026
[1151]  3.196825914  4.335325725  4.636308276  4.768167963  3.899441089
[1156]  4.825497855  4.341346039  3.422127742  4.453452837  3.982749141
[1161]  4.934254918  4.536634341  4.815653034  4.636340172  4.293548791
[1166]  4.141611085  3.548506409  5.307201705  3.697242999  4.036577804
[1171]  5.280496635  4.227982784  4.568048414  4.088471226  3.744998357
[1176]  4.454576723  4.341809324  4.400118637  5.188479763  2.084714643
[1181]  5.780174057  4.391162004  4.081178475  4.218827109  4.558507253
[1186]  4.549480349  4.110935349  4.494579170  4.392466855  4.381381744
[1191]  4.143290428  4.001455622  4.366323038  4.026277429  4.742242875
[1196]  6.913714580  6.732263558  3.509404128  3.660331304  3.193528618
[1201]  4.029171712  4.717297079  4.521118173  4.414060628  3.439394333
[1206]  3.755380345  3.593981382  4.270995783  4.026355559  3.876817389
[1211]  4.000922199  4.276885836  3.620420932  3.941037673  2.738385747
[1216]  3.820643669  5.807005938  3.928778404  3.433660175  1.900918575
[1221]  4.021648861  4.004846652  3.904731284  2.998224506  4.541260316
[1226]  5.512130164  1.824331645  4.142540413  4.616669382  4.190020291
[1231]  3.807823874  3.190585738  3.518578044  3.923839214  3.922084140
[1236]  4.013452095  4.394761665  4.174907006  3.065787238  3.627023446
[1241]  4.084628384  3.762774072  3.573319118  3.774370271  3.745138455
[1246]  3.751817220  3.229717503  3.925855008  4.155306693  3.143387953
[1251]  4.110684702  3.557279474  4.094203866  4.128537382  2.674892097
[1256]  3.143144614  4.108832834  4.174285635  4.989917688  3.946010705
[1261]  4.023263868  3.568393367  3.871370374  4.598960872  3.523031633
[1266]  4.056394331  3.162201257  5.404909849  3.576467932  4.000399075
[1271]  3.800629998  4.060176525  3.736139195  5.707016572  3.176867123
[1276]  3.110167195  3.059004551  3.665553518  2.805233293  3.702974707
[1281]  2.994993738  4.173502994  3.410983617  4.907631258  4.280859521
[1286]  4.005686617  3.646847922  3.527251629  3.772490031  2.380497135
[1291]  4.089569004  3.287022553  4.280336264  3.532569439  4.185058178
[1296]  4.595076740  3.079416922  4.019025611  3.569750667  3.732333851
[1301]  3.111049495  3.952208047  3.821220411  4.313908656  4.576276464
[1306]  3.607500555  3.777496863  3.967757588  4.137680353  4.030144694
[1311]  3.954347966  3.536040803  4.057060823  4.163797694  4.318853005
[1316]  3.983680573  1.821274853  4.551116826  3.460978610  3.886544361
[1321]  2.946895844  4.019386034  3.882395580  3.997092888  2.912008868
[1326]  5.329674915  3.583318241  6.414979735  3.798843555  4.452826289
[1331]  3.193398245  3.817180967  3.706375433  2.364259105  3.856551626
[1336]  4.296503399  3.259357153  4.337660137  3.580331682  3.572675474
[1341]  3.645439241  4.461790363  4.380179626  5.169637286  4.098281271
[1346]  3.969799538  4.125340838  3.869719745  1.538209144  3.518087459
[1351]  4.958567233  4.176200284  4.059872108  4.185672379  3.854471264
[1356]  4.063216978  5.400096465  5.021232475  3.817814534  4.119450742
[1361]  4.100343857  4.102666950  4.117921073  2.701420474  4.089811837
[1366]  3.953964575  3.451354146  3.120032360  3.095602107  4.260024999
[1371]  6.046089369  4.623520323  3.182819593  4.148717509  4.013372846
[1376]  4.731686506  4.051092390  3.923917748  3.767288792  3.143422993
[1381]  3.734558914  3.439463462  3.998758339  3.968295233  4.071960809
[1386]  3.501816089  2.843602660  4.137581785  4.606445223  4.110269538
[1391]  4.132844080  3.626934046  3.384659013  4.203705297  3.390897780
[1396]  4.276986497  2.849647866  4.271336303  3.672944759  3.850141220
[1401]  4.826917093  4.144323489  3.610820038  3.853428437  5.402339319
[1406]  1.920892825  4.014917941  4.247072296  4.086578887  3.860823526
[1411]  2.797756733  3.847285118  4.166460917  4.261636090  3.826063070
[1416]  4.055103614  5.420499802  4.721386724  4.283506553  4.063887029
[1421]  4.154323687  4.682240961  3.521261216  3.878114162  3.878286357
[1426]  3.746705753  4.399329495  4.476058216  4.187487843  3.995641692
[1431]  6.274503315  3.484380335  3.473271883  4.024439084  3.950458483
[1436]  4.231113716  4.259322227  3.924637644  4.000216549  4.258939129
[1441]  4.501960526  4.760441903  5.256198885  5.513933854  5.016582006
[1446]  5.236545348  4.313661063  3.753943092  4.136818320  4.349036880
[1451]  3.690649118  4.878078858  3.021870193  4.395628228  4.004282844
[1456]  4.393117216  4.230637352  4.621284608  3.425998279  3.460154084
[1461]  4.221801829  4.417898696  3.792773587  4.031657394  3.443516883
[1466]  3.826353745  3.671576426  3.658762039  2.917530839  4.261627716
[1471]  4.215427176  3.550219186  3.651027561  4.452077612  4.402177607
[1476]  4.660625149  3.757118467  6.033514234  5.583777193  5.149126156
[1481]  4.343491035  5.417799573  4.051590032  4.727740741  5.274356252
[1486]  4.538180598  3.227944563  4.220689174  4.175228314  4.110952122
[1491]  4.123637221  3.690851213  4.668635611  4.882801963  4.132391234
[1496]  4.104408968  3.193482241  4.528978982  4.440284105  3.073106166
[1501]  4.702344034  3.559712199  4.589327108  3.896444910  3.792735771
[1506]  2.810785021  4.431546721  3.648151767  4.199132733  2.934801708
[1511]  3.688211981  1.810893271  4.072784033  4.127712325  3.948859270
[1516]  4.236477270  2.944935218  3.510482915  4.319888737  3.967619255
[1521]  4.727801680  3.662755308  1.884938618  5.239156607  4.210079198
[1526]  4.550612590  3.748525905  3.569617832  4.396340769  3.606956661
[1531]  4.594108107  3.839268957  3.425847344  4.636426701  5.062929492
[1536]  3.939576317  3.438918691  3.676215761  4.891175047  4.568243705
[1541]  4.031128529  3.071652872  2.516452916  4.199202085  3.894984016
[1546]  4.328767973  3.692001390  5.595554829  4.122469011  4.349833664
[1551]  4.799385522  2.754557031  5.360675323  2.311107885  4.241266089
[1556]  3.505388351  3.845089277  4.250766973  3.656350611  4.200025233
[1561]  4.629475834  4.142823086  3.715254756  5.051337586  4.674659923
[1566]  3.907999284  4.142185642  3.543800774  4.221471046  5.567094078
[1571]  4.735168637  3.627379904  3.795463233  4.606657334  3.930985907
[1576]  6.302975992  4.064926371  3.473480357  3.699809171  3.323147593
[1581]  3.288327853  3.953251212  4.172649481  3.750416317  4.066209128
[1586]  3.752090650  3.958448407  4.301953117  3.606089179  3.710326284
[1591]  3.151898787  3.535292064  4.260981653  4.003296945  4.040696036
[1596]  3.914027585  3.114018658  4.839263651  3.595647534  4.935563819
[1601]  3.610479622  6.542538279  3.233591430  4.200719803  3.976010510
[1606]  4.651413967  3.869518320  4.745656796  4.883921011  4.462001116
[1611]  3.994343112  2.725070453  4.021230819  3.954828615  5.460574968
[1616]  4.501875886  3.721865998  2.901140921  4.157069701  5.430350692
[1621]  4.030075600  4.322986483  3.811124293  3.979338759  2.165390452
[1626]  4.482295325  4.981282548  4.355391076  4.133900078  3.933081958
[1631]  3.505059447  3.214219692  4.437354714  3.711536960  3.594925013
[1636]  3.890747532  4.084572201  4.008766501  5.046080002  2.596223593
[1641]  3.571152556  4.028027336  3.506952903  3.769834072  4.062073042
[1646]  3.162958889  3.590737957  4.373294470  3.807187221  3.573416948
[1651]  3.875457978  2.378386031  4.537623320  4.856918369  5.270468342
[1656]  4.238702341  4.745036673  4.120662573  3.564611469  3.973478696
[1661]  3.905320331  3.824813045  4.280290008  3.688567221  3.058775939
[1666]  4.266239855  3.651812614  3.481195571  4.739391502  3.733461321
[1671]  3.808514310  4.259250147  4.156336521  4.401939689  3.825182856
[1676]  4.001945661  5.229435851  3.492067344  4.208321540  4.341775527
[1681]  3.819373844  4.010520016  4.655677189  2.873784655  4.123920416
[1686]  3.798816436  4.626499997  7.238835542  4.773227522  3.424130012
[1691]  4.025216926  2.881256298  4.155460842  5.458221647  4.818437558
[1696]  5.154768236  3.594468731  4.458039890  4.166566313  3.231389453
[1701]  3.659546738  3.902001799  4.450699138  3.719122596  2.362764362
[1706]  3.919165687  4.593881458  5.269534804  4.079831389  3.429948601
[1711]  4.591668694  4.404462733  3.784599321  4.421218832  4.725494110
[1716]  4.195620917  3.332432639  4.659929054  3.663600118  3.548713262
[1721]  4.212352801  4.503713145  3.542180487  4.215005241  4.058849823
[1726]  3.508658535  3.625440800  2.606502045  4.409616777  4.796653573
[1731]  4.336527650  5.257386838  4.026976575  4.642143478  4.507439774
[1736]  3.772104392  3.401230691  4.043954721  4.149969537  4.355404350
[1741]  5.269685364  3.834366614  2.388532300  4.847129645  3.923938027
[1746]  3.759086330  4.268897100  4.726964903  3.862731078  3.567152428
[1751]  3.244036742  3.266226631  3.635110300  5.852254930  4.064768410
[1756]  3.976750093  4.104911147  3.998062450  3.779903324  4.402949758
[1761]  3.982432977  3.531310326  4.653112346  3.626776058  3.899033846
[1766]  2.868467488  5.411522210  4.484940620  3.919016292  5.156174154
[1771]  4.666572887  3.988550109  4.781336280  4.349447828  5.838671532
[1776]  3.697736020  3.898316598  4.084842227  4.503641216  3.954670254
[1781]  3.455327397  4.226790678  4.584005889  3.742100410  5.360645396
[1786]  3.656602937  4.083020707  3.814380587  4.202357919  3.219189374
[1791]  4.766770598  3.308760383  4.362172050  4.136849772  4.132899722
[1796]  3.267916516  4.047412068  4.389157812  3.984208137  4.366579296
[1801]  3.850751556  4.713986528  5.286156314  3.912734090  2.029033241
[1806]  4.336251035  4.457497928  3.640481518  5.219877436  4.088987168
[1811]  4.255989417  4.122349557  4.645392991  2.317363024  3.580799704
[1816]  4.107364934  3.817874471  3.876550259  4.274649117  4.773066374
[1821]  3.834481844  3.411071208  3.824887812  3.507476204  4.250889968
[1826]  3.715429148  3.617729622  4.115870018  4.250664599  3.552903696
[1831]  3.924571044  4.111195574  5.212300419  3.975617377  3.168390411
[1836]  4.527722033  5.015831071  3.087057250  4.012246212  4.724495272
[1841]  4.453302991  5.113391585  4.039265881  5.280930404  4.629920200
[1846]  4.260867317  4.902527739  4.755910251  5.808058108  5.496561811
[1851]  2.690851832  3.855946743  4.032005406  4.508185348  3.689129357
[1856]  3.160609875  3.998235594  3.674817136  3.218506182  4.885162236
[1861]  3.785357551  3.644890127  6.010037254  4.650825313  4.112176221
[1866]  3.244364033  3.805894869  3.750475344  4.598735179  3.422737541
[1871]  4.614752427  2.488255039  4.094022390  1.852264276  3.769025921
[1876]  4.914173534  4.275416943  3.334579824  4.472581113  3.835743594
[1881]  3.968402638  3.344995165  3.543962403  3.942850848  4.140101422
[1886]  4.275986591  3.427035980  3.774601788  3.520579827  4.619324428
[1891]  3.403825538  4.183566495  3.948805469  3.379228567  4.466265204
[1896]  3.984428401  4.313019015  3.829956280  3.748560094  3.297858629
[1901]  3.929794269  3.903158630  4.216097598  4.555656938  3.813316342
[1906]  2.740105056  4.222348872  5.067544780  4.766877523  3.226018101
[1911]  5.347321310  4.027262120  5.231000396  4.038275683  5.722101372
[1916]  4.459297732  4.065665719  3.806406741  4.821835974  4.287008775
[1921]  4.344662167  4.357595640  3.302946417  3.379445010  4.213472369
[1926]  4.760520190  4.071601499  4.274826403  4.287275186  3.849112213
[1931]  2.837906598  4.421591103  5.011121345  3.797042435  4.154549095
[1936]  3.992319773  4.698501411  4.098860162  3.752013630  2.937002813
[1941]  4.270730628  4.256435810  3.660312139  4.070092807  4.773121020
[1946]  2.127855316  3.761903300  3.739024726  3.238951901  4.011774063
[1951]  4.235763094  2.403982479  4.760077360  3.965941190  3.754069566
[1956]  3.989216587  4.025673236  4.134350367  2.799729427  3.413276177
[1961]  3.892429892  3.369669932  4.823134534  2.982014771  5.869526614
[1966]  3.683298372  5.142549560  4.106206413  5.022158680  3.998016411
[1971]  3.831359801  4.014803604  5.807883884  1.831934111  3.921803838
[1976]  3.983267238  4.028748447  4.032711612  4.625289455  3.180788889
[1981]  3.981594201  4.317534546  4.034412997  3.450388156  3.358939072
[1986]  5.046378796  3.176128613  3.726729392  3.856526320  3.850451161
[1991]  4.462392940 -0.399277114  4.927568357  4.138393124  4.077669856
[1996]  3.868772826  4.760038911  3.979710763  3.706813913  3.992845738
[2001]  4.764962668  4.031715124  3.681485449  3.443589974  3.533968495
[2006]  6.100335428  4.296404504  3.331069152  3.751417971  4.641266381
[2011]  4.189650575  3.374686805  4.030107126  3.206330127  4.641908540
[2016]  3.521714700  4.022784800  3.929941359  4.741466236  3.379302297
[2021]  3.502281132  3.549969629  4.009717086  3.364526483  3.632139667
[2026]  4.243451992  4.216288227  4.824010225  3.836499573  3.689973014
[2031]  3.415023758  1.069112010  3.400276569  4.030618685  4.169271408
[2036]  5.612138554  3.594021598  4.639005719  6.626571410  4.076270857
[2041]  4.235890077  3.692241406  4.315344324  3.751934374  5.053267660
[2046]  3.767443090  3.858726651  3.206983150  3.726736994  3.060295921
[2051]  3.617878335  4.488409788  4.145133580  5.781388644  5.017514764
[2056]  4.140157577  4.314112698  2.486996733  3.819947986  4.237381884
[2061]  2.874541431  3.478079677  6.026515405  2.397856690  3.005679404
[2066]  4.545060287  4.987473717  3.844065283  3.376601563  3.795919476
[2071]  2.852491320  3.636807168  3.759075692  4.168572813  5.059278333
[2076]  4.129918490  3.602058581  3.624122757  3.622592159  2.625104322
[2081]  3.806257245  3.822211310  4.489451642  3.803057326  4.289835244
[2086]  3.559719909  4.163330132  4.853628708  3.148815305  5.331084800
[2091]  4.394467115  3.910548259  3.962248786  1.962663998  3.627880177
[2096]  4.194936221  4.528897141  4.153377580  4.198676913  3.641511107
[2101]  4.182519017  3.333236997  3.842042621  3.803630288  4.097542787
[2106]  4.049841020  2.621667025  3.591177801  4.562327631  3.785569030
[2111]  4.701592984  4.185452376  3.972826363  4.071800921  3.858207653
[2116]  3.098819907  4.292582768  4.094884925  4.356484642  3.907456606
[2121]  3.750815850  4.285463981  4.216475830  4.004806267  4.378064879
[2126]  3.973972183  3.035781400  4.104227777  2.242503915  5.279026196
[2131]  4.046474669  4.024701792  5.013155520  3.535975387  3.964824530
[2136]  4.382507968  5.209490080  4.051933039  4.310798567  3.713690089
[2141]  3.471067625  4.719726979  3.319103928  4.110461839  3.745463149
[2146]  4.269857537  3.276596286  2.959048486  4.190260923  4.132948774
[2151]  4.288106848  4.265306672  3.680423351  4.036981286  3.261971578
[2156]  3.118175893  3.868563269  3.833734741  3.903572633  4.266859217
[2161]  3.383436539  2.725792422  4.694413562  4.362334168  2.467263353
[2166]  3.957804047  4.353080656  4.391399814  4.490616324  4.749604996
[2171]  3.707695447  3.535023363  3.107020776  3.006249193  3.729132900
[2176]  2.992423367  3.097151559  4.383448167  2.631382457  5.800453599
[2181]  3.816840959  4.144535260  4.624300693  4.224871821  4.398491647
[2186]  3.657838528  4.105631898  4.054089364  3.577778186  3.883055186
[2191]  4.984851736  3.387083103  3.340508355  3.226685065  3.581105569
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[2211]  4.345518281  3.891593669  4.401267351  4.019997664  3.068481321
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[2221]  4.046444953  3.815424706  4.005212214  4.105608927  3.713625198
[2226]  3.061117755  3.565617421  1.983356995  4.129780971  3.148738536
[2231]  4.662202288  4.311493444  4.348309099  2.518125003  3.984956227
[2236]  3.508222121  4.118387752  3.916105441  3.616594734  3.488356604
[2241]  4.528759376  3.214296503  4.113151916  2.649703740  3.445541815
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[2251]  3.629075315  4.151247865  2.828748262  4.694882832  4.074121408
[2256]  5.018512720  4.356814678  4.789738442  5.662723031  4.597999092
[2261]  3.903488973  3.497288923  4.371837055  3.626390695  3.712020267
[2266]  3.339915591  4.565439414  3.896307925  4.068754221  4.172040217
[2271]  4.358619076  3.357076380  4.280300068  3.389597491  3.038309037
[2276]  3.665933414  4.861330798  3.306010349  1.741751379  3.618035828
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[2311]  4.933196557  4.099252292  3.648165211  5.866296144  3.234385373
[2316]  4.979122548  4.040074033  3.936825759  3.783270206  2.263198253
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[2331]  3.674620346  3.548746628  4.210475762  4.366061262  3.669827983
[2336]  4.053904758  3.713462715  3.460071484  3.947889168  3.070148368
[2341]  4.075638381  5.146506619  5.117186009  2.647143309  5.549357414
[2346]  4.339424245  4.440173058  3.840777426  4.859304767  4.389756582
[2351]  3.839723259  3.914870141  2.962153203  4.737756334  4.301611578
[2356]  4.954014048  2.381619738  3.583738644  3.870036683  4.197320017
[2361]  3.973667167  3.381503852  3.382738459  4.675319926  4.327493633
[2366]  4.427391172  4.204045587  3.297909735  3.945153709  3.717654663
[2371]  1.725553921  4.198038471  4.373244062  3.583829857  2.892111073
[2376]  3.937123465  3.948675518  3.199492297  4.139557327  5.037656329
[2381]  3.804242791  4.464177580  3.770809624  3.655986598  4.035065425
[2386]  2.887277615  3.718792552  4.865386263  4.201995177  3.768323318
[2391]  3.778692985  4.006706739  4.253959673  3.930584825  5.936587985
[2396]  3.862618492  3.821495386  3.787036950  4.371825031  2.380459949
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[2436]  4.748133429  3.626993423  3.787848035  3.501284226  4.109189510
[2441]  4.955622265  3.727876808  3.974123183  4.133277794  4.376386503
[2446]  4.270796199  4.454143243  3.945567907  3.784248528  5.904180589
[2451]  4.372653014  4.404619304  2.509441183  4.573297406  3.707613565
[2456]  4.027688211  4.008213519  4.286847621  4.436031270  3.240612467
[2461]  4.983275162  3.692060962  4.290034027  2.897559444  4.355276342
[2466]  5.476703167  3.400143701  4.703125145  4.126243231  5.224043273
[2471]  3.854944070  3.650923240  4.211974412  4.739721608  5.448235091
[2476]  4.118265477  3.812843745  4.503528833  4.274777452  5.377852422
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[2491]  3.432773202  3.791891911  3.513077266  3.553656169  3.745846763
[2496]  4.038287848  3.437839154  5.256660321  3.838245826  3.160587081
[2501]  3.672436307  4.139323290  4.139836343  3.801514407  4.436523193
[2506]  3.898156412  3.710317523  2.509825330  4.098008594  3.833657807
[2511]  3.604464576  3.706018299  3.468830188  3.722124531  3.857443987
[2516]  3.800495609  2.532141905  4.004051568  3.956026222  4.593129736
[2521]  3.922839130  3.976735574  4.561352216  4.494189742  4.806739858
[2526]  4.186250068  4.246357481  3.526841680  4.270105172  6.234164515
[2531]  3.921905313  2.996877500  4.482050574  3.782610131  4.709246223
[2536]  4.139981706  5.223700766  4.350333429  3.757124474  4.582326796
[2541]  3.212004159  5.540046669  3.480099498  4.020483753  5.726990379
[2546]  3.668967122  4.319270992  3.678142017  5.688503463  3.972931124
[2551]  4.363981768  5.040871258  6.653773480  4.567373904  3.683302938
[2556]  3.743828446  3.774727616  3.814688877  5.309329762  3.257939370
[2561]  3.988181149  4.130322169  4.709342247  4.768558169  3.624727007
[2566]  5.208188170  3.865980834  2.495270047  3.338200030  4.532434515
[2571]  7.734742632  4.158611068  3.860037151  4.062636563  5.114433273
[2576]  3.996191155  5.364588537  4.002645948  4.184564826  3.130985701
[2581]  4.005270181  4.072671724  3.184557358  3.832389315  4.939314911
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[2591]  3.847590424  4.339600932  3.863489537  3.653670295  4.349517503
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[2651]  4.411483850  4.301685744  4.488076531  2.742331241  4.182699234
[2656]  4.458907783  3.457970655  4.763144180  4.506004225  3.914167456
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[17006]  3.576479961  4.158449713  3.950407739  4.466200323  3.803119479
[17011]  3.928199078  4.629763997  5.789085562  5.110344159  3.932504047
[17016]  4.185173175  3.053119588  3.578090675  4.738452788  3.982186601
[17021]  4.068220292  3.918586108  3.943705596  4.109277081  3.152366134
[17026]  3.708971592  4.658712048  4.273573738