Check files plz
Concordia University Department of Economics ECON 681: Econometric Theory II Assignment 3: Due on 05/04/2023 Winter 2023–20/03/2023 Question 1: (Checking the robustness of quantile estimators) The goal of this question is to investigate the robustness of quantile estimators compare to OLS. We will only consider the quantile estimator with ⌧ = 0.5 (the least absolute deviation estimator). Recall that the LAD estimator in the linear regression model is equivalently defined as: argmin � nX i=1 |yi � x0i�| or argmin � nX i=1 ui(⌧ � I(ui < 0));="" with="" ui="yi" �="" x0i�="" and="" ⌧="0.5." this="" optimization="" program="" can="" be="" done="" using="" the="" fminsearch="" routine="" of="" matlab="" which="" uses="" a="" simplex="" algorithm="" and="" can="" work="" well="" even="" when="" the="" objective="" function="" is="" not="" smooth.="" choose="" large="" values="" for="" ‘maxfunevals’="" and="" ‘maxiter’="" as="" option="" (e.g="" 10000="" and="" 2000,="" respectively).="" also,="" choose="" the="" ols="" (or="" mle,="" gmm)="" estimates="" (whichever="" is="" relevant)="" of="" the="" parameter="" of="" interest="" as="" starting="" value="" for="" the="" search="" algorithm.="" make="" sure="" you="" report="" your="" computation="" codes="" as="" this="" will="" count="" largely="" in="" the="" grade.="" 1.="" generate="" a="" vector="" y="" of="" n="" i.i.d="" variables="" from="" t="" distribution="" with="" ⌫="" degrees="" of="" freedom="" (t(⌫))="" and="" generate="" a="" vector="" x="" of="" n="" i.i.d="" variables="" from="" n(0,="" 1)="" in="" a="" way="" that="" x="" is="" independent="" of="" y="" .="" choose="" n="1000." 2.="" compute="" the="" ols="" estimator="" �̂="" of="" �="(�1,�2)0" from="" the="" regression:="" yi="�1" +="" �2xi="" +="" ui.="" store="" �̂2.="" compute="" the="" lad="" estimator="" �̃="" of="" �="" from="" the="" same="" model="" and="" store="" �̃2.="" 3.="" repeat="" 1.="" and="" 2.="" mc="10000" times.="" what="" is="" the="" true="" parameter="" value="" �20="" of="" �2="" in="" this="" simulation="" exercise?="" calculate="" the="" simulated="" bias="" and="" root-mean-square-error="" (rmse)="" of="" �̂2="" and="" �̃2="" through="" the="" mc="" replications.="" recall="" that="" the="" simulated="" bias="" and="" rmse="" are="" given="" by:="" bias(✓̂)="1" mc="" mcx="" j="1" ✓̂(j)="" �="" ✓0="" and="" rmse(✓̂)="vuut" 1="" mc="" mcx="" j="1" ⇣="" ✓̂(j)="" �="" ✓0="" ⌘2="" ,="" where="" ✓̂(j)="" is="" the="" value="" of="" ✓̂="" obtained="" in="" the="" jth="" replication.="" 4.="" perform="" 3.="" for="" ⌫="1.0," 1.1,="" 1.2,="" 1.3,="" 1.4,="" 1.6,="" 1.8,="" 2.0,="" 5.0,="" and="" 10.0.="" 5.="" report="" the="" results="" and="" comment="" on="" the="" choice="" of="" ols="" and="" lad="" estimators="" as="" well="" as="" the="" robustness="" of="" the="" latter.="" have="" also="" in="" mind="" that="" the="" t(⌫)="" has="" finite="" moments="" only="" up="" to="" ⌫="" �="" 1.="" 1="" question="" 2:="" (empirical="" application)="" use="" the="" data="" set="" in="" the="" file="" 401ksubs="" to="" estimate="" the="" quantile="" regression:="" nettfai="�1" +="" �2inci="" +="" �3agei="" +="" �4age="" 2="" i="" +="" �5e401ki="" +="" ui,="" quantile⌧="" (ui|inci,="" agei,="" e401ki)="0." (use="" the="" fminsearch="" matlab="" routine="" as="" indicated="" in="" the="" previous="" question="" and="" the="" ols="" estimate="" as="" starting="" value.="" make="" sure="" you="" report="" your="" computation="" codes="" as="" this="" will="" count="" largely="" in="" the="" grade.)="" report="" six="" (6)="" columns="" of="" outputs="" containing="" the="" ols="" estimates,="" and="" the="" quantile="" estimates="" of="" �="(�1,�2,�3,�4,�5)0" for="" ⌧="0.1," 0.25,="" 0.5="" (lad),="" 0.75="" and="" 0.9.="" report="" also="" their="" respective="" standard="" errors.="" comment="" your="" results.="" discuss="" in="" particular="" the="" variation="" of="" the="" e↵ect="" of="" the="" co-variates="" on="" the="" conditional="" distribution="" of="" nettfa="" at="" the="" considered="" locations.="" important="" note:="" see="" abadie="" (2003,="" section="" 6)="" for="" more="" background="" on="" the="" 401(k)="" retirement="" savings="" programs="" in="" the="" us="" and="" data="" description.="" question="" 3:="" (simulated="" method="" of="" moments="" (smm),="" gmm="" and="" indirect="" inference="" (ii)="" estimation.)="" assume="" that="" the="" process="" (xt)t="" follows="" the="" dynamics:="" xt="↵+" �xt�1ft="" +="" "t,="" �="" �="" 0,="" (1)="" where="" zt="(ft," "t)0="" ⇠="" nid(0,�2i2)="" and="" zt="" is="" independent="" of="" xs="" for="" all="" s="">< t. our goal is to generate several samples {xt : t = 1, . . . , t} of the process (xt)t and on each sample, we estimate the parameter of interest, ✓ = (↵,�,�2), by smm, gmm and ii and then compare their bias, rmse and mad (mean absolute deviation). for this we first choose a true value ✓0 = (0.2, 0.5, 1.0) for ✓. 1. show that the dynamics of (xt)t in (1) implies that the value of ✓ that governs this dynamics solves the moment condition model: e[g(xt, xt�1, ✓)] = 0 with g(xt, xt�1, ✓) = 0 @ xt � ↵ x2t � ↵2 � �2�2x2t�1 � �2 x2txt�1 � ↵2xt�1 � �2�2x3t�1 � �2xt�1 1 a (2) 2. repeat the following steps mc = 10, 000 times and store the smm, gmm and ii estimators: (a) generate a sample of size t = 200 of (xt)t under ✓0. [indication: set the initial value of xt to 0 and generate a sample of t + 100 observations and then take the last t observations for your sample. this helps to minimize the e↵ect of initial value.] (b) estimate ✓0 by smm by matching to the sample counterparts of the moments: e 0 @ xt x2t x2txt�1 1 a and store the estimates. 2 (c) estimate ✓0 by gmm using the moment condition (2) and store the estimates. (d) estimate ✓0 by ii based on gmm and store the estimates. 3. report the bias, rmse and mad of each estimator component by component. comment. 3 401ksubs 013.17004014.57501173.44891600 161.2301351154103749.1131225 012.85810442000165.32821936 098.881144221.8009777.2541936 022.6140053118.4500511.3932809 015106030002253600 037.155104953.483011380.4942401 031.89610385-2.1001017.3551444 047.295105225.29012236.8172704 129.10145129.601846.812025 023.45710613000550.23093721 031.7851040618.149001010.2861600 034.941104830.695001220.8742304 024.432106020.200596.92263600 025.13110435-4.2500631.56721849 019.07401431000363.81741849 138.772104724.15101503.2682209 112.4810272-1000155.7504729 145.3910572122.5012060.2523249 039.861103521.6011588.8991225 1102.61053540.9991110526.762809 039.5791036412.175001566.4971296 040.194104038.3011615.5581600 025.254013119.68701637.7645961 010.8004820.500116.642304 027014210.13007291764 017.85610425-15.49500318.83681764 138.94103520.2101516.3231225 012.2401322-2.501149.81761024 018004620013242116 121.45600251-21.0210460.3599625 014.025103951.400196.70061521 015.18611364-5.19201230.61461296 141.415103455.8111715.2021156 012.96600522-4.2500168.11712704 058.81041263.7013457.441681 163.849104455.899104076.6951936 147.10161259.8102218.413721 036.0721063372.225011301.1893969 1107.6410512691111586.372601 158.921049419.679003471.5662401 148.61510364-2.7002363.4181296 029.205103460.26800852.9321156 024.44100362200597.36251296 018.52510285-1.9800343.1756784 015.3610384-0.9500235.92961444 053.475105420.33002859.5752916 131.056104765.6410964.47512209 036.072104650001301.1892116 119.164105120.89900367.25892601 044.3760148124.999001969.2292304 028.3290054226.5301802.53232916 137.38014812.999001397.2652304 017.817014211.700317.44551764 171.02810602257.6115044.9773600 028.476005812701810.88263364 034.04110302-4001158.79900 025.860026110.500668.7396676 177.3551033430.9115983.7961089 015.414005040.14500237.59142500 073.9021044414.299005461.5061936 110.545012511.03110111.197625 024.17701251-1.30100584.5273625 133.42004628.412101116.8962116 053.22610518-1.2002833.0072601 031.869013611.6011015.6331296 026.94600642-3.800726.08694096 190.7261062213.6118231.2073844 028.8103180.100829.4399961 023.19310377-1.88600537.91531369 136.0360164118.25101298.5934096 056.082102829.8003145.191784 016.032012521.9300257.025625 152.23610386-3002728.61444 039.63104130.225001570.5371681 134.471050527.798101188.1812500 031.54810566-24.800995.27633136 131.210282-72.800973.4401784 119.8061039425.5710392.27761521 174.5291042417.95105554.5721764 126.682104353.610711.92911849 033.7501251-3001139.063625 1146.57710435778.6281121484.821849 023.7180032114.29901562.54351024 119.30200311-3.400372.5672961 029.41053227.9601864.362809 016.97700352-1.02500288.21851225 019.73410497-1.300389.43072401 014.2810434-0.500203.91841849 030.075104734.23201904.50572209 02710463-3.3007292116 133.9610361310.2101153.2811296 064.5104735.9004160.252209 024.0300312-400577.4409961 021.111006412.500445.67434096 051.7980038241.999002683.0331444 117.36410272-37.50410301.5085729 019.25400281-1.100370.7165784 027.603103547.55900761.92571225 031.4401331-100988.47361089 030.24004530.9200914.45762025 016.83012810.7400283.2489784 130.23110344-0.0310913.91341156 035.4013322.475001253.161089 146.1551055553.948112130.2843025 027.3310504-2.600746.92892500 124.678004430.58300609.00371936 136.0271159220.249101297.9453481 013.5900324000184.68811024 015.741004920.0500247.77912401 027.465105241.100754.32622704 054.9631055253.699003020.9313025 018.549106321900344.06543969 121.5760139114.511465.52381521 038.7610473-0.5001502.3382209 164.6621062219.444114181.1753844 143.158104628101862.6132116 017.8800433-3.15100319.69441849 123.71053213.210561.69012809 037.75510562-1.2001425.443136 140.97111293-9.968101678.623841 013.428102827.17900180.3112784 192.9911048583.9118647.3252304 035.0611041322001229.2741681 017.136013430.01500293.64251156 016.956104720.82600287.50592209 156.71063294.399113214.893969 070.27510414-2.157004938.5761681 013.464002720.400181.2793729 074.64910394-8.005005572.4741521 024.01200413-9.45600576.57611681 020.559003032.900422.6725900 039.52811552-15.718011562.4633025 039.30300341-12.188001544.7261156 017.715013114.0500313.8212961 155.081054244.043103033.8072916 120.76015517.95500430.97763025 014.283014010.02800204.00411600 020.43610314-0.200417.6301961 026.388102640.86600696.3266676 046.104103934.35002125.5791521 149.711042327.097012471.0841764 176.8061052280.049105899.1622704 139.7051039471.569011576.4871521 011.2200303000125.8884900 018.348005040.300336.64912500 013.9500496000194.60252401 015.2161032100.200231.52661024 036.1510324-2.2001306.8231024 047.3401272-10.43002241.076729 063.2251040610.571013997.41600 126.031004920.500677.6132401 020.410365000416.161296 017.92800363000321.41321296 131.81038512.51101011.241444 03011422-15.1009001764 026.4630043110.01101700.29031849 173.722104253.2105434.9331764 033.41410324-4.7001116.4951024 134.08103565.1001161.4471225 148.90061128.08112391.213721 12101411-2.347004411681 139.6091059248.684011568.8733481 180.8510455132.425116536.7222025 191.76110354-3.45008420.0811225 046.719104154002182.6651681 019.201251000368.64625 1102.7051035256.61010548.321225 054.966103331.4003021.2611089 012.7501382000162.56251444 152.8361050237.65102791.6432500 012.7210323000161.79841024 126.6460028162.67910710.0093784 059.6641044511.4013559.7931936 039.1510582189.4011532.7233364 021.310476-0.98600453.692209 030.870048310.9501952.9572304 016.5105722300272.253249 032.59210574-2.1001062.2383249 027.345103450.40900747.7491156 035.41810575-5.75001254.4353249 024.3004510.0500590.492025 152.365104626002742.0942116 026.86511294-1.94500721.7282841 039.481035340.2011558.671225 145.6931040218.576112087.851600 039.310425-4.9001544.491764 014.2440060112001202.89163600 043.51810273-7.5001893.816729 010.857012711.04600117.8745729 051.222003331.6002623.6931089 034.764116323001208.5363969 016.95910437-0.500287.60771849 023.6410265-6.00100558.8495676 156.3041045429.4103170.1412025 1107.0971054247.9220011469.772916 146.818103941.8112191.9251521 013.1100303000171.8721900 029.16003634.24500850.30561296 142.541052230.1101809.6522704 074.3110496-5.5005521.9762401 027.72910316-4.8800768.8975961 0150042349.538002251764 154.7231057221.948102994.6073249 061.5811044461.366013792.221936 172.031043221.998015188.3211849 137.33810487-18.89011394.1262304 027.354003932.601748.24131521 192.8980127130.957118630.039729 042.94210334-2.205001844.0161089 131.017103151.20901962.0543961 123.892003515.24910570.82771225 144.461039238.307111976.6921521 033.7211302-2.552001137.038900 052.821103753.3012790.0581369 186.41043445.1017464.961849 014.76310314-5.00700217.9462961 1107.30110503371.9011111513.52500 020.38500271-0.800415.5482729 141.52610352-1.5001724.4091225 027.37510414-1.200749.39061681 024.33610424-0.300592.24091764 134.42510404-6.46101185.0811600 043.1311045259.16011860.2832025 157.06310544138.999113256.1862916 141.5350130183.7011725.156900 061.72211323-2.48003809.6051024 099.1531043280.802019831.3171849 037.29610283-2001390.992784 127.060038337.110732.24361444 032.4600261-4.49001053.651676 128.491014634.0210811.73712116 119.59601412-1.210384.00321681 118.54003750.96410343.73161369 1102.43510542139.6291110492.932916 026.7103944600712.891521 143.7880043346.85111917.3891849 145.871047238.8112104.0572209 038.8801612-17.7001511.6553721 017.706004333.39900313.50241849 021.6300632-0.7400467.85693969 143.4371036312.818111886.7731296 157.15103442.2103266.1231156 122.9020151161.74911524.50162601 040.74104253.6011659.7481764 013.18210324-2.37300173.76511024 011.61004410.0500134.79211936 1108.5881062284.1960011791.353844 129.772105321.19800886.37192809 167.321045336.199104531.9822025 146.2361057322.398012137.7683249 032.589103141.3001062.043961 060.4981040210.05013660.0081600 030.21013023.101912.644900 155.1251035423.969113038.7661225 156.67610562-6.239003212.1693136 170.84510572200115019.0143249 046.8150044330.902012191.6441936 114.4300271-4.500208.2249729 158.1731031222.45003384.098961 150.6460040245.584112565.0171600 012.20701321-0.84300149.01081024 062.5261052269.1013909.5012704 144.70311325-14001998.3581024 085.3810254-30.24007289.744625 034.647013514.999001200.4151225 127.78611413-0.00100772.06181681 154.451063294.599112964.8023969 119.638015218.510385.65112704 133.3120036277.2101109.6891296 024.534102535.1500601.9172625 018.36012810.01500337.0896784 028.7401271-1.200825.9876729 036.16810253-1.501001308.124625 017.01104734.1500289.34012209 017.41200393000303.17781521 032.427103720.1001051.511369 038.058012815.2001448.411784 158.3171046336.5013400.8732116 015.8221026211.400250.3357676 043.27510262-3.073001872.726676 017.44510344-700304.3281156 121.639104240.24900468.24631764 048.0330061232.055012307.1693721 049.081054245.7012408.8472916 135.292016113001245.5253721 028.575002711.24900816.5306729 033.3660143112.599001113.291849 135.4720151260.398101258.2632601 042.9311353-18.88001842.9851225 017.581032212.201309.05641024 077.011036426015930.5411296 037.662103711-2.382001418.4261369 120.4310571-1.9410417.38493249 027.8400402000775.06561600 049.80600371110.103012480.6381369 024.67810343-0.31200609.00371156 015.8111603-3.200249.95613600 117.6281027412.3410310.7464729 020.40610374-10.51501416.40481369 037.64411443-6.656001417.0711936 089.17511433-0.2007952.1811849 030.16511563-0.10100909.92733136 027.29400342-2.500744.96251156 034.5090139113.3001190.8711521 028.71610304-19.17500824.6086900 115013812.85102251444 129.325103345.51310859.95571089 056.9131139335.883013239.0891521 151.0511029416.6102606.204841 1169.210492484.1981128628.642401 025.70400491-0.36900660.69562401 025.80037113.501665.641369 1110.9851036410.81012317.671296 035.62510345-8001269.1411156 045.7621039416.069012094.1611521 146.911105649.02012200.6423136 015.906002640.100253.0008676 150.4331029214.126102543.487841 153.844104444.73012899.1771936 028.356102624.59100804.0628676 150.4013925.8102540.161521 133.150043224.68101098.9231849 016.48810276-1.42200271.8542729 041.775015019.499011745.1512500 136.14710344-0.071111306.6061156 034.95004130.5001221.5031681 131.00501271000961.31729 148.528104633.22002354.9672116 034.6811454-57001202.7022025 012.600421-9.5500158.761764 020.0711522-400402.80492704 038.319103130.09001468.346961 020.73102841.900429.7329784 028.2480131115.1500797.9495961 031.0980055120.29900967.08563025 124.996014411.400624.81936 022.338012610.89200498.9862676 086.79112741.4007532.504729 014.65500273000214.769729 116.22400426-1.500263.21821764 025.18500591237.9501634.28423481 024014010005761600 048.027013911.9012306.5931521 017.400351-10.100302.761225 018.7510357000351.56251225 130.5760031113.510934.8918961 191.7761142512108422.8341764 017.8501251000318.6225625 129.31005414.800859.0762916 166.8521042310.901104469.1891764 123.07003012.1610532.2249900 166.1511284-1.29104375.823784 181.71110545249.6116676.6882916 031.5871054222.99800997.73862916 164.8780133127.343104209.1551089 036.0600281-5001300.324784 033.610392-9001128.961521 060.0310395-3.3003603.6011521 060.22501371-15.8003627.0511369 165.71043553.948104316.491849 132.490061320.6101055.63721 0109.60811334-90012013.911089 197.8871044460.196119581.8651936 150.2680141120.1102526.8721681 055.51063255013080.253969 150.484103648.6002548.6341296 070.905104161005027.5191681 016.140135112.99900260.49961225 017.96700304-200322.813900 124.48104433.410599.27041936 025.00510603-1.82900625.253600 031.4710312-0.7501990.3608961 026.6100251-5.800708.0921625 022.01110317-1.900484.4841961 042.4591037548.599001802.7671369 0271048547.5007292304 0101.9491053332.50110393.62809 022.741155715.99900517.10763025 020.58106322.99900423.53643969 196.86410423-9.38109382.6341764 047.40300463-0.301002247.0442116 011.09410513-0.300123.07682601 151.0511055262102606.2043025 134.7431056436.5111207.0763136 054.621003745.3012983.4531369 047.38510366-0.9002245.3381296 046.746105130.899002185.1882601 0103.4550144168.2480010702.941936 124.21104465.5910586.12411936 034.8910445-1.184001217.3121936 063.4321026223.397014023.618676 044.26810443-2001959.6561936 044.50810273-4.199001980.962729 126.191050263.24901685.91612500 038.949106020.599001517.0253600 012.87013112.800165.6369961 117.4840057327.99910305.69023249 036.87310292-4.9001359 t.="" our="" goal="" is="" to="" generate="" several="" samples="" {xt="" :="" t="1," .="" .="" .="" ,="" t}="" of="" the="" process="" (xt)t="" and="" on="" each="" sample,="" we="" estimate="" the="" parameter="" of="" interest,="" ✓="(↵,�,�2)," by="" smm,="" gmm="" and="" ii="" and="" then="" compare="" their="" bias,="" rmse="" and="" mad="" (mean="" absolute="" deviation).="" for="" this="" we="" first="" choose="" a="" true="" value="" ✓0="(0.2," 0.5,="" 1.0)="" for="" ✓.="" 1.="" show="" that="" the="" dynamics="" of="" (xt)t="" in="" (1)="" implies="" that="" the="" value="" of="" ✓="" that="" governs="" this="" dynamics="" solves="" the="" moment="" condition="" model:="" e[g(xt,="" xt�1,="" ✓)]="0" with="" g(xt,="" xt�1,="" ✓)="0" @="" xt="" �="" ↵="" x2t="" �="" ↵2="" �="" �2�2x2t�1="" �="" �2="" x2txt�1="" �="" ↵2xt�1="" �="" �2�2x3t�1="" �="" �2xt�1="" 1="" a="" (2)="" 2.="" repeat="" the="" following="" steps="" mc="10," 000="" times="" and="" store="" the="" smm,="" gmm="" and="" ii="" estimators:="" (a)="" generate="" a="" sample="" of="" size="" t="200" of="" (xt)t="" under="" ✓0.="" [indication:="" set="" the="" initial="" value="" of="" xt="" to="" 0="" and="" generate="" a="" sample="" of="" t="" +="" 100="" observations="" and="" then="" take="" the="" last="" t="" observations="" for="" your="" sample.="" this="" helps="" to="" minimize="" the="" e↵ect="" of="" initial="" value.]="" (b)="" estimate="" ✓0="" by="" smm="" by="" matching="" to="" the="" sample="" counterparts="" of="" the="" moments:="" e="" 0="" @="" xt="" x2t="" x2txt�1="" 1="" a="" and="" store="" the="" estimates.="" 2="" (c)="" estimate="" ✓0="" by="" gmm="" using="" the="" moment="" condition="" (2)="" and="" store="" the="" estimates.="" (d)="" estimate="" ✓0="" by="" ii="" based="" on="" gmm="" and="" store="" the="" estimates.="" 3.="" report="" the="" bias,="" rmse="" and="" mad="" of="" each="" estimator="" component="" by="" component.="" comment.="" 3="" 401ksubs="" 0="" 13.17="" 0="" 0="" 40="" 1="" 4.575="" 0="" 1="" 173.4489="" 1600="" 1="" 61.23="" 0="" 1="" 35="" 1="" 154="" 1="" 0="" 3749.113="" 1225="" 0="" 12.858="" 1="" 0="" 44="" 2="" 0="" 0="" 0="" 165.3282="" 1936="" 0="" 98.88="" 1="" 1="" 44="" 2="" 21.8="" 0="" 0="" 9777.254="" 1936="" 0="" 22.614="" 0="" 0="" 53="" 1="" 18.45="" 0="" 0="" 511.393="" 2809="" 0="" 15="" 1="" 0="" 60="" 3="" 0="" 0="" 0="" 225="" 3600="" 0="" 37.155="" 1="" 0="" 49="" 5="" 3.483="" 0="" 1="" 1380.494="" 2401="" 0="" 31.896="" 1="" 0="" 38="" 5="" -2.1="" 0="" 0="" 1017.355="" 1444="" 0="" 47.295="" 1="" 0="" 52="" 2="" 5.29="" 0="" 1="" 2236.817="" 2704="" 1="" 29.1="" 0="" 1="" 45="" 1="" 29.6="" 0="" 1="" 846.81="" 2025="" 0="" 23.457="" 1="" 0="" 61="" 3="" 0="" 0="" 0="" 550.2309="" 3721="" 0="" 31.785="" 1="" 0="" 40="" 6="" 18.149="" 0="" 0="" 1010.286="" 1600="" 0="" 34.941="" 1="" 0="" 48="" 3="" 0.695="" 0="" 0="" 1220.874="" 2304="" 0="" 24.432="" 1="" 0="" 60="" 2="" 0.2="" 0="" 0="" 596.9226="" 3600="" 0="" 25.131="" 1="" 0="" 43="" 5="" -4.25="" 0="" 0="" 631.5672="" 1849="" 0="" 19.074="" 0="" 1="" 43="" 1="" 0="" 0="" 0="" 363.8174="" 1849="" 1="" 38.772="" 1="" 0="" 47="" 2="" 4.15="" 1="" 0="" 1503.268="" 2209="" 1="" 12.48="" 1="" 0="" 27="" 2="" -10="" 0="" 0="" 155.7504="" 729="" 1="" 45.39="" 1="" 0="" 57="" 2="" 122.5="" 0="" 1="" 2060.252="" 3249="" 0="" 39.861="" 1="" 0="" 35="" 2="" 1.6="" 0="" 1="" 1588.899="" 1225="" 1="" 102.6="" 1="" 0="" 53="" 5="" 40.999="" 1="" 1="" 10526.76="" 2809="" 0="" 39.579="" 1="" 0="" 36="" 4="" 12.175="" 0="" 0="" 1566.497="" 1296="" 0="" 40.194="" 1="" 0="" 40="" 3="" 8.3="" 0="" 1="" 1615.558="" 1600="" 0="" 25.254="" 0="" 1="" 31="" 1="" 9.687="" 0="" 1="" 637.7645="" 961="" 0="" 10.8="" 0="" 0="" 48="" 2="" 0.5="" 0="" 0="" 116.64="" 2304="" 0="" 27="" 0="" 1="" 42="" 1="" 0.13="" 0="" 0="" 729="" 1764="" 0="" 17.856="" 1="" 0="" 42="" 5="" -15.495="" 0="" 0="" 318.8368="" 1764="" 1="" 38.94="" 1="" 0="" 35="" 2="" 0.2="" 1="" 0="" 1516.323="" 1225="" 0="" 12.24="" 0="" 1="" 32="" 2="" -2.5="" 0="" 1="" 149.8176="" 1024="" 0="" 18="" 0="" 0="" 46="" 2="" 0="" 0="" 1="" 324="" 2116="" 1="" 21.456="" 0="" 0="" 25="" 1="" -21.02="" 1="" 0="" 460.3599="" 625="" 0="" 14.025="" 1="" 0="" 39="" 5="" 1.4="" 0="" 0="" 196.7006="" 1521="" 0="" 15.186="" 1="" 1="" 36="" 4="" -5.192="" 0="" 1="" 230.6146="" 1296="" 1="" 41.415="" 1="" 0="" 34="" 5="" 5.8="" 1="" 1="" 1715.202="" 1156="" 0="" 12.966="" 0="" 0="" 52="" 2="" -4.25="" 0="" 0="" 168.1171="" 2704="" 0="" 58.8="" 1="" 0="" 41="" 2="" 63.7="" 0="" 1="" 3457.44="" 1681="" 1="" 63.849="" 1="" 0="" 44="" 5="" 5.899="" 1="" 0="" 4076.695="" 1936="" 1="" 47.1="" 0="" 1="" 61="" 2="" 59.8="" 1="" 0="" 2218.41="" 3721="" 0="" 36.072="" 1="" 0="" 63="" 3="" 72.225="" 0="" 1="" 1301.189="" 3969="" 1="" 107.64="" 1="" 0="" 51="" 2="" 69="" 1="" 1="" 11586.37="" 2601="" 1="" 58.92="" 1="" 0="" 49="" 4="" 19.679="" 0="" 0="" 3471.566="" 2401="" 1="" 48.615="" 1="" 0="" 36="" 4="" -2.7="" 0="" 0="" 2363.418="" 1296="" 0="" 29.205="" 1="" 0="" 34="" 6="" 0.268="" 0="" 0="" 852.932="" 1156="" 0="" 24.441="" 0="" 0="" 36="" 2="" 2="" 0="" 0="" 597.3625="" 1296="" 0="" 18.525="" 1="" 0="" 28="" 5="" -1.98="" 0="" 0="" 343.1756="" 784="" 0="" 15.36="" 1="" 0="" 38="" 4="" -0.95="" 0="" 0="" 235.9296="" 1444="" 0="" 53.475="" 1="" 0="" 54="" 2="" 0.33="" 0="" 0="" 2859.575="" 2916="" 1="" 31.056="" 1="" 0="" 47="" 6="" 5.64="" 1="" 0="" 964.4751="" 2209="" 0="" 36.072="" 1="" 0="" 46="" 5="" 0="" 0="" 0="" 1301.189="" 2116="" 1="" 19.164="" 1="" 0="" 51="" 2="" 0.899="" 0="" 0="" 367.2589="" 2601="" 0="" 44.376="" 0="" 1="" 48="" 1="" 24.999="" 0="" 0="" 1969.229="" 2304="" 0="" 28.329="" 0="" 0="" 54="" 2="" 26.53="" 0="" 1="" 802.5323="" 2916="" 1="" 37.38="" 0="" 1="" 48="" 1="" 2.999="" 0="" 0="" 1397.265="" 2304="" 0="" 17.817="" 0="" 1="" 42="" 1="" 1.7="" 0="" 0="" 317.4455="" 1764="" 1="" 71.028="" 1="" 0="" 60="" 2="" 257.6="" 1="" 1="" 5044.977="" 3600="" 0="" 28.476="" 0="" 0="" 58="" 1="" 27="" 0="" 1="" 810.8826="" 3364="" 0="" 34.041="" 1="" 0="" 30="" 2="" -4="" 0="" 0="" 1158.79="" 900="" 0="" 25.86="" 0="" 0="" 26="" 1="" 10.5="" 0="" 0="" 668.7396="" 676="" 1="" 77.355="" 1="" 0="" 33="" 4="" 30.9="" 1="" 1="" 5983.796="" 1089="" 0="" 15.414="" 0="" 0="" 50="" 4="" 0.145="" 0="" 0="" 237.5914="" 2500="" 0="" 73.902="" 1="" 0="" 44="" 4="" 14.299="" 0="" 0="" 5461.506="" 1936="" 1="" 10.545="" 0="" 1="" 25="" 1="" 1.031="" 1="" 0="" 111.197="" 625="" 0="" 24.177="" 0="" 1="" 25="" 1="" -1.301="" 0="" 0="" 584.5273="" 625="" 1="" 33.42="" 0="" 0="" 46="" 2="" 8.412="" 1="" 0="" 1116.896="" 2116="" 0="" 53.226="" 1="" 0="" 51="" 8="" -1.2="" 0="" 0="" 2833.007="" 2601="" 0="" 31.869="" 0="" 1="" 36="" 1="" 1.6="" 0="" 1="" 1015.633="" 1296="" 0="" 26.946="" 0="" 0="" 64="" 2="" -3.8="" 0="" 0="" 726.0869="" 4096="" 1="" 90.726="" 1="" 0="" 62="" 2="" 13.6="" 1="" 1="" 8231.207="" 3844="" 0="" 28.8="" 1="" 0="" 31="" 8="" 0.1="" 0="" 0="" 829.4399="" 961="" 0="" 23.193="" 1="" 0="" 37="" 7="" -1.886="" 0="" 0="" 537.9153="" 1369="" 1="" 36.036="" 0="" 1="" 64="" 1="" 18.25="" 1="" 0="" 1298.593="" 4096="" 0="" 56.082="" 1="" 0="" 28="" 2="" 9.8="" 0="" 0="" 3145.191="" 784="" 0="" 16.032="" 0="" 1="" 25="" 2="" 1.93="" 0="" 0="" 257.025="" 625="" 1="" 52.236="" 1="" 0="" 38="" 6="" -3="" 0="" 0="" 2728.6="" 1444="" 0="" 39.63="" 1="" 0="" 41="" 3="" 0.225="" 0="" 0="" 1570.537="" 1681="" 1="" 34.47="" 1="" 0="" 50="" 5="" 27.798="" 1="" 0="" 1188.181="" 2500="" 0="" 31.548="" 1="" 0="" 56="" 6="" -24.8="" 0="" 0="" 995.2763="" 3136="" 1="" 31.2="" 1="" 0="" 28="" 2="" -72.8="" 0="" 0="" 973.4401="" 784="" 1="" 19.806="" 1="" 0="" 39="" 4="" 25.57="" 1="" 0="" 392.2776="" 1521="" 1="" 74.529="" 1="" 0="" 42="" 4="" 17.95="" 1="" 0="" 5554.572="" 1764="" 1="" 26.682="" 1="" 0="" 43="" 5="" 3.6="" 1="" 0="" 711.9291="" 1849="" 0="" 33.75="" 0="" 1="" 25="" 1="" -3="" 0="" 0="" 1139.063="" 625="" 1="" 146.577="" 1="" 0="" 43="" 5="" 778.628="" 1="" 1="" 21484.82="" 1849="" 0="" 23.718="" 0="" 0="" 32="" 1="" 14.299="" 0="" 1="" 562.5435="" 1024="" 1="" 19.302="" 0="" 0="" 31="" 1="" -3.4="" 0="" 0="" 372.5672="" 961="" 0="" 29.4="" 1="" 0="" 53="" 2="" 27.96="" 0="" 1="" 864.36="" 2809="" 0="" 16.977="" 0="" 0="" 35="" 2="" -1.025="" 0="" 0="" 288.2185="" 1225="" 0="" 19.734="" 1="" 0="" 49="" 7="" -1.3="" 0="" 0="" 389.4307="" 2401="" 0="" 14.28="" 1="" 0="" 43="" 4="" -0.5="" 0="" 0="" 203.9184="" 1849="" 0="" 30.075="" 1="" 0="" 47="" 3="" 4.232="" 0="" 1="" 904.5057="" 2209="" 0="" 27="" 1="" 0="" 46="" 3="" -3.3="" 0="" 0="" 729="" 2116="" 1="" 33.96="" 1="" 0="" 36="" 13="" 10.2="" 1="" 0="" 1153.281="" 1296="" 0="" 64.5="" 1="" 0="" 47="" 3="" 5.9="" 0="" 0="" 4160.25="" 2209="" 0="" 24.03="" 0="" 0="" 31="" 2="" -4="" 0="" 0="" 577.4409="" 961="" 0="" 21.111="" 0="" 0="" 64="" 1="" 2.5="" 0="" 0="" 445.6743="" 4096="" 0="" 51.798="" 0="" 0="" 38="" 2="" 41.999="" 0="" 0="" 2683.033="" 1444="" 1="" 17.364="" 1="" 0="" 27="" 2="" -37.504="" 1="" 0="" 301.5085="" 729="" 0="" 19.254="" 0="" 0="" 28="" 1="" -1.1="" 0="" 0="" 370.7165="" 784="" 0="" 27.603="" 1="" 0="" 35="" 4="" 7.559="" 0="" 0="" 761.9257="" 1225="" 0="" 31.44="" 0="" 1="" 33="" 1="" -1="" 0="" 0="" 988.4736="" 1089="" 0="" 30.24="" 0="" 0="" 45="" 3="" 0.92="" 0="" 0="" 914.4576="" 2025="" 0="" 16.83="" 0="" 1="" 28="" 1="" 0.74="" 0="" 0="" 283.2489="" 784="" 1="" 30.231="" 1="" 0="" 34="" 4="" -0.03="" 1="" 0="" 913.9134="" 1156="" 0="" 35.4="" 0="" 1="" 33="" 2="" 2.475="" 0="" 0="" 1253.16="" 1089="" 1="" 46.155="" 1="" 0="" 55="" 5="" 53.948="" 1="" 1="" 2130.284="" 3025="" 0="" 27.33="" 1="" 0="" 50="" 4="" -2.6="" 0="" 0="" 746.9289="" 2500="" 1="" 24.678="" 0="" 0="" 44="" 3="" 0.583="" 0="" 0="" 609.0037="" 1936="" 1="" 36.027="" 1="" 1="" 59="" 2="" 20.249="" 1="" 0="" 1297.945="" 3481="" 0="" 13.59="" 0="" 0="" 32="" 4="" 0="" 0="" 0="" 184.6881="" 1024="" 0="" 15.741="" 0="" 0="" 49="" 2="" 0.05="" 0="" 0="" 247.7791="" 2401="" 0="" 27.465="" 1="" 0="" 52="" 4="" 1.1="" 0="" 0="" 754.3262="" 2704="" 0="" 54.963="" 1="" 0="" 55="" 2="" 53.699="" 0="" 0="" 3020.931="" 3025="" 0="" 18.549="" 1="" 0="" 63="" 2="" 19="" 0="" 0="" 344.0654="" 3969="" 1="" 21.576="" 0="" 1="" 39="" 1="" 14.5="" 1="" 1="" 465.5238="" 1521="" 0="" 38.76="" 1="" 0="" 47="" 3="" -0.5="" 0="" 0="" 1502.338="" 2209="" 1="" 64.662="" 1="" 0="" 62="" 2="" 19.444="" 1="" 1="" 4181.175="" 3844="" 1="" 43.158="" 1="" 0="" 46="" 2="" 8="" 1="" 0="" 1862.613="" 2116="" 0="" 17.88="" 0="" 0="" 43="" 3="" -3.151="" 0="" 0="" 319.6944="" 1849="" 1="" 23.7="" 1="" 0="" 53="" 2="" 13.2="" 1="" 0="" 561.6901="" 2809="" 0="" 37.755="" 1="" 0="" 56="" 2="" -1.2="" 0="" 0="" 1425.44="" 3136="" 1="" 40.971="" 1="" 1="" 29="" 3="" -9.968="" 1="" 0="" 1678.623="" 841="" 0="" 13.428="" 1="" 0="" 28="" 2="" 7.179="" 0="" 0="" 180.3112="" 784="" 1="" 92.991="" 1="" 0="" 48="" 5="" 83.9="" 1="" 1="" 8647.325="" 2304="" 0="" 35.061="" 1="" 0="" 41="" 3="" 22="" 0="" 0="" 1229.274="" 1681="" 0="" 17.136="" 0="" 1="" 34="" 3="" 0.015="" 0="" 0="" 293.6425="" 1156="" 0="" 16.956="" 1="" 0="" 47="" 2="" 0.826="" 0="" 0="" 287.5059="" 2209="" 1="" 56.7="" 1="" 0="" 63="" 2="" 94.399="" 1="" 1="" 3214.89="" 3969="" 0="" 70.275="" 1="" 0="" 41="" 4="" -2.157="" 0="" 0="" 4938.576="" 1681="" 0="" 13.464="" 0="" 0="" 27="" 2="" 0.4="" 0="" 0="" 181.2793="" 729="" 0="" 74.649="" 1="" 0="" 39="" 4="" -8.005="" 0="" 0="" 5572.474="" 1521="" 0="" 24.012="" 0="" 0="" 41="" 3="" -9.456="" 0="" 0="" 576.5761="" 1681="" 0="" 20.559="" 0="" 0="" 30="" 3="" 2.9="" 0="" 0="" 422.6725="" 900="" 0="" 39.528="" 1="" 1="" 55="" 2="" -15.718="" 0="" 1="" 1562.463="" 3025="" 0="" 39.303="" 0="" 0="" 34="" 1="" -12.188="" 0="" 0="" 1544.726="" 1156="" 0="" 17.715="" 0="" 1="" 31="" 1="" 4.05="" 0="" 0="" 313.8212="" 961="" 1="" 55.08="" 1="" 0="" 54="" 2="" 44.043="" 1="" 0="" 3033.807="" 2916="" 1="" 20.76="" 0="" 1="" 55="" 1="" 7.955="" 0="" 0="" 430.9776="" 3025="" 0="" 14.283="" 0="" 1="" 40="" 1="" 0.028="" 0="" 0="" 204.0041="" 1600="" 0="" 20.436="" 1="" 0="" 31="" 4="" -0.2="" 0="" 0="" 417.6301="" 961="" 0="" 26.388="" 1="" 0="" 26="" 4="" 0.866="" 0="" 0="" 696.3266="" 676="" 0="" 46.104="" 1="" 0="" 39="" 3="" 4.35="" 0="" 0="" 2125.579="" 1521="" 1="" 49.71="" 1="" 0="" 42="" 3="" 27.097="" 0="" 1="" 2471.084="" 1764="" 1="" 76.806="" 1="" 0="" 52="" 2="" 80.049="" 1="" 0="" 5899.162="" 2704="" 1="" 39.705="" 1="" 0="" 39="" 4="" 71.569="" 0="" 1="" 1576.487="" 1521="" 0="" 11.22="" 0="" 0="" 30="" 3="" 0="" 0="" 0="" 125.8884="" 900="" 0="" 18.348="" 0="" 0="" 50="" 4="" 0.3="" 0="" 0="" 336.6491="" 2500="" 0="" 13.95="" 0="" 0="" 49="" 6="" 0="" 0="" 0="" 194.6025="" 2401="" 0="" 15.216="" 1="" 0="" 32="" 10="" 0.2="" 0="" 0="" 231.5266="" 1024="" 0="" 36.15="" 1="" 0="" 32="" 4="" -2.2="" 0="" 0="" 1306.823="" 1024="" 0="" 47.34="" 0="" 1="" 27="" 2="" -10.43="" 0="" 0="" 2241.076="" 729="" 0="" 63.225="" 1="" 0="" 40="" 6="" 10.571="" 0="" 1="" 3997.4="" 1600="" 1="" 26.031="" 0="" 0="" 49="" 2="" 0.5="" 0="" 0="" 677.613="" 2401="" 0="" 20.4="" 1="" 0="" 36="" 5="" 0="" 0="" 0="" 416.16="" 1296="" 0="" 17.928="" 0="" 0="" 36="" 3="" 0="" 0="" 0="" 321.4132="" 1296="" 1="" 31.8="" 1="" 0="" 38="" 5="" 12.51="" 1="" 0="" 1011.24="" 1444="" 0="" 30="" 1="" 1="" 42="" 2="" -15.1="" 0="" 0="" 900="" 1764="" 0="" 26.463="" 0="" 0="" 43="" 1="" 10.011="" 0="" 1="" 700.2903="" 1849="" 1="" 73.722="" 1="" 0="" 42="" 5="" 3.2="" 1="" 0="" 5434.933="" 1764="" 0="" 33.414="" 1="" 0="" 32="" 4="" -4.7="" 0="" 0="" 1116.495="" 1024="" 1="" 34.08="" 1="" 0="" 35="" 6="" 5.1="" 0="" 0="" 1161.447="" 1225="" 1="" 48.9="" 0="" 0="" 61="" 1="" 28.08="" 1="" 1="" 2391.21="" 3721="" 1="" 21="" 0="" 1="" 41="" 1="" -2.347="" 0="" 0="" 441="" 1681="" 1="" 39.609="" 1="" 0="" 59="" 2="" 48.684="" 0="" 1="" 1568.873="" 3481="" 1="" 80.85="" 1="" 0="" 45="" 5="" 132.425="" 1="" 1="" 6536.722="" 2025="" 1="" 91.761="" 1="" 0="" 35="" 4="" -3.45="" 0="" 0="" 8420.081="" 1225="" 0="" 46.719="" 1="" 0="" 41="" 5="" 4="" 0="" 0="" 2182.665="" 1681="" 0="" 19.2="" 0="" 1="" 25="" 1="" 0="" 0="" 0="" 368.64="" 625="" 1="" 102.705="" 1="" 0="" 35="" 2="" 56.6="" 1="" 0="" 10548.32="" 1225="" 0="" 54.966="" 1="" 0="" 33="" 3="" 1.4="" 0="" 0="" 3021.261="" 1089="" 0="" 12.75="" 0="" 1="" 38="" 2="" 0="" 0="" 0="" 162.5625="" 1444="" 1="" 52.836="" 1="" 0="" 50="" 2="" 37.65="" 1="" 0="" 2791.643="" 2500="" 0="" 12.72="" 1="" 0="" 32="" 3="" 0="" 0="" 0="" 161.7984="" 1024="" 1="" 26.646="" 0="" 0="" 28="" 1="" 62.679="" 1="" 0="" 710.0093="" 784="" 0="" 59.664="" 1="" 0="" 44="" 5="" 11.4="" 0="" 1="" 3559.793="" 1936="" 0="" 39.15="" 1="" 0="" 58="" 2="" 189.4="" 0="" 1="" 1532.723="" 3364="" 0="" 21.3="" 1="" 0="" 47="" 6="" -0.986="" 0="" 0="" 453.69="" 2209="" 0="" 30.87="" 0="" 0="" 48="" 3="" 10.95="" 0="" 1="" 952.957="" 2304="" 0="" 16.5="" 1="" 0="" 57="" 2="" 23="" 0="" 0="" 272.25="" 3249="" 0="" 32.592="" 1="" 0="" 57="" 4="" -2.1="" 0="" 0="" 1062.238="" 3249="" 0="" 27.345="" 1="" 0="" 34="" 5="" 0.409="" 0="" 0="" 747.749="" 1156="" 0="" 35.418="" 1="" 0="" 57="" 5="" -5.75="" 0="" 0="" 1254.435="" 3249="" 0="" 24.3="" 0="" 0="" 45="" 1="" 0.05="" 0="" 0="" 590.49="" 2025="" 1="" 52.365="" 1="" 0="" 46="" 2="" 6="" 0="" 0="" 2742.094="" 2116="" 0="" 26.865="" 1="" 1="" 29="" 4="" -1.945="" 0="" 0="" 721.7282="" 841="" 0="" 39.48="" 1="" 0="" 35="" 3="" 40.2="" 0="" 1="" 1558.67="" 1225="" 1="" 45.693="" 1="" 0="" 40="" 2="" 18.576="" 1="" 1="" 2087.85="" 1600="" 0="" 39.3="" 1="" 0="" 42="" 5="" -4.9="" 0="" 0="" 1544.49="" 1764="" 0="" 14.244="" 0="" 0="" 60="" 1="" 120="" 0="" 1="" 202.8916="" 3600="" 0="" 43.518="" 1="" 0="" 27="" 3="" -7.5="" 0="" 0="" 1893.816="" 729="" 0="" 10.857="" 0="" 1="" 27="" 1="" 1.046="" 0="" 0="" 117.8745="" 729="" 0="" 51.222="" 0="" 0="" 33="" 3="" 1.6="" 0="" 0="" 2623.693="" 1089="" 0="" 34.764="" 1="" 1="" 63="" 2="" 3="" 0="" 0="" 1208.536="" 3969="" 0="" 16.959="" 1="" 0="" 43="" 7="" -0.5="" 0="" 0="" 287.6077="" 1849="" 0="" 23.64="" 1="" 0="" 26="" 5="" -6.001="" 0="" 0="" 558.8495="" 676="" 1="" 56.304="" 1="" 0="" 45="" 4="" 29.4="" 1="" 0="" 3170.141="" 2025="" 1="" 107.097="" 1="" 0="" 54="" 2="" 47.922="" 0="" 0="" 11469.77="" 2916="" 1="" 46.818="" 1="" 0="" 39="" 4="" 1.8="" 1="" 1="" 2191.925="" 1521="" 0="" 13.11="" 0="" 0="" 30="" 3="" 0="" 0="" 0="" 171.8721="" 900="" 0="" 29.16="" 0="" 0="" 36="" 3="" 4.245="" 0="" 0="" 850.3056="" 1296="" 1="" 42.54="" 1="" 0="" 52="" 2="" 30.1="" 1="" 0="" 1809.652="" 2704="" 0="" 74.31="" 1="" 0="" 49="" 6="" -5.5="" 0="" 0="" 5521.976="" 2401="" 0="" 27.729="" 1="" 0="" 31="" 6="" -4.88="" 0="" 0="" 768.8975="" 961="" 0="" 15="" 0="" 0="" 42="" 3="" 49.538="" 0="" 0="" 225="" 1764="" 1="" 54.723="" 1="" 0="" 57="" 2="" 21.948="" 1="" 0="" 2994.607="" 3249="" 0="" 61.581="" 1="" 0="" 44="" 4="" 61.366="" 0="" 1="" 3792.22="" 1936="" 1="" 72.03="" 1="" 0="" 43="" 2="" 21.998="" 0="" 1="" 5188.321="" 1849="" 1="" 37.338="" 1="" 0="" 48="" 7="" -18.89="" 0="" 1="" 1394.126="" 2304="" 0="" 27.354="" 0="" 0="" 39="" 3="" 2.6="" 0="" 1="" 748.2413="" 1521="" 1="" 92.898="" 0="" 1="" 27="" 1="" 30.957="" 1="" 1="" 8630.039="" 729="" 0="" 42.942="" 1="" 0="" 33="" 4="" -2.205="" 0="" 0="" 1844.016="" 1089="" 1="" 31.017="" 1="" 0="" 31="" 5="" 1.209="" 0="" 1="" 962.0543="" 961="" 1="" 23.892="" 0="" 0="" 35="" 1="" 5.249="" 1="" 0="" 570.8277="" 1225="" 1="" 44.46="" 1="" 0="" 39="" 2="" 38.307="" 1="" 1="" 1976.692="" 1521="" 0="" 33.72="" 1="" 1="" 30="" 2="" -2.552="" 0="" 0="" 1137.038="" 900="" 0="" 52.821="" 1="" 0="" 37="" 5="" 3.3="" 0="" 1="" 2790.058="" 1369="" 1="" 86.4="" 1="" 0="" 43="" 4="" 45.1="" 0="" 1="" 7464.96="" 1849="" 0="" 14.763="" 1="" 0="" 31="" 4="" -5.007="" 0="" 0="" 217.9462="" 961="" 1="" 107.301="" 1="" 0="" 50="" 3="" 371.901="" 1="" 1="" 11513.5="" 2500="" 0="" 20.385="" 0="" 0="" 27="" 1="" -0.8="" 0="" 0="" 415.5482="" 729="" 1="" 41.526="" 1="" 0="" 35="" 2="" -1.5="" 0="" 0="" 1724.409="" 1225="" 0="" 27.375="" 1="" 0="" 41="" 4="" -1.2="" 0="" 0="" 749.3906="" 1681="" 0="" 24.336="" 1="" 0="" 42="" 4="" -0.3="" 0="" 0="" 592.2409="" 1764="" 1="" 34.425="" 1="" 0="" 40="" 4="" -6.46="" 1="" 0="" 1185.081="" 1600="" 0="" 43.131="" 1="" 0="" 45="" 2="" 59.16="" 0="" 1="" 1860.283="" 2025="" 1="" 57.063="" 1="" 0="" 54="" 4="" 138.999="" 1="" 1="" 3256.186="" 2916="" 1="" 41.535="" 0="" 1="" 30="" 1="" 83.7="" 0="" 1="" 1725.156="" 900="" 0="" 61.722="" 1="" 1="" 32="" 3="" -2.48="" 0="" 0="" 3809.605="" 1024="" 0="" 99.153="" 1="" 0="" 43="" 2="" 80.802="" 0="" 1="" 9831.317="" 1849="" 0="" 37.296="" 1="" 0="" 28="" 3="" -2="" 0="" 0="" 1390.992="" 784="" 1="" 27.06="" 0="" 0="" 38="" 3="" 37.1="" 1="" 0="" 732.2436="" 1444="" 0="" 32.46="" 0="" 0="" 26="" 1="" -4.49="" 0="" 0="" 1053.651="" 676="" 1="" 28.491="" 0="" 1="" 46="" 3="" 4.02="" 1="" 0="" 811.7371="" 2116="" 1="" 19.596="" 0="" 1="" 41="" 2="" -1.2="" 1="" 0="" 384.0032="" 1681="" 1="" 18.54="" 0="" 0="" 37="" 5="" 0.964="" 1="" 0="" 343.7316="" 1369="" 1="" 102.435="" 1="" 0="" 54="" 2="" 139.629="" 1="" 1="" 10492.93="" 2916="" 0="" 26.7="" 1="" 0="" 39="" 4="" 46="" 0="" 0="" 712.89="" 1521="" 1="" 43.788="" 0="" 0="" 43="" 3="" 46.85="" 1="" 1="" 1917.389="" 1849="" 1="" 45.87="" 1="" 0="" 47="" 2="" 38.8="" 1="" 1="" 2104.057="" 2209="" 0="" 38.88="" 0="" 1="" 61="" 2="" -17.7="" 0="" 0="" 1511.655="" 3721="" 0="" 17.706="" 0="" 0="" 43="" 3="" 3.399="" 0="" 0="" 313.5024="" 1849="" 0="" 21.63="" 0="" 0="" 63="" 2="" -0.74="" 0="" 0="" 467.8569="" 3969="" 1="" 43.437="" 1="" 0="" 36="" 3="" 12.818="" 1="" 1="" 1886.773="" 1296="" 1="" 57.15="" 1="" 0="" 34="" 4="" 2.2="" 1="" 0="" 3266.123="" 1156="" 1="" 22.902="" 0="" 1="" 51="" 1="" 61.749="" 1="" 1="" 524.5016="" 2601="" 0="" 40.74="" 1="" 0="" 42="" 5="" 3.6="" 0="" 1="" 1659.748="" 1764="" 0="" 13.182="" 1="" 0="" 32="" 4="" -2.373="" 0="" 0="" 173.7651="" 1024="" 0="" 11.61="" 0="" 0="" 44="" 1="" 0.05="" 0="" 0="" 134.7921="" 1936="" 1="" 108.588="" 1="" 0="" 62="" 2="" 84.196="" 0="" 0="" 11791.35="" 3844="" 1="" 29.772="" 1="" 0="" 53="" 2="" 1.198="" 0="" 0="" 886.3719="" 2809="" 1="" 67.32="" 1="" 0="" 45="" 3="" 36.199="" 1="" 0="" 4531.982="" 2025="" 1="" 46.236="" 1="" 0="" 57="" 3="" 22.398="" 0="" 1="" 2137.768="" 3249="" 0="" 32.589="" 1="" 0="" 31="" 4="" 1.3="" 0="" 0="" 1062.043="" 961="" 0="" 60.498="" 1="" 0="" 40="" 2="" 10.05="" 0="" 1="" 3660.008="" 1600="" 0="" 30.21="" 0="" 1="" 30="" 2="" 3.1="" 0="" 1="" 912.644="" 900="" 1="" 55.125="" 1="" 0="" 35="" 4="" 23.969="" 1="" 1="" 3038.766="" 1225="" 1="" 56.676="" 1="" 0="" 56="" 2="" -6.239="" 0="" 0="" 3212.169="" 3136="" 1="" 70.845="" 1="" 0="" 57="" 2="" 200="" 1="" 1="" 5019.014="" 3249="" 0="" 46.815="" 0="" 0="" 44="" 3="" 30.902="" 0="" 1="" 2191.644="" 1936="" 1="" 14.43="" 0="" 0="" 27="" 1="" -4.5="" 0="" 0="" 208.2249="" 729="" 1="" 58.173="" 1="" 0="" 31="" 2="" 22.45="" 0="" 0="" 3384.098="" 961="" 1="" 50.646="" 0="" 0="" 40="" 2="" 45.584="" 1="" 1="" 2565.017="" 1600="" 0="" 12.207="" 0="" 1="" 32="" 1="" -0.843="" 0="" 0="" 149.0108="" 1024="" 0="" 62.526="" 1="" 0="" 52="" 2="" 69.1="" 0="" 1="" 3909.501="" 2704="" 1="" 44.703="" 1="" 1="" 32="" 5="" -14="" 0="" 0="" 1998.358="" 1024="" 0="" 85.38="" 1="" 0="" 25="" 4="" -30.24="" 0="" 0="" 7289.744="" 625="" 0="" 34.647="" 0="" 1="" 35="" 1="" 4.999="" 0="" 0="" 1200.415="" 1225="" 1="" 27.786="" 1="" 1="" 41="" 3="" -0.001="" 0="" 0="" 772.0618="" 1681="" 1="" 54.45="" 1="" 0="" 63="" 2="" 94.599="" 1="" 1="" 2964.802="" 3969="" 1="" 19.638="" 0="" 1="" 52="" 1="" 8.5="" 1="" 0="" 385.6511="" 2704="" 1="" 33.312="" 0="" 0="" 36="" 2="" 77.2="" 1="" 0="" 1109.689="" 1296="" 0="" 24.534="" 1="" 0="" 25="" 3="" 5.15="" 0="" 0="" 601.9172="" 625="" 0="" 18.36="" 0="" 1="" 28="" 1="" 0.015="" 0="" 0="" 337.0896="" 784="" 0="" 28.74="" 0="" 1="" 27="" 1="" -1.2="" 0="" 0="" 825.9876="" 729="" 0="" 36.168="" 1="" 0="" 25="" 3="" -1.501="" 0="" 0="" 1308.124="" 625="" 0="" 17.01="" 1="" 0="" 47="" 3="" 4.15="" 0="" 0="" 289.3401="" 2209="" 0="" 17.412="" 0="" 0="" 39="" 3="" 0="" 0="" 0="" 303.1778="" 1521="" 0="" 32.427="" 1="" 0="" 37="" 2="" 0.1="" 0="" 0="" 1051.51="" 1369="" 0="" 38.058="" 0="" 1="" 28="" 1="" 5.2="" 0="" 0="" 1448.411="" 784="" 1="" 58.317="" 1="" 0="" 46="" 3="" 36.5="" 0="" 1="" 3400.873="" 2116="" 0="" 15.822="" 1="" 0="" 26="" 2="" 11.4="" 0="" 0="" 250.3357="" 676="" 0="" 43.275="" 1="" 0="" 26="" 2="" -3.073="" 0="" 0="" 1872.726="" 676="" 0="" 17.445="" 1="" 0="" 34="" 4="" -7="" 0="" 0="" 304.328="" 1156="" 1="" 21.639="" 1="" 0="" 42="" 4="" 0.249="" 0="" 0="" 468.2463="" 1764="" 0="" 48.033="" 0="" 0="" 61="" 2="" 32.055="" 0="" 1="" 2307.169="" 3721="" 0="" 49.08="" 1="" 0="" 54="" 2="" 45.7="" 0="" 1="" 2408.847="" 2916="" 1="" 35.292="" 0="" 1="" 61="" 1="" 3="" 0="" 0="" 1245.525="" 3721="" 0="" 28.575="" 0="" 0="" 27="" 1="" 1.249="" 0="" 0="" 816.5306="" 729="" 0="" 33.366="" 0="" 1="" 43="" 1="" 12.599="" 0="" 0="" 1113.29="" 1849="" 1="" 35.472="" 0="" 1="" 51="" 2="" 60.398="" 1="" 0="" 1258.263="" 2601="" 0="" 42.93="" 1="" 1="" 35="" 3="" -18.88="" 0="" 0="" 1842.985="" 1225="" 0="" 17.58="" 1="" 0="" 32="" 2="" 12.2="" 0="" 1="" 309.0564="" 1024="" 0="" 77.01="" 1="" 0="" 36="" 4="" 26="" 0="" 1="" 5930.541="" 1296="" 0="" 37.662="" 1="" 0="" 37="" 11="" -2.382="" 0="" 0="" 1418.426="" 1369="" 1="" 20.43="" 1="" 0="" 57="" 1="" -1.94="" 1="" 0="" 417.3849="" 3249="" 0="" 27.84="" 0="" 0="" 40="" 2="" 0="" 0="" 0="" 775.0656="" 1600="" 0="" 49.806="" 0="" 0="" 37="" 1="" 110.103="" 0="" 1="" 2480.638="" 1369="" 0="" 24.678="" 1="" 0="" 34="" 3="" -0.312="" 0="" 0="" 609.0037="" 1156="" 0="" 15.81="" 1="" 1="" 60="" 3="" -3.2="" 0="" 0="" 249.9561="" 3600="" 1="" 17.628="" 1="" 0="" 27="" 4="" 12.34="" 1="" 0="" 310.7464="" 729="" 0="" 20.406="" 1="" 0="" 37="" 4="" -10.515="" 0="" 1="" 416.4048="" 1369="" 0="" 37.644="" 1="" 1="" 44="" 3="" -6.656="" 0="" 0="" 1417.071="" 1936="" 0="" 89.175="" 1="" 1="" 43="" 3="" -0.2="" 0="" 0="" 7952.181="" 1849="" 0="" 30.165="" 1="" 1="" 56="" 3="" -0.101="" 0="" 0="" 909.9273="" 3136="" 0="" 27.294="" 0="" 0="" 34="" 2="" -2.5="" 0="" 0="" 744.9625="" 1156="" 0="" 34.509="" 0="" 1="" 39="" 1="" 13.3="" 0="" 0="" 1190.871="" 1521="" 0="" 28.716="" 1="" 0="" 30="" 4="" -19.175="" 0="" 0="" 824.6086="" 900="" 1="" 15="" 0="" 1="" 38="" 1="" 2.85="" 1="" 0="" 225="" 1444="" 1="" 29.325="" 1="" 0="" 33="" 4="" 5.513="" 1="" 0="" 859.9557="" 1089="" 0="" 56.913="" 1="" 1="" 39="" 3="" 35.883="" 0="" 1="" 3239.089="" 1521="" 1="" 51.051="" 1="" 0="" 29="" 4="" 16.6="" 1="" 0="" 2606.204="" 841="" 1="" 169.2="" 1="" 0="" 49="" 2="" 484.198="" 1="" 1="" 28628.64="" 2401="" 0="" 25.704="" 0="" 0="" 49="" 1="" -0.369="" 0="" 0="" 660.6956="" 2401="" 0="" 25.8="" 0="" 0="" 37="" 1="" 13.5="" 0="" 1="" 665.64="" 1369="" 1="" 110.985="" 1="" 0="" 36="" 4="" 10.8="" 1="" 0="" 12317.67="" 1296="" 0="" 35.625="" 1="" 0="" 34="" 5="" -8="" 0="" 0="" 1269.141="" 1156="" 0="" 45.762="" 1="" 0="" 39="" 4="" 16.069="" 0="" 1="" 2094.161="" 1521="" 1="" 46.911="" 1="" 0="" 56="" 4="" 9.02="" 0="" 1="" 2200.642="" 3136="" 0="" 15.906="" 0="" 0="" 26="" 4="" 0.1="" 0="" 0="" 253.0008="" 676="" 1="" 50.433="" 1="" 0="" 29="" 2="" 14.126="" 1="" 0="" 2543.487="" 841="" 1="" 53.844="" 1="" 0="" 44="" 4="" 4.73="" 0="" 1="" 2899.177="" 1936="" 0="" 28.356="" 1="" 0="" 26="" 2="" 4.591="" 0="" 0="" 804.0628="" 676="" 1="" 50.4="" 0="" 1="" 39="" 2="" 5.8="" 1="" 0="" 2540.16="" 1521="" 1="" 33.15="" 0="" 0="" 43="" 2="" 24.68="" 1="" 0="" 1098.923="" 1849="" 0="" 16.488="" 1="" 0="" 27="" 6="" -1.422="" 0="" 0="" 271.8542="" 729="" 0="" 41.775="" 0="" 1="" 50="" 1="" 9.499="" 0="" 1="" 1745.151="" 2500="" 1="" 36.147="" 1="" 0="" 34="" 4="" -0.071="" 1="" 1="" 1306.606="" 1156="" 0="" 34.95="" 0="" 0="" 41="" 3="" 0.5="" 0="" 0="" 1221.503="" 1681="" 1="" 31.005="" 0="" 1="" 27="" 1="" 0="" 0="" 0="" 961.31="" 729="" 1="" 48.528="" 1="" 0="" 46="" 3="" 3.22="" 0="" 0="" 2354.967="" 2116="" 0="" 34.68="" 1="" 1="" 45="" 4="" -57="" 0="" 0="" 1202.702="" 2025="" 0="" 12.6="" 0="" 0="" 42="" 1="" -9.55="" 0="" 0="" 158.76="" 1764="" 0="" 20.07="" 1="" 1="" 52="" 2="" -4="" 0="" 0="" 402.8049="" 2704="" 0="" 38.319="" 1="" 0="" 31="" 3="" 0.09="" 0="" 0="" 1468.346="" 961="" 0="" 20.73="" 1="" 0="" 28="" 4="" 1.9="" 0="" 0="" 429.7329="" 784="" 0="" 28.248="" 0="" 1="" 31="" 1="" 15.15="" 0="" 0="" 797.9495="" 961="" 0="" 31.098="" 0="" 0="" 55="" 1="" 20.299="" 0="" 0="" 967.0856="" 3025="" 1="" 24.996="" 0="" 1="" 44="" 1="" 1.4="" 0="" 0="" 624.8="" 1936="" 0="" 22.338="" 0="" 1="" 26="" 1="" 0.892="" 0="" 0="" 498.9862="" 676="" 0="" 86.79="" 1="" 1="" 27="" 4="" 1.4="" 0="" 0="" 7532.504="" 729="" 0="" 14.655="" 0="" 0="" 27="" 3="" 0="" 0="" 0="" 214.769="" 729="" 1="" 16.224="" 0="" 0="" 42="" 6="" -1.5="" 0="" 0="" 263.2182="" 1764="" 0="" 25.185="" 0="" 0="" 59="" 1="" 237.95="" 0="" 1="" 634.2842="" 3481="" 0="" 24="" 0="" 1="" 40="" 1="" 0="" 0="" 0="" 576="" 1600="" 0="" 48.027="" 0="" 1="" 39="" 1="" 1.9="" 0="" 1="" 2306.593="" 1521="" 0="" 17.4="" 0="" 0="" 35="" 1="" -10.1="" 0="" 0="" 302.76="" 1225="" 0="" 18.75="" 1="" 0="" 35="" 7="" 0="" 0="" 0="" 351.5625="" 1225="" 1="" 30.576="" 0="" 0="" 31="" 1="" 13.5="" 1="" 0="" 934.8918="" 961="" 1="" 91.776="" 1="" 1="" 42="" 5="" 12="" 1="" 0="" 8422.834="" 1764="" 0="" 17.85="" 0="" 1="" 25="" 1="" 0="" 0="" 0="" 318.6225="" 625="" 1="" 29.31="" 0="" 0="" 54="" 1="" 4.8="" 0="" 0="" 859.076="" 2916="" 1="" 66.852="" 1="" 0="" 42="" 3="" 10.901="" 1="" 0="" 4469.189="" 1764="" 1="" 23.07="" 0="" 0="" 30="" 1="" 2.16="" 1="" 0="" 532.2249="" 900="" 1="" 66.15="" 1="" 1="" 28="" 4="" -1.29="" 1="" 0="" 4375.823="" 784="" 1="" 81.711="" 1="" 0="" 54="" 5="" 249.6="" 1="" 1="" 6676.688="" 2916="" 0="" 31.587="" 1="" 0="" 54="" 2="" 22.998="" 0="" 0="" 997.7386="" 2916="" 1="" 64.878="" 0="" 1="" 33="" 1="" 27.343="" 1="" 0="" 4209.155="" 1089="" 0="" 36.06="" 0="" 0="" 28="" 1="" -5="" 0="" 0="" 1300.324="" 784="" 0="" 33.6="" 1="" 0="" 39="" 2="" -9="" 0="" 0="" 1128.96="" 1521="" 0="" 60.03="" 1="" 0="" 39="" 5="" -3.3="" 0="" 0="" 3603.601="" 1521="" 0="" 60.225="" 0="" 1="" 37="" 1="" -15.8="" 0="" 0="" 3627.051="" 1369="" 1="" 65.7="" 1="" 0="" 43="" 5="" 53.948="" 1="" 0="" 4316.49="" 1849="" 1="" 32.49="" 0="" 0="" 61="" 3="" 20.6="" 1="" 0="" 1055.6="" 3721="" 0="" 109.608="" 1="" 1="" 33="" 4="" -9="" 0="" 0="" 12013.91="" 1089="" 1="" 97.887="" 1="" 0="" 44="" 4="" 60.196="" 1="" 1="" 9581.865="" 1936="" 1="" 50.268="" 0="" 1="" 41="" 1="" 20.1="" 1="" 0="" 2526.872="" 1681="" 0="" 55.5="" 1="" 0="" 63="" 2="" 55="" 0="" 1="" 3080.25="" 3969="" 1="" 50.484="" 1="" 0="" 36="" 4="" 8.6="" 0="" 0="" 2548.634="" 1296="" 0="" 70.905="" 1="" 0="" 41="" 6="" 1="" 0="" 0="" 5027.519="" 1681="" 0="" 16.14="" 0="" 1="" 35="" 1="" 12.999="" 0="" 0="" 260.4996="" 1225="" 0="" 17.967="" 0="" 0="" 30="" 4="" -2="" 0="" 0="" 322.813="" 900="" 1="" 24.48="" 1="" 0="" 44="" 3="" 3.4="" 1="" 0="" 599.2704="" 1936="" 0="" 25.005="" 1="" 0="" 60="" 3="" -1.829="" 0="" 0="" 625.25="" 3600="" 0="" 31.47="" 1="" 0="" 31="" 2="" -0.75="" 0="" 1="" 990.3608="" 961="" 0="" 26.61="" 0="" 0="" 25="" 1="" -5.8="" 0="" 0="" 708.0921="" 625="" 0="" 22.011="" 1="" 0="" 31="" 7="" -1.9="" 0="" 0="" 484.4841="" 961="" 0="" 42.459="" 1="" 0="" 37="" 5="" 48.599="" 0="" 0="" 1802.767="" 1369="" 0="" 27="" 1="" 0="" 48="" 5="" 47.5="" 0="" 0="" 729="" 2304="" 0="" 101.949="" 1="" 0="" 53="" 3="" 32.5="" 0="" 1="" 10393.6="" 2809="" 0="" 22.74="" 1="" 1="" 55="" 7="" 15.999="" 0="" 0="" 517.1076="" 3025="" 0="" 20.58="" 1="" 0="" 63="" 2="" 2.999="" 0="" 0="" 423.5364="" 3969="" 1="" 96.864="" 1="" 0="" 42="" 3="" -9.38="" 1="" 0="" 9382.634="" 1764="" 0="" 47.403="" 0="" 0="" 46="" 3="" -0.301="" 0="" 0="" 2247.044="" 2116="" 0="" 11.094="" 1="" 0="" 51="" 3="" -0.3="" 0="" 0="" 123.0768="" 2601="" 1="" 51.051="" 1="" 0="" 55="" 2="" 62="" 1="" 0="" 2606.204="" 3025="" 1="" 34.743="" 1="" 0="" 56="" 4="" 36.5="" 1="" 1="" 1207.076="" 3136="" 0="" 54.621="" 0="" 0="" 37="" 4="" 5.3="" 0="" 1="" 2983.453="" 1369="" 0="" 47.385="" 1="" 0="" 36="" 6="" -0.9="" 0="" 0="" 2245.338="" 1296="" 0="" 46.746="" 1="" 0="" 51="" 3="" 0.899="" 0="" 0="" 2185.188="" 2601="" 0="" 103.455="" 0="" 1="" 44="" 1="" 68.248="" 0="" 0="" 10702.94="" 1936="" 1="" 24.21="" 1="" 0="" 44="" 6="" 5.59="" 1="" 0="" 586.1241="" 1936="" 0="" 34.89="" 1="" 0="" 44="" 5="" -1.184="" 0="" 0="" 1217.312="" 1936="" 0="" 63.432="" 1="" 0="" 26="" 2="" 23.397="" 0="" 1="" 4023.618="" 676="" 0="" 44.268="" 1="" 0="" 44="" 3="" -2="" 0="" 0="" 1959.656="" 1936="" 0="" 44.508="" 1="" 0="" 27="" 3="" -4.199="" 0="" 0="" 1980.962="" 729="" 1="" 26.19="" 1="" 0="" 50="" 2="" 63.249="" 0="" 1="" 685.9161="" 2500="" 0="" 38.949="" 1="" 0="" 60="" 2="" 0.599="" 0="" 0="" 1517.025="" 3600="" 0="" 12.87="" 0="" 1="" 31="" 1="" 2.8="" 0="" 0="" 165.6369="" 961="" 1="" 17.484="" 0="" 0="" 57="" 3="" 27.999="" 1="" 0="" 305.6902="" 3249="" 0="" 36.873="" 1="" 0="" 29="" 2="" -4.9="" 0="" 0="">