数学建模 城市表层土壤重金属污染分析

城市表层土壤重金属污染分析摘要：本文在查阅大量文献资料的基础上，概括了重金属污染及传播的特点，危害及主要来源。对于问题一，考虑到对原始数据的分析、研究与处理，运用SPSS16.0中的TRANSFORM和GRAPHES功能，依据分组三维空间法建立空间分布模型，结合微积分的思想，将连续的空间分割后，分别研究8种主要重金属的空间分布。同时采用数形结合的方式分析该城区内不同区域重金属的污染程度。在问题二中，通过线性规划和数理统计来分析重金属元素污染主要原因，对每种污染所带来的影响加以权重，得出综合污染程度：山区〈公园绿地区〈生活区〈交通区〈工业区，从功能区判定污染的主要原因。问题三，采用因子分析法，综合污染指数，模糊数学来确定污染源的位置。并在原有模型的基础上，采用克里金插值法以及内梅罗综合污染评价指数法对原模型加以改进和优化，结合层次分析法研究城市地质环境的演变模式。关键词：重金属污染；因子分析；综合污染指数；层次分析法；SPSS一、问题重述随着城市经济的快速发展和城市人口的不断增加，人类活动对城市环境质量的影响日显突出。对城市土壤地质环境异常的查证，以及如何应用查证获得的海量数据资料开展城市环境质量评价，研究人类活动影响下城市地质环境的演变模式，日益成为人们关注的焦点。按照功能划分，城区一般可分为生活区、工业区、山区、主干道路区及公园绿地区等，分别记为1类区、2类区、……、5类区，不同的区域环境受人类活动影响的程度不同。现对某城市城区土壤地质环境进行调查。为此，将所考察的城区划分为间距1公里左右的网格子区域，按照每平方公里1个采样点对表层土（0~10厘米深度）进行取样、编号，并用GPS记录采样点的位置。应用专门仪器测试分析，获得了每个样本所含的多种化学元素的浓度数据。另一方面，按照2公里的间距在那些远离人群及工业活动的自然区取样，将其作为该城区表层土壤中元素的背景值。附件1列出了采样点的位置、海拔高度及其所属功能区等信息，附件2列出了8种主要重金属元素在采样点处的浓度，附件3列出了8种主要重金属元素的背景值。现要求你们通过数学建模来完成以下任务：(1)给出8种主要重金属元素在该城区的空间分布，并分析该城区内不同区域重金属的污染程度。(2)通过数据分析，说明重金属污染的主要原因。(3)分析重金属污染物的传播特征，由此建立模型，确定污染源的位置。(4)分析你所建立模型的优缺点，为更好地研究城市地质环境的演变模式，还应收集什么信息？有了这些信息，如何建立模型解决问题？二、问题分析土壤重金属污染是指由于人类活动，土壤中的微量有害元在土壤中的含量超过背景值，过量沉积而引起的含量过高，统称为土壤重金属污染。污染土壤的重金属主要包括汞、镉、铅、铬和类金属砷等生物毒性显著的元素，以及有一定毒性的锌、铜、镍等元素。主要来自农药、废水、污泥和大气沉降等，如汞主要来自含汞废水，镉、铅污染主要来自冶炼排放和汽车废气沉降，砷则被大量用作杀虫剂、杀菌剂、杀鼠剂和除草剂。问题一分析：对8种主要重金属污染在该城区的空间分布，将连续型的数据离散化，分割成块，立体展现。运用线性规划和改进的平均综合评价法解决对于该城区内不同区域重金属的污染程度。问题二分析：通过重金属污染本身的特征，考虑空间位置以及不同金属流动性等特点，分析金属污染主要原因。问题三分析：要求分析重金属污染物的传播特征，由此建立模型，确定污染源的位置。真对这一问题，首先我们做出假设，每种重金属都是可以在外界因素下可以自由传播的，不存在重金属元素在一个地区堆积，只有传播能力的不同。由于海拔因素对其影响不大，故忽略海拔因素对其传播的影响。问题四分析：我们通过查阅大量的资料，在原有模型的基础上，加以改进和优化，通过层次分析法建立模型。三、模型建立3.1问题一模型3.1.1空间分布模型我们对X轴，Y轴进行分组处理(附录一），形成空间模块，再将各种重金属污染指数进行污染程度转化，从而建立八副立体直观图，分别对每种重金属元素进行研究，分析它们的空间分布，用SPSS分别画出图像（表1、表2）。图1重金属元素平均浓度的空间分布重金属As重金属Cd金属Cr金属Cu金属Hg金属Ni金属Pb金属Zn图2各重金属元素在城区中的污染程度比例表1污染程度标准等级12345污染指数P≤0.70.7＜P≤11＜P≤22＜P≤33＜P污染程度清洁警界限轻度污染中度污染重度污染污染水平安全尚清洁超过背景值受中度污染污染相当严重3.1.2不同城区的污染程度我们将原始数据进行比较分析，对数据进行一定程度的处理，分别算出不同重金属元素在不同区域的平均值(附录二），再分别除以它们各自的背景值，形成表3，再画出它们的柱状图和折线图，用数型结合的范式进行分析，得出结果。表3不同区重金属元素在不同区的污染指数数据生活区工业区山区交通区公园绿地区As1.531.591.481.571.56Cd2.272.402.012.332.27Cr1.701.801.341.731.70Cu3.574.592.584.173.49Hg5.969.695.918.585.79Ni1.391.441.311.401.39Pb1.932.081.681.991.91Zn2.843.161.972.922.78图3各地区各重金属平均污染指数柱状图图4各地区各重金属平均污染指数折线图从图表我们可以分析得到工业区和主干道路区的污染指数明显高于其他城区，而山区的污染指数非常低。从而我们也可知道，在现代工业发达的年代，随着工业的迅猛发展，人们生活水平的提高，它所带来的环境影响也非常的巨大，环境的污染指数远远的高于正常值。对于Cu、Cr、Ni和As在各城区的差异不大，也比较接近背景值。而Zn、Hg、和Cd的变化就有明显差异，在工业区和主干道路区的含量极高，同时也影响到了生活区及附近城区的土壤。而事实也表明大气中重金属沉降，大气中的重金属主要来源于工业生产、汽车尾气排放及汽车轮胎磨损产生的大量含重金属的有害气体和粉尘等。它们主要分布在工矿的周围和公路、铁路的两侧。总的来说：工业化程度越高的地区污染越严重，市区高于远郊和农村，以大气传播媒介土壤重金属污染土壤的具有很强的叠加性,熟化程度越高重金属含量越高。

3.2问题二模型3.2.1重金属污染原因分析城市是受人类活动影响最强烈的区域,矿山开采、金属冶炼、交通活动和城市生活等极易造成城市土壤中重金属的富集。这些重金属元素在城市土壤中重新分布,使得土壤介质既是重金属的汇,又是重金属污染的源。重金属污染主要由采矿、废气排放、污水灌溉以及使用重金属制品等人为因素所致；因人类活动导致环境中的重金属含量增加，超出正常范围，并导致环境质量恶化。事实表明大气中重金属沉降，大气中的重金属主要来源于工业生产、汽车尾气排放及汽车轮胎磨损产生的大量含重金属的有害气体和粉尘等。它们主要分布在工矿的周围和公路、铁路的两侧。它们来自于含铅汽油的燃烧，汽车轮胎磨损产生的含锌粉尘等。它们成条带状分布，以公路、铁路为轴向两侧重金属污染强度逐渐减弱；随着时间的推移，公路、铁路土壤重金属污染具有很强的叠加性。对于该城区的生活区、工业区、山区、主干道路区及公园绿地区的土壤重金属污染分析，采用线性规划的思想，对重金属加以权重，建立模型，进行数据的处理与分析。3.2.2符号说明i表示八种重金属元素（Hg、Cd、Pb、As、Cu、Cr、Ni、Zn），i取1-8表示第i种重金属的权重系数表示第i种金属的含量表示该点的重金属的综合污染量3.2.3模型建立综合污染量为为找出重金属污染的主要原因，要先判断哪里的污染比较严重，确定污染源，从而分析污染原因。由于8种金属含量的背景值有很大差异，故权重系数不适合全为1，我们对此进行比例的调整，对数据加以权重，做出如下数据表。体现了每个点的综合污染量及其所对应的功能区。为找出重金属污染的主要原因，要先判断哪里的污染相对比较严重，就可以确定污染源应该在其周围不远，从而分析重金属的污染原因。表2综合污染综合功能区综合功能区综合功能区综合功能区综合功能区82278.2422974.92141977.75231432.2211061.092565318.4542936.96541962.60711426.1611058.728457496.1442924.80541957.07911425.91411054.697553321.4442921.59921955.01341394.21111049.292125188.5142914.61841936.8141393.9931041.554112636.3722897.24441921.17131385.03651039.798410880.1442879.63331920.95641380.72731036.85159466.17912835.62841917.27331369.82421029.68849395.32842812.94321907.74841364.05141029.3539250.76422770.44341905.11541346.74331027.52939117.97912762.93441905.10821342.40641022.87638932.56522698.24921897.14141341.93831020.38138056.44122693.111890.31541332.25841014.34917585.6442691.94321863.6311330.00751003.92437495.05242662.2141840.49141329.07611002.46947160.03412634.31841839.82721325.8965998.7616896.3852582.50841834.58611320.4994991.87446794.75542553.62541831.09921320.3625987.52936649.71152551.51411815.4411319.8954986.20935949.4142535.86341796.66831314.921985.25435716.72242514.07841764.73911308.6772984.89745661.00842514.02441759.64521299.9024982.7435486.29242501.78621753.75741292.5754977.0435449.27842497.90741737.16841286.0641968.355198.64442476.53441700.51341273.5041962.26935047.35242467.41341698.02841273.2563955.71445023.35622439.77451676.92551263.5293950.04754738.22322416.13551671.29251259.463945.97534704.88942408.52341671.19141258.643944.34434586.03242388.11641661.21641254.1781936.84454559.08212384.6241654.2741251.1183935.21134530.27442359.14441652.09341232.5734915.33344503.11142341.61141650.16451209.5482898.09434460.20942327.56641649.98751198.9021892.82934453.42942325.66841647.48441188.0535889.0734442.96122319.61441642.10341187.9533887.38244412.42642298.60941634.81641184.7714884.53834400.8322270.78341630.75631182.5683873.98934374.41922245.9341613.60641180.7333870.51444335.15242241.86111602.57751175.8774861.69934296.17652218.09651577.75241174.8712848.64134160.64442211.27851574.59841174.8213845.14844083.13312200.31941568.92551173.5934834.72544069.70742190.39621554.42431163.2453829.44133809.5322186.39111536.21151162.8813790.0253795.05242174.20411522.65111162.8542783.99853741.45812155.79311514.22911148.1123766.96433698.47712147.37951505.37641146.1633766.46733584.9922143.19321498.70651141.2714765.66333576.37542139.25851491.35431135.2684760.4913562.61342115.42251487.13641133.1324755.39633558.65212098.04451477.89841125.9884742.0533511.10212087.69941476.87341107.0044729.39533496.54512083.83541476.85641106.7443712.06633463.97442077.59241476.7741103.951672.62133452.07822053.17141469.28321092.4914661.9733389.00842052.87341465.70941089.4292661.01133290.48942042.39931463.12331087.6095641.43333186.30822039.05221459.21141086.8891635.85743150.30742021.10341448.65631086.6654614.48433049.39512007.03641447.54541082.3874613.3513014.98821992.03921438.37941077.4665549.56632998.17541989.39541434.18831073.3712513.19532975.77811986.99121433.46341065.7053503.0923表3不同功能区的平均综合污染功能区12345生活区工业区山区交通区公园绿地区平均综合污染2446.80554499.431129.8863887.8991970.789分析表中数据可以说明综合污染量越高，重金属的污染程度越高，从以上数据表明污染最严重的城区主要实在工业区和交通区，而分数低的（污染程度低）城区则大部分是在山区。由模型可以将城区的污染程度视为：山区〈公园绿地区〈生活区〈交通区〈工业区3.2.4模型结果分析资料显示胡永定通过研究徐州荆马河区域土壤重金属污染的成因中指出：Cr、Cu、Zn、Pb是由垃圾施用引起的，As是由农灌引起的，Cd是由农灌和垃圾施用引起的，Hg是各种途径都具备。王文祥通过对山东省耕地重金属元素污染状况的研究说明，工业快速发展地区铅高于农业环境，铅与距公路远近有关。因为重金属的由此可知污染源主要在工业区和交通区。事实表明，重金属污染物在土壤中移动性很小，不易随水淋滤，不为微生物降解，潜在危害极大。说明工业区和交通区为重金属的污染源头。说明该城区的污染原因主要有两类：<一>工业污染。工业污染大多通过废渣、废水、废气排入环境，而土壤的重金属污染又主要来源于污水灌溉污染，工业污水含有一些不利于水稻生长的重金属盐类，许多工业废水没经过任何处理，直接流入农田等土壤地，从而造成了严重的污染。〈二〉交通污染。它们来自于含铅汽油的燃烧，汽车轮胎磨损产生的含锌粉尘等。它们成条带状分布，以公路、铁路为轴向两侧重金属污染强度逐渐减弱；随着时间的推移，公路、铁路土壤重金属污染具有很强的叠加性。3.3问题三模型3.3.1问题分析重金属污染的移动能力低，在土壤中的传播性差，而大气沉降，则会使重金属迁移，所以土壤浓度高的区域不一定是重金属污染源，然而不同重金属的污染产生因素也不同，从以上几个模型可以看出，污染源大致在工业区和交通区，将目标锁定，再对8种不同重金属进行来源分析，进行建模。表4不同重金属污染的来源来源

污染物矿产开采、冶炼、加工排放的废气、废水、废渣Cr、Hg、、As、Pb、Ni、Mo煤和石油燃烧过程中排放的飘尘Cr、Hg、As、Pb电镀工业废水Cr、Cd、Ni、Pb、Cu、Zn塑料、电池、电子工业排放的废水Hg、Cd、Pb、Ni、Zn燃料、化工制革工业排放的废水Cr、Cd汽车尾气Pb农药、化肥As、Cu、Cd3.3.2因子分析对于污染源位置的确定，我们采用因子分析法加以研究分析。因子分析的基本目的就是用少数几个因子去描述许多指标或因素之间的联系，即将相关比较密切的几个变量归在同一类中，每一类变量就成为一个因子（之所以称其为因子，是因为它是不可观测的，即不是具体的变量），以较少的几个因子反映原资料的大部分信息。设有n个原有变量，且每个变量的均值均为0，标准差均为1，则有X=AF+，式中，F称为因子。A称为因子载荷矩阵，称为特殊因子，表示原有变量不能被因子解释的部分，其均值为0，相当于多元线性回归模型中的残值。运用SPSS16.0统计软件包进行因子分析。找出主因子和每个因子所代表的污染源。由因子分析结果可以看出，不同重金属来自不同的污染源，Cu、Pb、Zn主要来自于交通污染，As起源为自然源，Hg起源于燃煤源，Cd和Cr主要起源于工业源和化肥源。3.3.3重金属的污染源模型对上述模型进行评价分析，将污染源重点放在交通区和工业区。下面对8种重金属进行分析，寻找污染源。首先分析Hg，经过数据的筛选，发现有四个点的浓度明显高于其他点，对此四个点进行分析。表5Hg的严重污染点图5对应的坐标图编号x(m)y(m)Hg(ng/g)92708229516000.0018213694235714901.0025715248910613800.0082383369213500.00我们综合考虑四个点的坐标和浓度，以及其他周围的点的Hg的浓度，分析得到四个位置可以由一个污染源扩散得到。找到污染源点（10180.1，5154.6），并作出图像。图6Hg的污染源对于Ni，可以判定该重金属的污染源不止一个，如下图，可直观表现得到Ni金属的污染源并不是单独的，而是有多个污染源共同作用的。图7Ni的污染源表6各重金属污染源坐标用同样的模型与方法，可得到：重金属污染源坐标As（1060．3，8098.5）Cd（11851.1，7152.1）Cr（2483.9，5294.1）Cu（4777.3692）、（1647，6018）Hg（10180.1，5154.6）Ni（3063.18，7395）Zn（3500，14000）Pb（3430.4，4019.4）四、模型改进与评价4.1模型评价4.1.1优点：本文在正确、清晰地分析了题意的基础上，建立了合理、科学的可计算模型。合理的将连续空间分组，运用SPSS分割原始数据，分析了不同区域内的污染程度。根据线性规划、模糊数学和层次分析法对城区进行了重金属污染的综合指数评价。同时应用因子分析好的确定了污染位置。4.1.2缺点在研究8种主要重金属在该城区的空间分布时，忽略了海拔对模型的影响。确定污染源时，没有考虑大气沉降对区域重金属浓度的影响。为了模型的可行性，忽略了许多实际中会发生的因素影响。4.2模型改进首先，是对模型条件的改进。在考虑重金属污染浓度时，应当考虑不同区域的母体土质不同，它所对应的重金属含量也不同。应该具体到实际问题，查找当地的土壤土质，建立最合理的模型。其次是对原模型的不足加以改进，可以运用克里格插值法法，更好的解决8种主要重金属元素的空间分布。应用克里格法首先要明确三个重要的概念。一是区域化变量，当一个变量呈空间分布时，就称之为区域化变量。这种变量反映了空间某种属性的分布特征；二是协方差函数，协方差又称半方差，是用来描述区域化随机变量之间的差异的参数；三是变异函数，变异函数又称变差函数、变异矩，是地统计分析所特有的基本工具。分析重金属传播特征，建立模型，运用因子分析法确定污染源的位置，只能分别了解每种重金属在标称土壤的污染状况。二用综合指数法评价城市表层土壤的综合污染状况。进而采用内梅罗综合污染指数法。经过改进做出改进模型的研究路线。图8改进模型的研究路线参考文献：【1】姜启源、谢金星、叶俊；数学模型第三版；北京；高等教育出版社；2003【2】刘先勇、袁长迎、段宝福、周方杰；SPSS10.0统计分析软件与应用；北京；国防工业出版社；2002【3】兰天水、林健、陈建安;\o"公路旁土壤中重金属污染分布及潜在生态危害的研究"公路旁土壤中重金属污染分布及潜在生态危害的研究；海峡预防医学杂志2003年第01期【4】董文勇、刘进等；最优化技术与数学建模；北京；清华大学出版社；2010附录一：xmymx分组y分组AS污染比例As污染程度Cd污染比例Cd污染程度Cr污染比例Cr污染程度74781112.1841.1831.4331,373731111.6531.1231.4531,3211,791111.3633.3850.94201,787111.8231.7231.2931,0492,127111.7634.0451.9131,6472,728113.9158.4152.1942,8833,617112.4842.0843.0952,3833,692122.6748.2059.2152,7082,295112.0648.6552.8442,9331,767112.4242.0542.1144,233895111.6531.5531.4634,0431,895112.5542.2141.4232,4273,971121.5931.4932.5943,5264,357121.2532.7748.3355,0624,339121.5333.9752.9744,7774,897123.1858.0353.0655,8684,904221.7133.4352.6746,5345,641222.1842.6841.8635,4816,004122.0642.6645.1454,5924,603122.3644.72524.0152,4865,999121.5331.9831.7633,2996,018122.7349.33529.7053,5736,213122.6142.5145.5654,7416,434120.9221.6331.6235,3758,643131.1430.7011.1335,6357,965131.7134.4953.0755,3948,631131.4832.8241.3735,2917,349121.0332.4941.1334,7427,293126.0853.2752.3744,9487,293125.1154.8553.1255,5676,782122.9344.8952.0747,0046,226220.9723.5653.6257,3045,230221.7634.0951.8637,0484,600221.5335.9952.4148,1804,496221.2535.8153.2259,3284,311220.9723.0554.4659,0905,365221.5335.2952.7648,0495,439221.1934.0551.7838,0776,401221.1933.4552.1748,0177,210221.8236.5652.3446,8697,286224.6153.5353.0657,0568,348232.0642.5942.4947,7478,260231.6534.3752.4248,4578,991231.3034.6152.2349,4608,311231.3634.8952.2149,0627,639231.4834.6251.4439,3196,799221.1934.3751.94310,6316,472221.5331.7631.59310,6855,528221.3034.3759.87510,6434,472222.0031.6531.62311,7024,480321.4831.1731.52311,7305,532321.3632.6441.36311,4826,354321.3632.2641.94310,7008,184231.0832.4141.09310,6308,774231.0332.4341.47311,6788,618330.8623.2051.87311,9027,709331.0832.8841.46313,2447,056321.0832.6541.14312,7468,450330.8121.9531.48312,8558,945330.9223.8751.25313,7979,621331.3632.3441.81314,3258,666331.1430.9820.89215,4678,658330.8122.0441.15312,4424,329320.7622.1541.40313,0934,339320.8625.7851.71313,9205,354320.9222.7841.53314,8445,519320.9223.7551.65316,5696,055321.7131.7531.36316,3876,609321.0332.6741.22316,0617,352321.2531.0531.18315,6587,594330.8622.5240.84214,2987,418332.2440.8721.69314,1776,684321.0332.0841.07315,0926,936321.0331.2331.24312,7785,799320.9722.3541.27317,04410,691330.7620.5510.63117,08711,933342.3642.0141.48317,07512,924340.4910.9220.49117,96212,823440.7023.6151.19318,41311,721441.0331.1631.92319,00711,488441.7130.7721.21318,73810,921433.0550.8421.81317,81410,707431.7630.7121.17318,13410,046438.3755.7251.58317,1989,810431.0833.2151.19317,1449,081330.8122.8441.17318,3939,183430.5411.4930.58119,7678,810431.9430.3911.32321,0068,819430.8121.5330.91221,0919,482431.6536.8251.38322,8469,149431.6530.9921.53323,6649,790532.0640.8821.56322,30410,527431.1931.7930.94221,41810,721431.3031.0231.16321,43911,383441.59312.4651.40320,55411,228441.8832.1741.35320,10110,774431.2531.3931.20321,07210,404430.8622.9741.16320,2159,951430.8122.6541.31318,99312,371441.1930.7420.73219,96812,961442.1240.6711.48321,76612,348441.6531.5631.16322,67412,173440.6512.7240.79222,53511,293440.8121.7930.80225,2215,795521.5931.3431.09326,4535,577520.6510.6710.60126,4166,508521.8231.8931.18327,8165,581521.3031.2931.07325,3616,423521.7630.8620.93224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921.4330.75219,04115,769450.9422.2240.84218,90616,346450.8820.7010.52118,46717,001450.8322.2040.87217,41415,476451.9830.7721.49315,74815,728351.5632.3641.36315,51717,034351.6232.4641.40316,60717,365351.1030.7720.70115,95218,397350.8821.6831.27322,60514,301440.7721.8430.84223,14615,382550.8821.2130.64122,04617,634450.8322.1640.92223,78517,643550.8821.1031.19325,98118,051550.5011.5030.92227,38018,202550.8821.1830.67125,02116,290551.0530.8020.98223,32516,701551.3330.5512.11426,85216,114550.9921.4731.01317,98118,449451.8032.1841.70314,48212,692342.0441.1531.43314,31813,569342.2940.9321.40310,35217,133252.9843.6953.1159,09516,414253.2456.7052.29410,51015,314252.0442.1541.65313,9545,615321.6831.2531.17310,1421,662211.5036.9851.39317,7653,561411.7431.0231.3736,9245,696221.8031.5231.2334,6783,765121.8030.7721.1736,1822,005211.3330.9221.1535,9852,567212.1040.4911.0937,6531,952212.6041.2031.853Cu污染比例Cu污染程度Hg污染比例Hg污染程度Ni污染比例Ni污染程度Pb污染比例Pb污染程度Zn污染比例Zn污染程度1.5637.6051.4831.1431.0531.7132.4641.4031.1731.3734.8953.1150.8622.4043.1651.91327.1451.2531.0431.7038.90522.8651.6435.48510.52523.38529.7152.29414.03514.0153.3953.4651.4532.0342.424191.555385.7153.39512.31520.55511.495457.1452.1045.56513.4352.2541.8031.7631.1931.4631.8937.4051.1931.1631.4933.4754.8051.6032.0243.2352.0143.1751.6131.8631.2939.3452.2041.0533.43512.3856.7555.4051.6133.9357.17510.3855.7751.81315.2458.73512.6854.1151.5033.5955.6557.3656.0951.5932.2844.4555.3852.4341.4732.8845.5259.8954.4652.6747.38514.6952.2042.9741.0732.8343.245103.4053.29511.5955.85526.3557.9552.3442.5642.9346.2252.9343.9750.8622.1642.7040.9020.4610.8520.9420.68117.7054.4351.7233.1454.5154.9055.3751.4132.1642.6542.6341.4331.1332.1143.6754.52543.4352.2642.7042.5548.70518.4352.8344.21523.5757.6855.4352.3045.2558.9155.5353.3751.1531.9532.8046.3555.4651.5932.3744.3157.0159.4351.6033.5555.1057.4256.9452.0243.2554.6954.4754.8651.9732.96441.9355.5255.7451.5433.3355.8456.1752.6641.6233.2555.3653.9159.0051.2833.4554.27512.0258.8951.7234.0155.4753.57554.2951.6232.3043.12518.8552.5741.6333.2153.0458.9553.8651.9333.6058.3059.2653.4651.6133.3156.19517.2555.0351.5933.1157.8153.4251.4631.2632.1242.7043.6951.3131.3132.0643.0252.3441.7731.8631.4831.4835.33525.7151.3732.5742.8543.0454.4651.6931.5435.8551.8534.0051.4131.2131.3434.4652.2941.1232.5544.0053.8751.5131.0232.4544.03521.0551.5731.1432.2044.2852.5841.5731.0232.0342.8543.6154.7750.9723.7553.5153.8051.0021.2231.8732.2843.6352.8641.2334.3152.0445.4250.9221.1731.3932.1242.3141.0430.5911.7331.4934.9951.8133.2652.93454.5051.8230.8620.9721.8531.2432.2340.7020.7521.9531.7832.4741.8430.8021.7231.9734.0850.8020.8521.9432.2543.9650.7320.7423.6653.1652.6241.0730.8821.7631.8235.0851.4131.3331.1131.2031.5130.7720.8121.7633.2151.7530.6111.2231.1031.1431.8030.7320.8022.0642.0041.5831.8731.6030.9520.9024.3850.7321.1032.0041.7131.9830.7321.1631.2931.2032.3440.8921.2032.0032.1640.6910.4310.5810.7320.4811.8831.4731.4631.4031.2231.0130.2410.5010.8520.6912.4341.2930.9922.1042.5941.4430.9822.0341.2431.2931.5330.9821.2130.9420.9025.2351.6831.6831.2530.9221.2831.0431.0230.8720.6911.9830.8021.4432.3542.6441.8030.6410.9321.7631.5233.9850.6410.6511.3631.2231.2330.7720.5711.3031.3731.0830.4911.0930.8620.5911.4630.4010.7821.5431.3732.1341.2631.7233.0552.3741.2430.3711.4431.0831.3331.6331.0131.3431.1630.9323.03548.9850.8021.2531.3831.3130.5811.2631.1931.2031.1730.5811.2531.0020.8324.0050.8021.4931.5831.5231.4230.8020.9721.1830.9322.0030.7021.0021.9432.28411.5350.6711.2631.8732.4741.3032.4540.8220.9020.9721.1230.8621.1930.9420.7121.2830.4311.1831.4831.3030.9620.3410.7321.9031.2931.6432.4540.6811.4631.4532.2340.5811.0631.3631.0430.7420.4010.7220.7920.6314.6451.5931.1531.5231.6631.4431.7131.3031.0830.8124.4855.9150.9520.9020.8921.5430.6712.3340.8420.8520.9220.8920.7010.8720.6411.8831.0430.9220.8620.9321.7130.7321.3031.2831.2032.6941.4431.0230.8220.7620.8621.2630.9020.9720.9020.9520.4911.3930.6311.1430.7721.1630.6310.9320.9921.0831.5031.0230.8820.8420.7121.0130.7221.0431.0131.4131.2232.2540.9121.3430.9820.8621.0530.9421.0931.1630.3111.6230.9220.9320.9120.8920.4511.7431.1530.5810.7020.6610.8820.8420.9721.0731.4430.9421.4030.6910.8620.7820.7320.8420.9721.5331.5230.9521.0132.0840.2813.7050.6811.2730.9322.2741.2632.6941.4431.9130.5510.5412.1442.0740.9520.5510.8020.8420.8920.5710.7720.6210.7120.7720.9221.2230.9220.9020.7521.1030.5510.7721.1130.6912.1141.1936.0251.8033.3350.6010.5810.9120.8020.5010.1710.4310.6410.7820.7921.8830.3412.5640.7011.1132.9244.0750.7024.1551.9432.1243.6151.1131.2131.1032.3846.0951.1131.4731.8532.8143.9551.3431.9232.2445.4053.6751.5737.34520.1452.7044.0751.0933.6851.7232.85438.2750.9224.5451.6131.3730.7021.2030.9320.7222.1641.9331.2333.0351.2331.7132.5441.0231.2330.9521.2331.0331.0531.0230.9223.4956.8651.9932.2043.7654.5553.9451.5633.1253.3056.6351.8031.5732.8642.6844.6853.2051.9632.1643.0254.3359.3152.0944.2653.7252.4340.8020.9421.6332.1041.8031.4930.8021.6131.7232.12415.7151.5431.4831.5831.4531.2930.9521.3131.2633.7051.2331.1431.7333.0951.8332.4941.3531.7132.014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