Sharp tools make good work

--The Analects of Confucius 



Software for measure and attribution of stratified heterogeneity (SH)



1. Introduction

2. Tutorial

3. Output

4. Download, with Datasets

5. Citations

6. Bibliography

7. FAQs

8. Developers and Contact


1.        Introduction

Stratified heterogeneity (SH) refers to the phenomena that within strata are more similar than between strata. Examples are landuse types and climate zones in spatial data, seasons and years in time series, incomes in strata, etc. SH is ubiquitous in universe and has been a window for humans to recognize the nature and to understand its principles behind since Aristotle time. In another aspect, SH of a population is the sources of sample bias and statistical confounding.

Geographical detector is a novel tool to measure and attribution of SH (Fig. 1): (1) to measure and find SH of a variable Y; (2) to test the coupling between two variables Y and X, according to their spatial distributions, without assumption of linearity of the association; and (3) to investigate interaction between two explanatory variables X1 and X2 to a response variable Y, without any specific form such as assumed product in econometrics (Fig. 2). Each of the tasks can be accomplished by the geographical detector q-statistic:




Fig. 1. Principle of Geodetector

(The bottom map, the color indicates the values of a population Y. The top map, the population Y is stratified into strata {h}; the terms “stratification” and “partition” are equivalent, can be either classification or zonation. Between the two maps is the equation q(Y|{h}), in which the numerator is the summation of the within strata variance and the denominator is the pooled variance.)


where N and s2 stand for the number of units and the variance of Y in a study area, respectively; the population Y is composed of L strata (h = 1, 2, …, L). The strata of Y (red polygons in Fig.1) are a partition of Y, either by itself h(Y) or by an explanatory variable X which is a categorical h(X). X should be stratified if it is a numerical variable, the number of strata L might be 2-10 or more, according to prior knowledge or a classification algorithm. [(N-L)q]/[(L-1)(1-q)] ~ F(L-1, N-L, g), where g is a non central parameter (Wang et al 2016).

The strata of Y (red polygons in Fig.1) are a partition of Y, either by Y itself or by an explanatory variable X. X is a categorical variable or should be stratified if it is a numerical variable. The number of strata L might be 2-10 or more, according to prior knowledge or a classification algorithm. The terms “stratified heterogeneity (SH)”, “stratification”, “classification” and “partition” are equivalent. SH can be either spatial (spatial stratified heterogeneity, SSH) or aspatial such as time and some attributes.

Interpretation of q value (Fig.1).

The value of q is strictly within [0, 1].

(1)  If Y is stratified by Y itself, then q = 0 indicates that Y is absent of SH; q = 1 indicates that Y is SH perfectly; 100q% measures the degree of SH of Y.

(2)  If Y is stratified by an explanatory variable X, then q = 0 indicates that there is no coupling between Y and X; q = 1 indicates that Y is completely determined by X; X explains 100q% of Y. Please notice that the q-statistic measures the association between X and Y, both linearly and nonlinearly.

Geodetector q statistic helps understand spatial confounding, sample bias and overfitting.

(1)    Confounding arises if applying a global model to SH population, appeared as insignificant or misleading statistical results. The problem can be simply avoided if SH is identified (by Geodetector q statistic) then modelling in the strata, separately.

(2)    A sample would be biased if a population is SH and the sample do not cover all strata. The problem can be solved if SH is identified (by Geodetector q statistic) then apply stratified sampling or bias remedy models such as Heckman regression and Bshade method.

(3)    Local models aim to overcome heterogeneity but often suffer overfitting and too many parameters to interpret. The problems can be avoided if modelling in strata or stratifying the parameters of a local model then interpreting the parameters in the strata.

Functions of Geodetector:

(1)    The risk detector maps response variable in strata: Y(X);

(2)    The factor detector q-statistic measures the degree of SH of a variable Y; and the determinant power of an explanatory variable X of Y;

(3)    The ecological detector identifies the difference of the impacts between two explanatory variables X1 ~ X2;

(4)    The interaction detector reveals whether the risk factors X1 and X2 (and more X) have an interactive influence on a response variable Y (Fig.2).








Fig. 2. Interaction between explanatory variables X1 and X2 impacting on a response variable Y: q(Y|X1X2).


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2.        Tutorial

The Geodetector software was developed using Excel and R, respectively. The tools are free of charge, freely downloadable, and easy to use, and were designed without any GIS plug-in components and with “one click” execution. Users can run the following demo, then simply replace the demo data in the software using your own data, click Run and you get results ! We henceforth describe Excel Geodetector software. R users can download the R Geodetector software in the following section “Download of Geodetector Software and Example Datasets”.

As a demo, neural-tube birth defects (NTD) Y and suspected risk factors or their proxies Xs in villages are provided, including data for the health effect layers “NTD prevalence” and environmental factor layers, “elevation”, “soil type”, and “watershed”. Their field names are defined as Y and X1, X2, X3 respectively.

Step 1. Download the software and input your data in Excel

(1)  Download the Excel Geodetector software (In the following section “Software and Examples Data Download”), one click to download any one of the three Examples, unzip the downloaded file, you will find an Excel file (this is Geodetector software with an Example dataset!) and double click the Excel file, Fig. 3 and Fig. 5 appear. Fig. 3 is the format of the input data for the Geodetector: each row denotes a sample unit (e.g. a village); the 1st column record the response variable Y; the 2nd and following columns denote partitions of Y or factors X, the latter were partitioned according to the similarity within strata.

(2)  Input your data into the Excel Geodetector software in the format of Fig. 3. Then go to Step 2.


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: image004


Fig. 3. Input data in Excel and the execution interface

(Note: Y is numerical; X MUST be categorical, e.g. landuse types, seasons. If X is numerical it should be transformed to be categorical, e.g. GDP per capita is stratified into 5 strata)


(3)  If your data is in GIS format, as Fig. 4, please transform the GIS data into Excel data as Fig. 3.



Fig. 4. Data in GIS format


Step 2. Run Geodetector software

Only one operation interface was designed (Fig. 5). The function of the “Read Data” button is to load data; thus, when the button is clicked, all variables are listed in the “variables” list box. Then, disease and partition of Y or environmental factor variables are selected into their corresponding list boxes Y and X on the right of the interface. Finally, Geodetector is executed by clicking the “Run” button.


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: UI


Fig. 5. User interface for Geodetector

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3.        Output

Geodetector outputs results from the risk detector, factor detector, ecological detector, and interaction detector in four Excel spreadsheets (Fig. 6).


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: image014


Fig. 6. Interface for Geodetector results


In the “Risk detector” sheet (Fig. 7), result information for each environmental risk factor is presented in two tables. The first table gives the average disease incidence in each stratum of a risk factor, the name of which is written at the top left of the table. The second table gives the statistically significant difference in the average disease incidence between two strata; if there is a significant difference, the corresponding value is “Y”, else it is “N”.




Fig. 7. Results of risk detector


The Fig. 8 shows the output format of the q values for each environmental risk factor, as given in the “Factor detector” sheet. The table header gives the names of the environmental risk factors, while the associated q values (q1, q2, …, qn) and their corresponding p values are presented in the row below.




Fig. 8. Results of factor detector


In the “Ecological detector” sheet (Fig. 9), results of the statistically significant differences between two environmental risk factors are presented. If Y(X1) (risk factor names in row) was significantly bigger than Y(X2) (risk factor names in column), the associated value is “Y”, while “N” expresses the opposite meaning.



Fig. 9. Results of ecological detector


The format of the results for the interaction detector is shown in Fig. 10.Interaction relationships” below the table represent the interaction relationship for the two factors. The relationship is defined in a coordinate axis. It has 5 intervals, including “(-min(q(x), q(y)))”,“(min(q(x), q(y)), max(q(x), q(y)))”, “(max(q(x), q(y)), q(x) + q(y))”,“q(x) + q(y)”,“( q(x) + q(y),+∞)”, and the interaction relationship is determined by the location of q(xÇy) in the 5 intervals (see Table 1).




Fig. 10. Results of interaction detector


Table 1 Redefined interaction relationships

Graphical representation




q(X1ÇX2) < Min(q(X1), q(X2))


Weaken, nonlinear

Min(q(X1),q(X 2))<q(X1Ç X2)<Max(q(X1)), q(X2))


Weaken, uni-


q(X1Ç X2) > Max(q(X1), q(X2))


Enhance, bi-


q(X1Ç X2) = q(X1)+ q(X2)




q(X1Ç X2) > q(X1)+ q(X2)


Enhance, nonlinear


说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: 说明: image029


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4.        Download, with Datasets

The software was developed using Excel 2007 and R, respectively. It is completely free. You can click any one of the following links to download the Geodetector software. The first three are Geodetector software in Excel: (1) click one and unzip the file, an Excel file appears; (2) click the Excel file to start the Geodetector, you may exercise the demo data; then (3) input your own data to get your own results.

1: Geodetector Software in Excel, enclosed an Example of a Disease Dataset

2: Geodetector Software in Excel, enclosed an Example of a Toy Dataset

3: Geodetector Software in Excel, enclosed an Example of a NDVI Dataset

4: Geodetector Software in R

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5.  Citations. The Geodetector can be cited as:

[1] Wang JF, Li XH, Christakos G, Liao YL, Zhang T, Gu X & Zheng XY. 2010. Geographical detectors-based health risk assessment and its application in the neural tube defects study of the Heshun region, China. International Journal of Geographical Information Science 24(1): 107-127.

[2] Wang JF, Zhang TL, Fu BJ. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 67(2016): 250-256.


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6.  Geodetector Bibliography

[1] Wang JF, Li XH, Christakos G, Liao YL, Zhang T, Gu X & Zheng XY. 2010. Geographical detectors-based health risk assessment and its application in the neural tube defects study of the Heshun region, China. International Journal of Geographical Information Science 24(1): 107-127.

[2] Luo W, Jasiewicz J, Stepinski T, Wang JF, Xu CD, Cang XZ. 2016. Spatial association between dissection density and environmental factors over the entire conterminous United States. Geophysical Research Letters 43(2): 692-700.

[3] 刘彦随,     . 2012. 中国县域城镇化的空间特征与形成机理. 地理学报 67(8):1011-1020.

[4] 王劲峰,徐成东. 2017. 地理探测器:原理与展望. 地理学报 72(1): 116-134.

[5] Lecture ppt_181203: Geodetector & its Applications in Natural and Social Sciences











































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1.         Wang JF, Li XH, Christakos G, Liao YL, Zhang T, Gu X & Zheng XY. 2010. Geographical detectors-based health risk assessment and its application in the neural tube defects study of the Heshun region, China. International Journal of Geographical Information Science 24(1): 107-127.

2.         Liao YL,Wang JF, Wu JL, Driskell L, Wang WY, Zhang T, Gu X, Zheng XY. 2010. Spatial analysis of neural tube defects in a rural coal mining area. International Journal of Environmental Health Research 20(6): 439-450.

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3.         Hu Y, Wang JF, Li XH, Ren D, Zhu J. 2011. Geographical detector-based risk assessment of the under-five mortality in the 2008 Wenchuan earthquake, China. PLoS ONE 6(6): e21427.

4.         Zou B, Wilson JG, Zhan FB, Zeng YN, Wu KJ. 2011. Spatial-temporal variations in regional ambient sulfur dioxide concentration and source-contribution analysis: A dispersion modeling approach. Spatial-temporal variations in regional ambient sulfur dioxide concentration and source-contribution analysis: A dispersion modeling approach. Atmospheric Environment 45: 4977-4985.

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5.         Gajos M. 2012. Geoinformation technologies in biomedicine and health care: review of scientific journals. E. Piętka and J. Kawa (Eds.): ITIB 2012, LNCS 7339: 510–524.

6.         Li LF, Wang JF, Wu J. 2012. A spatial model to predict the incidence of neural tube defects. BMC Public Health 12: 951.

7.         Wang JF, Hu Y. 2012. Environmental health risk detection with GeogDetector. Environmental Modelling & Software 33: 114-115.

8.         刘彦随, 杨忍, 2012. 中国县域城镇化的空间特征与形成机理. 地理学报 67(8): 1011-1020.

Liu YS, Yang R.2012.Spatial characteristics and formation mechanism of the county urbanization in China. Acta Geographica Sinica 67(8): 1011-1020.

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9.         Cao F, Ge Y, Wang JF. 2013. Optimal discretization for geographical detectors-based risk assessment. GIScience & Remote Sensing 50(1): 78-92.

10.     Li XW, Xie YF, Wang JF, Christakos G, Si JL, Zhao HN, Ding YQ, Li J. 2013. Influence of planting patterns on Fluoroquinolone residues in the soil of an intensive vegetable cultivation area in north China. Science of the Total Environment 458-460: 63-69.

11.     Lee WC. 2013. Assessing causal mechanistic interactions: a peril ratio index of synergy based on multiplicativity. PLoS ONE 8(6): e67424. doi:10.1371/journal.pone.0067424.

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14.     Wang JF, Xu CD, Tong SL, Chen HY, Yang WZ. 2013. Spatial dynamic patterns of hand-foot-mouth disease in the People’s Republic of China. Geospatial Health 7(2): 381-390.

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15.     Bai HX, Ge Y, Wang JF, Li DY, Liao YL, Zheng XY. 2014. A method for extracting rules from spatial data based on rough fuzzy sets. Knowledge-Based Systems 57: 28-40.

16.     Hu Y, Gao J, Chi M, Luo C, Lynn H, Sun LQ, Tao B, Wang DC, Zhang ZJ, Jiang QW. 2014. Spatio-temporal patterns of schistosomiasis Japonica in lake and marshland areas in China: the effect of snail habitats. American Journal of Tropical Medicine and Hygiene 91(3): 547–554.

17.     Hu Z, Tang GA, Lu GN. 2014. A new geographical language: a perspective of GIS. Journal of Geographical Sciences 24(3): 560-576.

18.     Huang JX, Wang JF, Bo YC, Xu CD, Hu MG. 2014. Identification of health risks of Hand, Foot and Mouth Disease in China using the Geographical Detector Technique. International Journal of Environmental Research and Public Health 11: 3407-3423.

19.     Luo W. 2014. Impact cratering as a major factor controlling valley dissection density on MARS - a geographical detector approach. 45th Lunar and Planetary Science Conference. 2580.pdf.

20.     Qian Q, Zhao J, Fang LQ, Zhou H, Zhang WJ, Wei L, Yang H, Yin WW, Cao WC, Li Q. 2014. Mapping risk of plague in Qinghai-Tibetan Plateau, China. BMC Infectious Diseases 14: 382.

21.     Ren Y, Deng LY, Zuo SD, et al. 2014. Geographical modeling of spatial interaction between human activity and forest connectivity in an urban landscape of southeast China. Landscape Ecology 29(10): 1741-1758.

22.     Wu JL, Zhang CS, Pei LJ, Chen G, Zheng XY. 2014. Association between risk of birth defects occurring level and arsenic concentrations in soils of Lvliang, Shanxi province of China. Environmental Pollution 191: 1-7.

23.     Xu EQ, Zhang HQ. 2014. Characterization and interaction of driving factors in karst rocky desertification: a case study from Changshun, China. Solid Earth 5: 1329-1340.

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Cai FF, Pu LJ. 2014. Spatial-Temporal characteristics and formation mechanism of Urban-Rural construction land in Nantong City. Resources Science 36(4): 0731-0740.

25.         悦,蔡建明,任周鹏,杨振山. 2014. 基于地理探测器的国家级经济技术开发区经济增长率空间分异及影响因素. 地理科学进展 33(5): 657-666.

Ding Y, Cai JM, Ren ZP, Yang ZS. 2014. Spatial disparities of economic growth rate of China’s National-level ETDZs and their determinants based on geographical detector analysis. Progress in Geography 33(5): 657-666.

26.         丹,舒晓波,尧    波,曹安庆. 2014. 江西省县域人均粮食占有量的时空格局演变. 地域研究与开发 33(4): 157-162.

Hu D, Shu XB, Yao B, Cao QA. 2014. The evolvement of spatial-temporal pattern of per capita grain possession in counties of Jiangxi Province. Areal Research And Development 33(4): 157-162.

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Tong LG, Xu XL, Fu Y, Wei FH. 2014. Impact of environmental factors on snail distribution using geographical detector model. Progress in Geography 33(5): 625-635.

30.     魏凤娟,李江风,刘艳中. 2014. 湖北县域土地整治新增耕地的时空特征及其影响因素分析. 农业工程学报 30(14): 267-275.

Wei FJ, Li JF, Liu YZ.2014. Spatial-temporal characteristics and impact factors of newly increased farmland by land consolidation in Hubei province at county level. Transactions of the Chinese Society of Agricultural Engineering 30(14): 267-276.

31.         ,  石培基. 2014. 甘肃省县域城镇化地域差异及形成机理. 干旱区地理 37(4): 838-845.

Yang B, Shi PJ. 2014. Geographical features and formation mechanism of county level urbanization in Gansu Province. Arid Land Geography 37(4): 838-845.

32.     俞佳根,叶世康. 2014. 空间视角下中国对外直接投资与产业结构升级水平研究. 商业经济研究 34: 127-128.

Yu JG, Ye SK.2014. Outward foreign direct investment and industrial structure upgrade level from the perspective of spatial in China. Journal of Commercial Economics 34: 127-128.

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33.     Chen YH, Ge Y, Heuvelink GBM, Hu JL, Jiang Y. 2015. Hybrid constraints of pure and mixed pixels for soft-then-hard super-resolution mapping with multiple shifted images. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 8(5): 2040-2052.

34.     Hu Y, Bergquist R, Lynn H, Gao FH, Wang QZ, Zhang SQ, Li R, Sun LQ, Xia CC, Xiong CL, Zhang ZJ, Jiang QW. 2015. Sandwich mapping of schistosomiasis risk in Anhui Province, China. Geospatial Health 10: 324.

35.     Hu Y, Li R, Bergquist R, Lynn H, Gao FH, Wang QZ, Zhang AQ, Sun LQ, Zhang ZJ, Jiang QW. 2015. Spatio-temporal transmission and environmental determinants of schistosomiasis Japonica in Anhui Province, China. PLoS Neglected Tropical Diseases 9(2): e0003470. doi:10.1371/journal.pntd.0003470.

36.     Lee WC. 2015. Testing for sufficient-cause gene-environment interactions under the assumptions of independence and Hardy-Weinberg equilibrium. American Journal of Epidemiology 182(1): 9–16.

37.     Shen J, Zhang N, Gexi geduren, He B, Liu CY, Li Y, Zhang HY, Chen XY, Lin H. 2015. Construction of a GeogDetector-based model system to indicate the potential occurrence of grasshoppers in Inner Mongolia steppe habitats. Bulletin of Entomological Research 105: 335-346.

38.     Yang R, Liu YS, Long HL, Qiao LY. 2015. Spatio-temporal characteristics of rural settlements and land use in the Bohai Rim of China. Journal of Geographical Sciences 25(5): 559-572.

39.     Zhu H, Liu JM, Chen C, Lin J, Tao H. 2015. A spatial-temporal analysis of urban recreational business districts: A case study in Beijing, China. Journal of Geographical Sciences 25(12): 1521-1536.

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Bi SB, Ji H, Chen CC, Yang HR, Shen X.2015.Application of geographical detector in human-environment relationship study of prehistoric settlements. Progress in Geography 34(1): 118-127

41.     崔日明,  俞佳根. 2015. 基于空间视角的中国对外直接投资与产业结构升级水平研究. 福建论坛 (人文社会科学版) 2015(2): 26-33.

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Xu QR, Zheng XQ.2015. Analysis of influencing mechanism of urban growth using geographical detector. Acta Geodaetica at Cartographica Sinica 44(S0): 96-101.

44.        , 刘彦随, 龙花楼, 陈呈奕. 2015. 基于格网的农村居民点用地时空特征及空间指向性的地理要素识别——以环渤海地区为例. 地理研究 34(6): 1077-1087.

Yang R, Liu YS, Long HL, Chen CY. 2015. Spatial-temporal characteristics of rural residential land use change and spatial directivity identification based on grid in the Bohai Rim in China. Geographical Research 34(6): 1077-1087.

45.         佳,刘吉平. 2015. 基于地理探测器的东北地区气温变化影响因素定量分析. 湖北农业科学 54(19): 4682-4687.

Yu J, Liu JP.2015. Quantitative Analysis with Geographical Detector on the influence factor of temperature variation in Northeast China. Hubei Agricultural Sciences 54(19): 4682-4687.

46.     湛东升, 张文忠, 余建辉,   , 党云晓. 2015. 基于地理探测器的北京市居民宜居满意度影响机理. 地理科学进展 34(8): 966-975.

Zhan DS, Zhang WZ, Yu JH, Meng B, Dang XY.2015. Analysis of influencing mechanism of residents’ livability satisfaction in Beijing using geographical detector. Progress in Geography 34(8): 966-975.

47.         , 任志远. 2015. 基于Whittaker滤波的陕西省植被物候特征. 中国沙漠 45(4): 901-906.

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49.     Chen K, Ni MJ, Cai MG, Wang J, Huang DR, Chen HR, Wang X, Liu MY. 2016. Optimization of a coastal environmental monitoring network based on the Kriging method: a case study of Quanzhou Bay, China. BioMed Research International.

50.     Du Z, Xu X, Zhang H, Wu Z, Liu Y. 2016. Geographical detector-based identification of the impact of major determinants on aeolian desertification risk. PLoS ONE 11(3): e0151331.

51.     Fan LX, Wu EQ, Liu J, Qu XC, Ning BA, Liu Y. 2016. Distribution Characteristics of Spermophilus dauricus in Manchuria City in China in 2015 through “3S” Technology. Biomedical Environmental Sciences 29(8): 603-608.

52.     Fei XF, Wu JP, Liu QM, Ren YJ, Lou ZH. 2015. Spatiotemporal analysis and risk assessment of typhoid cancer in Hangzhou, China. Stochastic Environmental Research and Risk Analysis 30: 2155–2168.

53.     Fei XF, Wu JP, Liu QM, Ren YJ, Lou ZH. 2015. Spatiotemporal analysis and risk assessment of thyroid cancer in Hangzhou, China. Stochastic Environmental Research and Risk Assessment 30: 2155–2168.

54.     Ju HR, Zhang ZX, Zuo LJ, Wang JF, Zhang SR, Wang X, Zhao XL. 2016. Driving forces and their interactions of built-up land expansion based on the geographical detector – a case study of Beijing, China. International Journal of Geographical Information Science 30(11): 2188–2207.

55.     Liang P, Yang XP. 2016. Landscape spatial patterns in the Maowusu (Mu Us) Sandy Land, northern China and their impact factors. Catena 145: 321-333.

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