Research on deformation prediction method for mining-induced overburden in coal mines based on BP neural network

Coal mining triggers the initiation, propagation, and coalescence of fractures in overburden strata, which can readily induce geological disasters such as mine water inrush and surface subsidence. This study employed distributed optical fiber sensing (DOFS) technology to capture strain distribution curves in overburden strata during coal extraction via physical similarity modeling of Longwall Face 22,107 at Jinfeng Cuncaota Coal Mine. Based on the geological conditions of the overburden and coal mining parameters, seven key factors influencing mining-induced deformation were identified. A neural network architecture was constructed to establish a prediction model for overburden deformation states using measured strain data. Results indicate that the distribution of the caved and fractured zones is closely related to the positions of the main roof and key strata. Predictions from the backpropagation neural network (BPNN) align well with measured strain values, achieving a coefficient of determination (R²) greater than 0.9 and a root mean square error (RMSE) below 10%, demonstrating high applicability. These findings validate the feasibility of integrating DOFS with BPNN for predicting mining-induced overburden deformation.

1 Introduction

Coal serves as the cornerstone of China’s energy security, playing a vital role in ensuring stable energy supply (Yuan et al., 2023). Coal extraction triggers the initiation, propagation, and coalescence of cracks within overlying rock-soil masses, leading to gradual subsidence. This process frequently induces ecological issues including groundwater depletion, surface subsidence, and infrastructure damage (Guo, 2017). Consequently, accurately understanding deformation mechanisms of mining-induced overburden and predicting fracture characteristics provides a theoretical foundation for water resource conservation and environmental remediation in coal mining areas.

In recent years, distributed optical fiber sensing (DOFS) technology has gained prominence due to its high precision, real-time capability, and long-range monitoring advantages (Li, 2022; Cheng et al., 2022). Through physical modeling and field tests, researchers have analyzed overburden deformation behavior using DOFS, significantly enhancing prediction capabilities (Chai et al., 2022). Despite substantial research achievements, the complexity of geological conditions and diversity of mining methods continue to challenge the development of multifactor-inclusive prediction approaches. Machine learning derives patterns from data through automated algorithmic analysis (Liu et al., 2021). Common techniques such as Genetic Algorithms (GA), Support Vector Machines (SVM), Particle Swarm Optimization (PSO), Backpropagation Neural Networks (BPNN) (Shi et al., 2021; Bi et al., 2022; Zhao and Wu, 2018; Xu et al., 2024), have laid a foundation for predicting surface subsidence and overburden fracture heights (Wang et al., 2025; Wang et al., 2024; Zheng et al., 2024; Razavi-Termeh et al., 2025; Ji et al., 2025; Meng et al., 2024), recent research has increasingly focused on developing integrated monitoring-prediction frameworks. For example, Lou et al. (Lou and Tan, 2021) established a PSO-BP model to predict the height of the water-conducting fracture zone, yet its efficacy is constrained by the empirical setting of PSO parameters, which lack an adaptive mechanism. Similarly, Qiao et al. (Qiao et al., 2022) developed a PSO-SVM model for predicting the “two zones” height, but its application is limited due to a training set derived from a single geological basin (Ordos Basin), resulting in poor cross-regional generalization. In a complementary approach, Chen et al. (Chen et al., 2023; Chen et al., 2025; Chen et al., 2024) synergized DS-InSAR with the PIM model for monitoring, developed the AWC-LSTM model for time-series prediction, and created the STMD method for high-precision signal extraction. Collectively, these studies demonstrate a clear trend towards methodological integration; however, they also reveal shared challenges in achieving an optimal balance between generalization capability, adaptive learning, and computational efficiency for robust deformation prediction.

Addressing the concealed, abrupt, and protracted nature of mining-induced overburden deformation (Qian et al., 1994), this study conducts physical similarity simulations based on geological data from Jinfeng Cuncaota Coal Mine. Brillouin Optical Time Domain Reflectometry (BOTDR) technology captures distributed strain patterns during extraction, revealing dynamic failure mechanisms. A BPNN-based strain prediction model is established by identifying key governing factors, enabling strata deformation forecasting and accuracy evaluation to advance intelligent hazard prediction systems.

2 Distributed optical fiber sensing technology for mining-induced overburden

2.1 Technical principles

The measurement principle of BOTDR (Brillouin Optical Time Domain Reflectometry) distributed optical fiber sensing technology is as follows: When pulsed light is injected into an optical fiber, it interacts with acoustic phonons within the fiber, generating spontaneous Brillouin scattering. The backscattered Brillouin light propagates backward along the fiber to the incident end (Figure 1A), entering BOTDR’s receiver unit and signal processing module. A photodiode converts the optical signal into an electrical signal, which undergoes averaging via a digital signal processor to obtain the distributed Brillouin scattered light power at each sampling point along the fiber (Figure 1B). The Brillouin scattered light power peaks at a specific frequency offset with a Lorentzian line shape distribution (Figure 1C). By sweeping the output signal frequency, Brillouin scattered light power measurements at different frequencies are acquired, yielding the Brillouin scattering spectrum (Figure 1A). The strain measurement principle of BOTDR is illustrated in Figure 1 (Hong et al., 2017).

Figure 1

Figure 1. Strain measurement principle diagram of BOTDR. (A) Frequency distribution of backscattered Brillouin light along the optical fiber; (B) Spatial distribution of optical power along the optical fiber; (C) Frequency corresponding to peak optical power represents the center frequency of backscattered Brillouin light.

The distance Z between any scattering location along the optical fiber and the incident end of the pulsed light can be calculated using Equation 1:

$Z=\frac{cT}{2n}(1)$

Where: $c$ denotes the speed of light in vacuum; $n$ represents the refractive index of the optical fiber; $T$ is the time interval between the emitted pulse and the received scattered light.

The frequency shift of backscattered Brillouin light is simultaneously influenced by strain and temperature variations. Under laboratory-controlled constant-temperature conditions, temperature effects on Brillouin frequency shift are eliminated using a temperature compensation method. Under these conditions, the relationship between fiber strain and Brillouin frequency shift is expressed by Equation 2 (Zhang et al., 2019).

$v_B\left(\epsilon \right)=v_B\left(0\right)+\frac{d{V}_B\left(\epsilon \right)}{d\epsilon }\epsilon (2)$

Where: $v_B\left(\epsilon \right)$ denotes the Brillouin frequency shift at strain $\epsilon$; $v_B\left(0\right)$ represents the initial Brillouin frequency shift in the unstrained state; $\frac{d{V}_B\left(\epsilon \right)}{d\epsilon }$ is the strain sensitivity coefficient, with a magnitude of approximately 493 $MHz/\mu \epsilon$; $\epsilon$ is the strain applied to the sensing fiber.

2.2 Distributed optical fiber monitoring method for mining-induced overburden

Based on geological conditions of mining-disturbed rock masses and monitoring objectives, sensing optical cables are installed via borehole implantation. After positioning cables at target strata levels, boreholes are sealed using concrete grouting materials to ensure effective coupling between fibers and rock masses. Communication cables connect the borehole-collar fibers to an optical demodulator in the monitoring room. This enables acquisition of full-section strain distribution in borehole strata during longwall face advancement, facilitating analysis of overburden deformation characteristics during underground coal extraction. The schematic diagram of this distributed optical fiber monitoring system for mining-induced overburden deformation is presented in Figure 2.

Figure 2

Figure 2. Schematic diagram of distributed optical fiber monitoring for mining-induced overburden deformation.

3 Prediction model for mining-induced overburden deformation based on BP neural network

3.1 Data preprocessing

Deformation and failure of mining-induced overburden are governed by geological conditions of overlying strata and coal extraction parameters. This study selects seven primary governing factors influencing overburden deformation, as listed in Table 1.

Table 1

Table 1. Factors affecting deformation and failure of overlying strata during mining.

The width-to-depth ratio in Table 1 reflects the extraction sufficiency of coal seam mining, while the compressive-to-tensile strength ratio characterizes the rock brittleness index.

Given the disparate measurement units among governing factors in Table 1, accurate assessment of their individual impacts on overburden prediction accuracy is challenging. To ensure equivalent feature representation, dimensionless processing of all data is implemented using z-score standardization (He et al., 2024). The mathematical formulation is given by Equation 3:

$y_i=\frac{x_i-\overline{x}}{s}(3)$

Where: $y_i$ denotes the $i$-th value in the standardized data sequence; $x_i$ represents the $i$-th value in the original data sequence; $\overline{x}$ is the mean of the original data; $s$ is the standard deviation of the original data.

3.2 Prediction model training

According to dataset requirements for the BPNN model, the original data is partitioned into a training set and a testing set. The training set optimizes model parameters, while the testing set evaluates the model’s generalization capability. The workflow for establishing the prediction model is illustrated in Figure 3.

Figure 3

Figure 3. Development of mining-induced overburden prediction model.

In BP neural networks, strain data propagation follows a unidirectional path. Strain data transmits from the input layer through activation functions to hidden layers, then propagates to the output layer, completing one forward propagation cycle. The output values are compared against actual strain measurements via a loss function to compute prediction errors. These errors subsequently undergo backpropagation to update neuronal weights and biases. This process iterates until model convergence. Given that coal seam extraction disrupts in situ stress in overlying strata, the resulting stress evolution exhibits complex nonlinear behavior. Consequently, utilizing overburden strain data as training inputs leverages BPNN’s nonlinear fitting capability to approximate continuous nonlinear functions with high precision, enabling accurate input-output mapping.

To mitigate overfitting risks inherent in stochastic neural network training, the root mean square error (RMSE) function is selected as the BPNN loss function, expressed in Equation 4:

$Loss\left(\widehat{y},y,W\right)=\frac{1}{2}{‖\widehat{y}-y‖}_2^2(4)$

Where: $\widehat{y}$ denotes the predicted value from the model; $y$ represents the true value; $W$ is the parameter matrix of the model.

To prevent overfitting, L₂ regularization is applied to Equation 4, yielding the regularized loss function in Equation 5:

$Loss\left(\widehat{y},y,W\right)=\frac{1}{2}{‖\widehat{y}-y‖}_2^2+\frac{\alpha }{2}{‖W‖}_2^2(5)$

Where α is a non-negative hyperparameter that controls the penalty intensity of the L₂ regularization term on the model. Its value is determined through systematic hyperparameter optimization, which involves selecting the optimal value from a predefined parameter space based on the model’s average performance during 10-fold cross-validation. In this study, α is set to 0.001.

The coefficient of determination (R²) and root mean square error (RMSE) are adopted as complementary evaluation metrics to assess model accuracy. Their computational formulations are given by Equations 6, 7 (Rawal and Ahmad, 2024):

$R^2=1-\frac{{\displaystyle {\sum }_{i=1}^n}{\left(y_i-{\widehat{y}}_i\right)}^2}{{\displaystyle {\sum }_{i=1}^n}{\left(y_i-\overline{y}\right)}^2}(6)$

$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n}{\left(y_i-{\widehat{y}}_i\right)}^2}(7)$

Where $y_i$ represents the measured value of the $i$-th sample; ${\widehat{y}}_i$ represents the model-predicted value of the $i$-th sample; $\overline{y}$ denotes the mean of all measured values; $n$ is the total number of samples.

Higher values of the coefficient of determination (R²) and lower root mean square error (RMSE) indicate closer alignment between model predictions and actual measurements.

4 Physical similarity simulation testing for mining-induced overburden

4.1 Experimental design

4.1.1 Model configuration

Based on engineering geological survey data from Longwall Face 22,107 at Jinfeng Cuncaota Coal Mine, China, the 2^–2 coal seam has a mining thickness of 3 m and an average mining depth of 255 m. Physico-mechanical properties of the roof strata in this mine are presented in Table 2.

Table 2

Table 2. Physico-mechanical properties of roof strata in the 2^–2 coal seam.

Based on the physico-mechanical parameters of rock and soil strata in Table 2, similarity coefficients for the experimental model were determined by integrating similarity theory with laboratory facility constraints. The geometric dimensions and similarity coefficients of the physical model are presented in Table 3.

Table 3

Table 3. Geometric dimensions and similarity coefficients of the physical model.

The model utilized river sand, lime, gypsum, and other materials following the proportioning scheme for each rock stratum. This enabled the construction of a physical similarity model simulating mining-induced overburden strata for Longwall Face 22,107 at Jinfeng Cuncaota Coal Mine. Due to height constraints of the model, counterweights were applied above the (10) th siltstone layer to simulate the overburden pressure of the surface soil layer.

4.1.2 Overburden monitoring and coal seam extraction scheme

Four vertically oriented, tightly sheathed strain-sensitive optical fibers were deployed within the physical similarity model of mining-induced overburden. Their horizontal distances from the leftmost boundary were 50 cm, 120 cm, 180 cm, and 240 cm, respectively, labeled sequentially from left to right as A1, A2, A3, and A4. To enhance measurement accuracy, a fine sand layer was adhered to the external surface of each fiber during vertical embedding, ensuring intimate coupling with the surrounding rock mass. Prior to coal seam extraction, all sensing fibers were daisy-chained in series and connected to a BOTDR demodulator. Figure 4 illustrates the fiber layout and testing scheme within the model.

Figure 4

Figure 4. The layout and testing scheme of the sensing optical fibers in the model.

This experiment employed an AV6419 BOTDR strain demodulator to collect strain distribution data in overburden strata during coal extraction. Within the model, coal mining commenced from the open-off cut at 50 cm from the left boundary. With each mining step advancing the working face by 5 cm, strain data along the optical fibers were acquired after strata stabilization following each excavation increment.

4.2 Deformation evolution characteristics of mining-induced overburden

The key stratum refers to a rock layer that controls the movement of partially or entirely overlying strata up to the surface within the mining area. The methodology for identifying key stratum positions in overburden involves three sequential steps: first, locating competent strata upward from the coal seam; second, calculating the fracturing span of each competent stratum; and third, comparing these fracturing spans to determine key stratum positions (Zhang et al., 2021).

The criterion for identifying competent strata is given by Equation 8:

$E_{m+1}{h}_{m+1}^2{\displaystyle \sum _{i=1}^m}{h}_i{\gamma }_i>{\gamma }_{m+1}{\displaystyle \sum _{i=1}^m}{E}_i{h}_i^3(8)$

Where: $h_i$, ${\gamma }_i$, $E_i$ denote the thickness, unit weight, and elastic modulus of the i-th stratum (i = 1,2, … ,m), respectively.

The fracturing span $l_k$ of the $k$-th competent stratum is calculated using Equation 9:

$l_k=h_k\frac{{2\sigma }_k}{q_k}(9)$

Where $h_k$ is the thickness (m) of the $k$-th competent stratum, ${\sigma }_k$ denotes its tensile strength (MPa), and $q_k$ represents the load borne (MPa) by the $k$-th competent stratum.

Based on Equations 8, 9, the positions of competent strata and their fracturing spans in the overburden were calculated, revealing four competent strata above the No. 2^–2 coal seam: Stratum (5) (fine sandstone), Stratum (7) (fine sandstone), Stratum (9) (medium sandstone), and Stratum (10) (siltstone), with fracturing spans of $l_1$ = 11.4 m, $l_2$ = 20.47 m, $l_3$ = 9.23 m, $l_4$ = 17.91 m. Because of $l_2>l_4>l_1>l_3$, Stratum (7) (fine sandstone) is identified as the primary key stratum while the remaining three constitute secondary key strata.

This study focuses on the vertically installed A3 sensing optical fiber within the overburden strata. Strain curves measured after the passage of the 2^–2 coal seam working face through the A3 monitoring cross-section were selected to analyze deformation and failure characteristics of the overburden. The corresponding mining-induced strain distribution curves in the overburden are presented in Figure 5.

Figure 5

Figure 5. Mining-induced strain distribution curves in overburden strata.

Analysis of Figure 5 reveals that coal extraction induces overburden movement toward the goaf area, placing the strata under tensile stress. As the working face advances, the tensile strain zone progressively expands within the overburden. Based on measured strain data and applying the discrimination methodology for water-flowing fractured zone development height (Piao et al., 2021), the observed development heights of the caved zone and fractured zone are identified at 10 cm and 35 cm above the coal seam roof, respectively.

Deformation and failure characteristics of mining-induced overburden in the physical model are illustrated in Figure 6.

Figure 6

Figure 6. Deformation and failure characteristics of mining-induced overburden.

Based on Figures 5, 6, the deformation of mining-induced overburden strata undergoes three evolutionary stages following the passage of the 2^–2 coal seam working face through the A3 monitoring section: Stage I features minimal strain curve fluctuations as the immediate roof remains intact bearing overburden pressure when the face advances 15 cm beyond A3; Stage II exhibits strain concentration in the caved zone 10 cm above the coal seam roof due to immediate roof collapse at 20–25 cm advancement, coupled with progressive bed separation between the (5)th layer fine-grained sandstone (sub-key stratum) and underlying strata—induced by its stiff lithology—causing secondary strain concentration at 35 cm above the roof; Stage III shows strata above the fractured zone undergoing integral subsidence to form a bending subsidence zone as the (7)th layer fine-grained sandstone (primary key stratum) controls overlying movement, with strains asymptotically approaching zero while the caved zone height stabilizes near 9.5 cm above the roof. Analysis confirms that mining-induced overburden failure is principally governed by primary and sub-key strata, with measured strain magnitudes and gradients demonstrating fundamental consistency with physically modeled failure heights—validating the reliability of distributed optical fiber sensing (DOFS) for overburden deformation monitoring.

4.3 Deformation prediction model for mining-induced overburden

To construct and validate the Backpropagation Neural Network (BPNN) prediction model, this study utilized raw strain data acquired from the A3 sensing optical fiber throughout the full monitoring period as the total sample set. To ensure robust model generalization, the complete dataset was randomly partitioned into two independent subsets: a training set and a test set. Specifically, 70% of the total samples were allocated to the training set for model development and parameter tuning, while the remaining 30% were reserved as the test set, which was strictly isolated during training and solely used for final evaluation of the model’s predictive performance. This partitioning strategy adheres to standard machine learning protocols, effectively mitigating overfitting and ensuring the model’s applicability and reliability on unseen data.

Based on the factors influencing mining-induced overburden deformation and failure listed in Table 1, the number of input neurons in the neural network was set to seven. A 10-fold cross-validated grid search was employed to determine the network architecture, resulting in two hidden layers with 10 and 5 neurons, respectively, and a single-neuron output layer, thereby finalizing the 7-10-5-1 network topology. The structure of the BPNN-based overburden prediction model is illustrated in Figure 7.

Figure 7

Figure 7. Architecture of BPNN-based overburden prediction model.

Utilizing the BPNN-based overburden prediction model structure depicted in Figure 7, 70% of the strain data measured by the A3 sensing optical fiber in the similarity model test were designated as the training set, with the remaining 30% allocated as the test set. The model was trained using the training dataset to output predicted strain values, which were then compared against the test set data to evaluate prediction performance. For model parameter optimization, the training set underwent 10-fold cross-validation to solve numerically optimal solutions for nonlinear minimization (Cao et al., 2024). The relationship between training epochs and root mean square error (RMSE) for the prediction model is illustrated in Figure 8.

Figure 8

Figure 8. Relationship between model training epochs and root mean square error.

As shown in Figure 8, the prediction model demonstrates rapid convergence during training. The root mean square error (RMSE) decreases significantly and stabilizes after 10 epochs, reaching 0.03 by the 98th epoch—meeting model precision requirements. Fitting analysis of computational results yields test-set coefficients of determination (R²) consistently exceeding 0.98, with no severe overfitting or underfitting observed, indicating robust model generalization capability.

To evaluate prediction accuracy, model training results were compared against test dataset values. Following passage of the 2^–2 coal seam working face through the A3 monitoring section, mining-induced strain values within the 25–45 cm face advancement range were selected to predict overburden strain distribution during mining progression, as illustrated in Figure 9.

Figure 9

Figure 9. Comparison between measured and model-predicted strain values in overburden strata.

As evidenced in Figure 9, the strain values predicted by the BPNN-based model closely align with measured strain data in the overburden strata, demonstrating that the neural network effectively captures the actual deformation behavior of rock strata and exhibits strong applicability.

5 Error analysis of mining-induced overburden strain prediction

5.1 Error analysis of predicted strain values

To ascertain model prediction accuracy, measured and predicted strain values at the caved zone (10 cm above coal seam roof) and fractured zone (35 cm above coal seam roof) were selected for relative error calculation, with comparative results presented in Figure 10.

Figure 10

Figure 10. Error analysis between measured and predicted strain values at caved zone and fractured zone locations.

As shown in Figure 10, the relative error between the predicted and measured overburden strain values is less than 5%, indicating high overall prediction reliability of the model. However, the error distribution exhibits slight spatial variations, characterized by “overestimation in the caved zone and underestimation in the fractured zone.” In the caved zone, the inadequate coupling between the optical fiber and the fractured rock mass results in the measured strain data representing averaged values over a certain length. This averaging effect leads to measured strains being smaller than the actual local strains, consequently causing the predicted values in the caved zone to appear relatively larger compared to the measurements. In the fractured zone, although the actual rock deformation is minor and the measured strains are generally low, localized high strains occur at fracture openings within limited areas. To achieve overall prediction stability, the model “sacrifices” accuracy at these localized high-strain peaks, effectively smoothing the predictions toward the predominant low-strain background. As a result, the predicted high-strain peaks in the fractured zone are “pulled down” closer to the surrounding broader low-strain regions, leading to the observed underestimation in this zone.

5.2 Applicability assessment of prediction model

Model performance was evaluated using the coefficient of determination (R²) and root mean square error (RMSE) metrics. Predictive accuracy of both Backpropagation Neural Network (BPNN) and Kernel Ridge Regression (KRR) models for overburden strain is comparatively assessed, with model evaluation results presented in Figure 11.

Figure 11

Figure 11. Accuracy assessment of the strain prediction model.

As shown in Figure 11, the prediction models based on BPNN and Kernel Ridge Regression exhibit progressively declining R² values and increasing RMSE values with advancing mining steps. The BPNN model demonstrates R² values approaching 1 initially, which gradually decrease over time. Nevertheless, even at the fifth mining step, the BPNN achieves R² = 0.90 with RMSE<10%, confirming its high accuracy in predicting mining-induced overburden strain. Conversely, the Kernel Ridge Regression model yields test-set R² values consistently below 0.85 and higher RMSE than the BPNN model, indicating significantly inferior predictive performance for overburden strain.

6 Conclusion

The study yielded the following key findings:

1. Through analysis of overburden geological conditions and coal extraction parameters in underground mining, seven primary governing factors influencing mining-induced overburden deformation were identified. The ten-fold cross-validation method was employed to adjust parameters of the model training dataset, establishing a 7-10-5-1 neural network architecture for mining-induced overburden. Physical similarity modeling of Longwall Face 22,107 at Jinfeng Cuncaota Coal Mine predicted overburden strain values and evaluated prediction model accuracy. Results demonstrate close alignment between BPNN-predicted and measured strain values (R² = 0.90, RMSE<10% at the fifth mining stage), exhibiting high applicability.

2. Physical similarity modeling of mining-induced overburden strata at Jinfeng Cuncaota Coal Mine yielded strain distribution curves that revealed three evolutionary deformation stages, fundamentally governed by main roof caving and key stratum positioning. Based on strain magnitude and gradient characteristics, development heights of the caved and fractured zones were determined at 10 cm and 35 cm above the coal seam roof, respectively—consistent with actual failure patterns. Comparative analysis demonstrated <5% relative error between predicted and measured values, validating distributed optical fiber sensing (DOFS) as an effective technology for accurately capturing strain evolution characteristics in mining-induced overburden deformation monitoring.

3. In mining-induced overburden monitoring, the performance of monitoring instruments directly dictates the data acquisition frequency. The BOTDR instrument employed in this study operates on a frequency-scanning principle, which prevents real-time monitoring of overburden deformation. However, the model developed in this research serves as a post-processing analytical tool that, when provided with real-time monitoring data, enables real-time prediction of deformation and failure states in mining-induced overburden strata.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

JL: Writing – review and editing, Methodology, Software, Writing – original draft, Resources. CP: Funding acquisition, Formal Analysis, Writing – review and editing, Project administration, Supervision, Conceptualization. YY: Writing – review and editing, Investigation, Data curation. YL: Validation, Visualization, Writing – review and editing. HL: Writing – review and editing, Data curation. WD: Data curation, Writing – review and editing.

Funding

The author(s) declared that financial support was not received for this work and/or its publication.

Conflict of interest

Author JL was employed by Shenhua Geological and Exploration Company Ltd.

The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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