Marketing mix modeling in Python: a step-by-step guide for B2C brands
Analytical Alley Team
Marketing Analytics Experts

Building your own marketing mix modeling workflow in Python gives you full control over how you measure incremental impact acros...
Building your own marketing mix modeling workflow in Python gives you full control over how you measure incremental impact across channels. This guide walks through data preparation, Bayesian model specification, diagnostics, and ROI attribution with practical code examples for B2C marketing strategists and data teams.
Why Python for marketing mix modeling
Python offers the statistical rigor and flexibility needed for econometric analysis without expensive proprietary software. You can implement Bayesian approaches that produce probability ranges rather than single-point estimates, which better accounts for the uncertainty inherent in marketing effectiveness measurement. Bayesian statistical frameworks are increasingly standard for MMM, providing more robust estimates than classical regression alone.
The typical workflow requires at least two years of weekly data to capture seasonal patterns and marketing response curves. For B2C brands operating in European markets where privacy restrictions limit user-level tracking, aggregate modeling in Python becomes essential for reliable ROI measurement.
Data preparation and structuring
Your first task is assembling a clean time-series dataset. Each row represents one observation period (typically one week), and columns include all marketing spend, business KPIs, and external control variables.
import pandas as pd
import numpy as np
# Load your historical data
data = pd.read_csv('marketing_data.csv')
# Ensure date column is datetime
data['date'] = pd.to_datetime(data['date'])
data = data.sort_values('date').reset_index(drop=True)
# Check for missing values
print(data.isnull().sum())
# Basic structure: one row per week
print(data.head())
Your dataframe should include media spend columns (TV, paid search, paid social, display, radio, print, outdoor as separate columns for each channel), media delivery metrics (impressions, reach, GRPs where available), business KPI (revenue or sales volume), control variables (promotions, pricing changes, seasonality indicators, weather, economic indicators), and a date column for chronological ordering. Key data inputs for MMM also encompass print and online display ads, paid search, direct mail, radio and TV ads, social media, plus seasonal factors, weather conditions, and economic indicators like inflation and consumer confidence.
Handle missing values carefully. For spend data, zero often means you did not invest that week rather than missing data. For continuous metrics like temperature or stock prices, interpolate or use forward-fill. Document any outliers (major sales events, product launches) so they can be controlled for in modeling.
# Fill zeros for channels where no spend occurred
spend_cols = ['tv_spend', 'search_spend', 'social_spend', 'display_spend']
data[spend_cols] = data[spend_cols].fillna(0)
# Interpolate external variables
data['temperature'] = data['temperature'].interpolate(method='linear')
data['cpi'] = data['cpi'].fillna(method='ffill')
# Create week-of-year seasonality dummies
data['week'] = data['date'].dt.isocalendar().week
Check for multicollinearity between channels. If two variables move together (correlation above 0.8), the model struggles to separate their individual effects. Use variance inflation factors (VIF) to detect problematic collinearity and consider combining correlated channels or applying informative Bayesian priors to constrain coefficients.
from statsmodels.stats.outliers_influence import variance_inflation_factor
# Calculate VIF for each channel
vif_data = pd.DataFrame()
vif_data['feature'] = spend_cols
vif_data['VIF'] = [variance_inflation_factor(data[spend_cols].values, i)
for i in range(len(spend_cols))]
print(vif_data)
# VIF > 10 indicates high multicollinearity
Scale your variables so coefficients reflect true effectiveness rather than arbitrary units. Standardization (mean 0, standard deviation 1) works well for interpretation, though min-max scaling preserves zero as zero.
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
data[spend_cols] = scaler.fit_transform(data[spend_cols])
This marketing mix modeling data science groundwork ensures your downstream estimates are reliable. Poor data quality produces misleading ROI numbers regardless of modeling sophistication.
Transformation functions: adstock and saturation
Marketing effects rarely occur instantaneously or linearly. Adstock models carryover (how last week's TV ad still influences this week's sales), while saturation curves capture diminishing returns (doubling spend does not double impact).
Implementing adstock transformation
Adstock represents lagged, decaying influence using a geometric decay parameter theta:
def adstock_transform(x, theta):
"""
Apply adstock transformation to spending array.
Parameters:
x : array-like, spending by period
theta : float, carryover rate (0 to 1)
Returns:
array of adstocked values
"""
adstocked = np.zeros(len(x))
adstocked[0] = x[0]
for t in range(1, len(x)):
adstocked[t] = x[t] + theta * adstocked[t-1]
return adstocked
# Apply adstock to TV with theta=0.6 (typical for video/brand channels)
data['tv_adstock'] = adstock_transform(data['tv_spend'].values, theta=0.6)
# Apply adstock to paid search with theta=0.3 (typical for lower-funnel)
data['search_adstock'] = adstock_transform(data['search_spend'].values, theta=0.3)
Typical theta ranges vary by channel. Video, TV and brand channels typically fall between 0.5 and 0.7. Display and social sit in the 0.3 to 0.5 range. Paid search usually ranges from 0.2 to 0.4, while email and direct response cluster between 0.1 and 0.3.
Implementing saturation transformation
The Hill saturation curve models diminishing returns:
def hill_saturation(x, alpha, K):
"""
Apply Hill saturation transformation.
Parameters:
x : array-like, adstocked spending
alpha : float, shape parameter (controls steepness)
K : float, half-saturation point
Returns:
array of saturated values
"""
return x**alpha / (K**alpha + x**alpha)
# Apply saturation after adstock
data['tv_transformed'] = hill_saturation(
data['tv_adstock'].values,
alpha=1.5,
K=np.median(data['tv_adstock'])
)
data['search_transformed'] = hill_saturation(
data['search_adstock'].values,
alpha=2.0,
K=np.median(data['search_adstock'])
)
Always apply adstock first, then saturation. This order reflects reality: carryover accumulates spend over time, and the accumulated exposure saturates. Higher alpha values create steeper curves (faster saturation), while K sets the spend level at which you reach half of maximum effect. Accounting for diminishing returns through adstock modeling is a critical best practice in MMM.
For initial modeling, use conservative priors or grid-search to find theta and alpha values that maximize out-of-sample prediction accuracy. More sophisticated approaches estimate these parameters directly within the Bayesian model.
Building a Bayesian regression model with PyMC
Bayesian methods shine in marketing mix modeling because they quantify uncertainty and allow you to encode domain knowledge through priors. The Bayesian statistical approach provides probability ranges of outcomes rather than single-point estimates, which better accounts for uncertainty in marketing effectiveness. PyMC is Python's leading library for probabilistic programming.
Basic model specification
Start with a linear additive structure where sales decompose into baseline (non-marketing drivers), marketing effects, control effects, and residual error. Base sales are influenced by non-marketing factors like seasonality and pricing, while incremental sales are driven by marketing activities.
import pymc as pm
import arviz as az
# Prepare modeling data
y = data['revenue'].values
X_marketing = data[['tv_transformed', 'search_transformed',
'social_transformed', 'display_transformed']].values
X_controls = data[['promotion_dummy', 'holiday_dummy',
'temperature', 'week_sin', 'week_cos']].values
with pm.Model() as mmm_model:
# Baseline intercept
baseline = pm.Normal('baseline', mu=y.mean(), sigma=y.std())
# Marketing coefficients (constrained positive via Half-Normal)
beta_marketing = pm.HalfNormal('beta_marketing',
sigma=10,
shape=X_marketing.shape[1])
# Control coefficients (can be positive or negative)
beta_controls = pm.Normal('beta_controls',
mu=0,
sigma=5,
shape=X_controls.shape[1])
# Linear predictor
mu = baseline + pm.math.dot(X_marketing, beta_marketing) + pm.math.dot(X_controls, beta_controls)
# Likelihood with noise term
sigma = pm.HalfNormal('sigma', sigma=y.std())
likelihood = pm.Normal('revenue', mu=mu, sigma=sigma, observed=y)
This specification encodes reasonable assumptions: marketing spend should have positive impact (HalfNormal priors prevent negative coefficients), while control variables can go either way. The baseline captures average revenue when all inputs are zero (after standardization).
Fitting the model
Use MCMC sampling to estimate posterior distributions:
with mmm_model:
# Sample from posterior
trace = pm.sample(2000, tune=1000, chains=4,
target_accept=0.95,
return_inferencedata=True)
# Check convergence diagnostics
print(az.summary(trace, var_names=['baseline', 'beta_marketing', 'sigma']))
# R-hat should be < 1.01 for all parameters
# Effective sample size should be > 400 per chain
Convergence diagnostics are critical. R-hat values above 1.01 indicate chains have not mixed properly (try more tuning steps or reparameterize). Low effective sample size means autocorrelation is high (increase sampling iterations). Target R-hat below 1.01 and effective sample size above 1000 for all key parameters.
Interpreting posterior distributions
Unlike frequentist point estimates, Bayesian posteriors give you full probability distributions:
# Extract posterior samples
posterior = trace.posterior
# Marketing channel coefficients
tv_coef = posterior['beta_marketing'].sel(beta_marketing_dim_0=0).values.flatten()
search_coef = posterior['beta_marketing'].sel(beta_marketing_dim_0=1).values.flatten()
# Calculate posterior means and credible intervals
print(f"TV coefficient: {tv_coef.mean():.2f} (95% CI: {np.percentile(tv_coef, 2.5):.2f} to {np.percentile(tv_coef, 97.5):.2f})")
print(f"Search coefficient: {search_coef.mean():.2f} (95% CI: {np.percentile(search_coef, 2.5):.2f} to {np.percentile(search_coef, 97.5):.2f})")
A coefficient mean of 3.2 with a 95% credible interval of [2.8, 3.6] means every standardized euro in search generates roughly €3.20 in incremental revenue, and you can be 95% confident the true value lies between €2.80 and €3.60. Narrow intervals indicate precise estimates; wide intervals signal data limitations or high uncertainty.
Model validation and diagnostics
Rigorous validation ensures your model produces reliable business decisions rather than spurious correlations.
In-sample fit metrics
from sklearn.metrics import r2_score, mean_absolute_percentage_error
# Generate predictions from posterior mean
with mmm_model:
posterior_pred = pm.sample_posterior_predictive(trace)
y_pred = posterior_pred.posterior_predictive['revenue'].mean(dim=['chain', 'draw']).values
# R-squared
r2 = r2_score(y, y_pred)
print(f"R-squared: {r2:.3f}")
# MAPE
mape = mean_absolute_percentage_error(y, y_pred) * 100
print(f"MAPE: {mape:.2f}%")
R-squared above 0.80 is standard for reliable models. Values below 0.70 suggest missing variables or poor specification. MAPE thresholds: below 5% is excellent, 5 to 10% is good, above 15% is problematic and requires investigation.
Residual analysis
Plot residuals to detect patterns that indicate model misspecification:
import matplotlib.pyplot as plt
residuals = y - y_pred
# Time series plot
plt.figure(figsize=(12, 4))
plt.plot(data['date'], residuals)
plt.axhline(0, color='red', linestyle='--')
plt.title('Residuals over time')
plt.xlabel('Date')
plt.ylabel('Residual')
plt.show()
# Q-Q plot for normality
from scipy import stats
fig, ax = plt.subplots(figsize=(6, 6))
stats.probplot(residuals, dist="norm", plot=ax)
plt.title('Q-Q plot of residuals')
plt.show()
Residuals should look like random noise. Systematic patterns (trends, cycles, clusters) mean your model is missing something important. Non-normal residuals suggest outliers or the need for transformation.
Out-of-sample validation
Reserve the most recent 15 to 20% of data as a holdout set to test predictive accuracy:
# Split data chronologically
train_size = int(0.8 * len(data))
train_data = data.iloc[:train_size]
test_data = data.iloc[train_size:]
# Refit model on training data only
y_train = train_data['revenue'].values
X_marketing_train = train_data[['tv_transformed', 'search_transformed',
'social_transformed', 'display_transformed']].values
X_controls_train = train_data[['promotion_dummy', 'holiday_dummy',
'temperature', 'week_sin', 'week_cos']].values
# Fit model as before with training data
# Predict on test set
X_marketing_test = test_data[['tv_transformed', 'search_transformed',
'social_transformed', 'display_transformed']].values
X_controls_test = test_data[['promotion_dummy', 'holiday_dummy',
'temperature', 'week_sin', 'week_cos']].values
# Generate predictions
with mmm_model:
mu_test = (posterior['baseline'].mean().values +
(X_marketing_test @ posterior['beta_marketing'].mean(dim=['chain', 'draw']).values) +
(X_controls_test @ posterior['beta_controls'].mean(dim=['chain', 'draw']).values))
y_test = test_data['revenue'].values
test_mape = mean_absolute_percentage_error(y_test, mu_test) * 100
print(f"Test MAPE: {test_mape:.2f}%")
Holdout MAPE should be within 2 to 3 percentage points of training MAPE. Larger gaps indicate overfitting. If test performance degrades significantly, simplify the model (fewer parameters) or gather more data.
Coefficient plausibility checks
Review estimated coefficients for business sense:
# Check signs: marketing should be positive
marketing_coefs = posterior['beta_marketing'].mean(dim=['chain', 'draw']).values
print("Marketing coefficients (should be positive):")
for i, channel in enumerate(['TV', 'Search', 'Social', 'Display']):
print(f"{channel}: {marketing_coefs[i]:.2f}")
Negative marketing coefficients are red flags (unless you're explicitly modeling cannibalization). Coefficients that imply ROI above 10:1 for direct-response channels deserve scrutiny. Cross-reference with incrementality tests or historical performance when available.
Extracting ROI and attribution
Once validated, the model's primary output is incremental contribution and ROI by channel.
Calculating channel contributions
For each channel, multiply its transformed spend by its coefficient across all time periods:
# Get posterior mean coefficients
coef_tv = posterior['beta_marketing'].sel(beta_marketing_dim_0=0).mean().values
coef_search = posterior['beta_marketing'].sel(beta_marketing_dim_0=1).mean().values
coef_social = posterior['beta_marketing'].sel(beta_marketing_dim_0=2).mean().values
coef_display = posterior['beta_marketing'].sel(beta_marketing_dim_0=3).mean().values
# Calculate contributions (incremental revenue)
data['tv_contribution'] = data['tv_transformed'] * coef_tv
data['search_contribution'] = data['search_transformed'] * coef_search
data['social_contribution'] = data['social_transformed'] * coef_social
data['display_contribution'] = data['display_transformed'] * coef_display
# Sum to get total incremental revenue per channel
total_tv = data['tv_contribution'].sum()
total_search = data['search_contribution'].sum()
total_social = data['social_contribution'].sum()
total_display = data['display_contribution'].sum()
print(f"TV incremental revenue: €{total_tv:,.0f}")
print(f"Search incremental revenue: €{total_search:,.0f}")
print(f"Social incremental revenue: €{total_social:,.0f}")
print(f"Display incremental revenue: €{total_display:,.0f}")
These contributions represent incremental sales driven by each channel, controlling for all other factors. They answer: how much revenue would we lose if we turned off this channel?
Calculating ROI by channel
Divide incremental revenue by actual spend (in original units before standardization):
# Total spend per channel (use original unstandardized spend)
data_original = pd.read_csv('marketing_data.csv')
total_tv_spend = data_original['tv_spend'].sum()
total_search_spend = data_original['search_spend'].sum()
total_social_spend = data_original['social_spend'].sum()
total_display_spend = data_original['display_spend'].sum()
# Calculate ROI
roi_tv = (total_tv / total_tv_spend) * 100
roi_search = (total_search / total_search_spend) * 100
roi_social = (total_social / total_social_spend) * 100
roi_display = (total_display / total_display_spend) * 100
print(f"TV ROI: {roi_tv:.1f}%")
print(f"Search ROI: {roi_search:.1f}%")
print(f"Social ROI: {roi_social:.1f}%")
print(f"Display ROI: {roi_display:.1f}%")
Express ROI as percentage (200% means €2 revenue per €1 spent) or as a ratio (2:1). According to digital marketing return on investment research, typical B2C benchmarks show paid search delivering 200 to 400% ROI, paid social achieving 150 to 350%, and display generating 50 to 150%, though your results will vary by category, competition, and execution quality.
Marginal ROI for optimization
Average ROI tells you past performance; marginal ROI tells you where to invest the next euro. Derive marginal ROI from the saturation curve:
def marginal_roi(current_spend, coef, alpha, K, total_revenue, total_spend):
"""
Calculate marginal ROI at current spend level.
"""
# Derivative of Hill saturation function
numerator = alpha * K**alpha * current_spend**(alpha - 1)
denominator = (K**alpha + current_spend**alpha)**2
marginal_effect = coef * numerator / denominator
# Marginal ROI = marginal effect / marginal cost
marginal_roi = (marginal_effect / 1.0) * 100
return marginal_roi
# Example for TV at current spend level
current_tv = data_original['tv_spend'].mean()
tv_marginal_roi = marginal_roi(
current_spend=current_tv,
coef=coef_tv,
alpha=1.5,
K=np.median(data['tv_adstock']),
total_revenue=data_original['revenue'].sum(),
total_spend=total_tv_spend
)
print(f"TV marginal ROI at current spend: {tv_marginal_roi:.1f}%")
Optimal allocation equalizes marginal ROI across channels. If TV has 150% marginal ROI and search has 250%, you should shift budget from TV to search until their marginal returns converge. This is the core principle behind marketing mix optimization.
Decomposing total sales
Understand how much of your total sales comes from baseline versus marketing:
# Baseline contribution
baseline_contribution = posterior['baseline'].mean().values * len(data)
# Marketing contribution
marketing_contribution = (total_tv + total_search +
total_social + total_display)
# Control contribution
control_coefs = posterior['beta_controls'].mean(dim=['chain', 'draw']).values
data_original['promotion_contribution'] = (
data['promotion_dummy'] * control_coefs[0]
)
control_contribution = data_original['promotion_contribution'].sum()
# Total observed sales
total_sales = data_original['revenue'].sum()
print(f"Baseline: €{baseline_contribution:,.0f} ({baseline_contribution/total_sales*100:.1f}%)")
print(f"Marketing: €{marketing_contribution:,.0f} ({marketing_contribution/total_sales*100:.1f}%)")
print(f"Controls: €{control_contribution:,.0f} ({control_contribution/total_sales*100:.1f}%)")
print(f"Total: €{total_sales:,.0f}")
For typical B2C brands, baseline accounts for 40 to 70% of sales and marketing 30 to 60%. If marketing contribution seems too low, you may be underestimating long-term brand effects or missing channels. If it's too high, double-check for model overfitting or data quality issues.
Scenario planning and forecasting
The real payoff from MMM is forward-looking: simulate different spend plans to predict outcomes. MMM enables scenario testing to simulate how budget reallocation across channels would impact sales, providing data-driven guidance for marketing investment decisions.
Building scenario forecasts
# Define a future spend plan (e.g., next quarter)
future_weeks = 13
future_tv = np.full(future_weeks, 50000) # €50k per week
future_search = np.full(future_weeks, 30000)
future_social = np.full(future_weeks, 20000)
future_display = np.full(future_weeks, 15000)
# Transform future spend through adstock and saturation
future_tv_adstock = adstock_transform(future_tv, theta=0.6)
future_tv_transformed = hill_saturation(future_tv_adstock, alpha=1.5, K=np.median(data['tv_adstock']))
future_search_adstock = adstock_transform(future_search, theta=0.3)
future_search_transformed = hill_saturation(future_search_adstock, alpha=2.0, K=np.median(data['search_adstock']))
# Create future design matrix
X_future_marketing = np.column_stack([
future_tv_transformed,
future_search_transformed,
np.full(future_weeks, np.mean(data['social_transformed'])),
np.full(future_weeks, np.mean(data['display_transformed']))
])
X_future_controls = np.column_stack([
np.zeros(future_weeks),
np.zeros(future_weeks),
np.full(future_weeks, data['temperature'].mean()),
np.sin(2 * np.pi * np.arange(future_weeks) / 52),
np.cos(2 * np.pi * np.arange(future_weeks) / 52)
])
# Generate predictions from full posterior
baseline_samples = posterior['baseline'].values.flatten()
beta_marketing_samples = posterior['beta_marketing'].values.reshape(-1, X_marketing.shape[1])
beta_controls_samples = posterior['beta_controls'].values.reshape(-1, X_controls.shape[1])
predictions = []
for i in range(len(baseline_samples)):
mu_future = (baseline_samples[i] +
(X_future_marketing @ beta_marketing_samples[i]) +
(X_future_controls @ beta_controls_samples[i]))
predictions.append(mu_future.sum())
predictions = np.array(predictions)
# Report predictive distribution
print(f"Forecast revenue: €{predictions.mean():,.0f}")
print(f"90% credible interval: [€{np.percentile(predictions, 5):,.0f}, €{np.percentile(predictions, 95):,.0f}]")
Present scenarios with credible intervals to quantify risk. A forecast of €5.2M with a 90% interval of [€4.8M, €5.6M] communicates both expected value and downside or upside range. Finance teams and CFOs appreciate this transparency far more than overconfident point estimates.
Comparing scenarios
Simulate multiple allocation plans to identify the optimal strategy:
scenarios = {
'Current plan': {
'tv': 50000, 'search': 30000, 'social': 20000, 'display': 15000
},
'Shift to search': {
'tv': 40000, 'search': 45000, 'social': 20000, 'display': 10000
},
'Balanced increase': {
'tv': 55000, 'search': 35000, 'social': 25000, 'display': 15000
}
}
results = []
for name, spend in scenarios.items():
# Transform and predict (same process as above)
mean_revenue = predictions.mean()
total_spend = sum(spend.values()) * future_weeks
roi = (mean_revenue / total_spend) * 100
results.append({
'Scenario': name,
'Revenue': mean_revenue,
'Spend': total_spend,
'ROI': roi
})
scenario_df = pd.DataFrame(results)
print(scenario_df.sort_values('ROI', ascending=False))
This analysis powers strategic budget planning. If "Shift to search" delivers 15% higher ROI than "Current plan," that's a clear directional signal for reallocation. Remember to impose practical constraints (minimum spend thresholds, strategic objectives) rather than blindly following pure mathematical optimization.
Advanced considerations and next steps
This workflow provides a solid foundation, but production-grade MMM often requires additional sophistication.
Handling non-stationarity
If your business is growing rapidly or markets are shifting, coefficients may not be stable over time. Consider time-varying parameters:
# Example: allow baseline to trend
with pm.Model() as dynamic_model:
trend = pm.Normal('trend', mu=0, sigma=1)
time_index = np.arange(len(y))
baseline = pm.Normal('baseline_intercept', mu=y.mean(), sigma=y.std()) + trend * time_index
Or fit separate models for recent periods (last 12 months) if you suspect channel effectiveness has changed due to competition, creative fatigue, or platform algorithm updates.
Incorporating incrementality test results
If you've run geo-holdout experiments or conversion lift studies, use those results as informative priors:
# Example: Facebook lift study showed ROI between 1.5:1 and 2.5:1
with pm.Model() as calibrated_model:
# Informative prior for social coefficient based on lift study
beta_social = pm.TruncatedNormal('beta_social',
mu=2.0,
sigma=0.5,
lower=0)
This hybrid approach combines the strengths of MMM (comprehensive cross-channel) with the causal rigor of experiments.
Automating refresh cycles
For ongoing optimization, wrap your workflow in scheduled pipelines:
def run_mmm_pipeline(data_path, output_path):
"""
End-to-end MMM pipeline: load data, fit model, generate reports.
"""
# Load and prep data
data = load_and_prep_data(data_path)
# Fit model
trace = fit_bayesian_model(data)
# Validate
metrics = validate_model(trace, data)
# Calculate ROI
roi_results = calculate_roi(trace, data)
# Generate scenarios
scenarios = forecast_scenarios(trace, future_spend_plans)
# Save outputs
save_results(metrics, roi_results, scenarios, output_path)
return roi_results
Leading B2C organizations refresh MMM monthly or quarterly to capture changing market dynamics and course-correct budgets mid-cycle. Regular model iteration is among the critical best practices for maintaining accuracy.
Integrating with multi-touch attribution
Use MMM for cross-channel strategy and attribution for within-channel tactics. Calibrate attribution outputs with MMM incrementality to correct platform self-attribution bias. This hybrid measurement framework gives you both macro allocation guidance and micro creative optimization.
Taking the next step in marketing measurement
You now have a complete Python workflow to build, validate, and deploy marketing mix modeling for B2C brands. This approach quantifies incremental impact with statistical rigor, handles carryover and saturation realistically through transformations, and produces probabilistic forecasts that communicate uncertainty to stakeholders.
The fundamentals covered here (data prep, Bayesian regression, diagnostics, ROI calculation, scenario planning) form the backbone of professional MMM practice. From here, explore advanced extensions like hierarchical models for multi-brand portfolios, dynamic coefficients for non-stationary environments, or integrated models that jointly estimate media, pricing, and distribution effects.
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