Contributors
Index
In this project, we obtained multiple novel insights through computational simulations and wet lab experiments to validate the functionality of the LEAPS system.
For the Generator, we achieved substantial improvements in training efficiency by introducing a data augmentation method based on sequence shuffling of the training data. For the Predictor, we progressively improved prediction accuracy through the implementation of multiple data augmentation techniques (BLOSUM matrix-based similar amino acid substitutions and introduction of disruptive mutations) and custom dropout layers. Notably, the combination of these novel architectures enabled high prediction accuracy even with a limited training dataset of only 40 samples. Furthermore, integration of sequence likelihood scoring using EVmutation confirmed improvements in the quality of generated sequences.
Below, we report detailed results from notable experiments in the Predictor, Integrated System, and Wet Lab.
The predictor is the most critical component determining the performance of LEAPS. We designed and constructed this predictor as a regression model that takes vector representations generated by ESM2 as input. To enable effective learning even with small datasets, we devised and implemented multiple novel methods. Through these efforts, we successfully achieved prediction accuracy sufficient for practical use from extremely limited training data of only 40 samples. The following sections describe the progressive improvement of the Predictor’s performance.
While the ESM2 + LASSO regression model (previous model) demonstrated high performance in predicting fluorescence maximum wavelength, it showed poor correlation between predicted and measured values for brightness prediction, and it was impractical. The underlying cause was likely that LASSO regression, a linear model, could not adequately capture the complex nonlinear relationships inherent in brightness. Since brightness depends on diverse factors including chromophore formation efficiency, protein folding, and quantum yield, we determined that a model capable of learning nonlinear interactions was necessary. Therefore, in this cycle, we adopted random forest regression to improve brightness prediction accuracy.
In this cycle, we compared two models. The first was ESM2 + LASSO, which uses ESM2 embedding vectors (1280 dimensions × n residues) as features and predicts brightness through LASSO regression. The second was ESM2 + RF, which uses the same ESM2 embedding vectors as features but predicts brightness through random forest regression. For random forest regression, we used scikit-learn’s Random Forest Regressor with 1000 decision trees, while other parameters were set to default values. For training and testing, we used 40 sequences and brightness data obtained from FPbase, and employed the coefficient of determination (R² value) on test data as the evaluation metric.
Figure 1 shows ① the scatter plot and linear regression line with R² value for ESM2 + LASSO. These results confirmed almost no correlation between predicted and measured values. In contrast, Figure 2 shows ② the scatter plot and linear regression line with R² value for ESM2 + RF. Random forest regression demonstrated improved R² values compared to LASSO regression, clearly indicating enhanced prediction accuracy.
Random forest regression substantially improved brightness prediction accuracy compared to LASSO regression. While LASSO regression showed almost no correlation, random forest regression achieved improved R² values. This improvement can be attributed to the nonlinear learning capability of random forests. Brightness is a property involving complex interactions among multiple factors, and we infer that the decision tree-based random forest could flexibly learn interactions between features that linear models failed to capture. The results from this cycle demonstrate that models capable of capturing nonlinear relationships are necessary for high-accuracy prediction of complex properties.
Although the introduction of random forest regression maintained reasonable prediction accuracy even for challenging tasks such as brightness prediction, room for improvement remained, requiring the introduction of models with higher representational capacity. While random forest regression can learn nonlinear relationships, its learning mechanism is based on progressive partitioning by an ensemble of decision trees. In contrast, protein properties are thought to depend on complex interactions among multiple amino acid residues and hierarchical structural features. Neural networks were considered more suitable for learning such highly nonlinear and hierarchical feature representations.
Therefore, in this cycle, we introduced a neural network model constructed with fully connected layers on top of ESM2 embedding vectors. In fully connected layers, each input element is connected to all output elements, and by combining linear transformations using weight matrices with activation functions, complex nonlinear mappings can be learned. By stacking multiple fully connected layers, models can hierarchically extract features and represent more complex input-output relationships. Each layer’s nonlinear transformation of the previous layer’s output was expected to enable learning of higher-order feature interactions that simple linear models or random forests cannot capture.
We constructed a neural network regression model that takes Mean Pooling-processed ESM2 embedding vectors as input. Specifically, after extracting representation vectors (1280 dimensions × n residues) for each sequence from the pre-trained ESM2 model, we applied an attention mask-weighted Mean Pooling operation to aggregate them into a fixed-length vector of 1280 dimensions. The parameters of the ESM2 model were frozen and used as a fixed feature extractor.
The neural network architecture consisted of a first layer with a fully connected layer from 1280 to 640 dimensions followed by ReLU activation, and a second layer with a fully connected layer from 640 to 1 dimension. Only the parameters (weights and biases) of these fully connected layers were trained and optimized for the regression task. For training data, we used a brightness dataset of 40 sequences obtained from FPbase. Model training was performed using PyTorch, with mean squared error (MSE) as the loss function and Adam (learning rate 0.001) as the optimization algorithm. Training was conducted for 100 epochs with early stopping and hyperparameter optimization using Optuna. Model prediction accuracy was evaluated by the coefficient of determination (R²) on test data.
Figure 2 shows a scatter plot of predicted versus measured brightness on test data. Pink circles represent prediction results from random forest regression + Max Pooling, and green circles represent prediction results from ESM2 + fully connected layers. The dashed line represents the diagonal indicating ideal prediction (predicted value = measured value). ESM2 + fully connected layers clearly demonstrated superior prediction performance compared to random forest regression + Max Pooling.
The introduction of a neural network model with fully connected layers constructed on ESM2 embedding vectors confirmed improved prediction accuracy compared to random forest regression. This can be attributed to the multi-layer fully connected architecture hierarchically extracting features and learning higher-order feature interactions that random forests could not capture. In particular, through gradient descent optimization, the model could selectively extract information truly necessary for brightness prediction from ESM2’s representation space and learn smooth, continuous mappings, which we infer contributed to improved prediction accuracy for unknown sequences.
Although the introduction of a neural network model with fully connected layers achieved improved prediction accuracy, neural networks’ high representational capacity comes with many parameters, making them prone to overfitting. With a limited sample size of approximately 40 sequences, the risk of overfitting posed a serious challenge. To prevent overfitting and improve model generalization performance, effective expansion of the training data itself was considered beneficial in addition to introducing regularization methods. However, simple random sequence mutations could potentially destroy protein structure and function, making them biologically invalid data augmentation.
Therefore, in this cycle, we introduced a data augmentation method based on function-preserving mutations utilizing the BLOSUM62 substitution matrix. BLOSUM62 is a matrix indicating scores for evolutionarily conserved amino acid substitutions, based on substitution patterns actually observed in nature. Positive scores indicate substitutions that occur frequently during evolution, meaning substitutions that tend to maintain protein function, while negative scores indicate rare substitutions that tend to impair function.
In this method, by allowing only substitutions to similar amino acids with BLOSUM62 scores of positive or zero or higher, we achieve sequence mutations within a range that does not significantly impair protein function. Generated sequences are assigned labels by adding small noise to the original label values, thereby expanding the training data. This method was expected to enable generation of biologically meaningful diverse sequence variations from limited experimental data, allowing the model to make robust predictions against slight sequence changes.
The basic structure of the prediction model consisted of ESM2 embedding vectors, Mean Pooling, and two fully connected layers (1280 dimensions → 640 dimensions → 1 dimension). For data augmentation implementation, we introduced function-preserving mutations based on the BLOSUM62 matrix to sequences randomly sampled from existing training data. Specifically, we randomly selected X positions in each sequence and substituted the amino acid at those positions with similar amino acids having BLOSUM62 scores of positive or zero or higher. Generated mutant sequences were assigned labels by adding random noise within ±10% to the original sequence label values.
Through this operation, we generated X additional mutant sequences for the original 40 training sequences, training the model on an expanded dataset of (40 + X) total sequences. Training settings included MSE as the loss function and Adam as the optimization algorithm, with 100 epochs of training, early stopping, and hyperparameter optimization using Optuna.
Figure 3 shows a scatter plot of predicted versus measured brightness on test data. Green circles represent prediction results from ESM2 + fully connected layers, and yellow-green circles represent prediction results from ESM2 + fully connected layers + data augmentation. The dashed line represents the diagonal indicating ideal prediction (predicted value = measured value). ESM2 + fully connected layers + data augmentation clearly demonstrated superior prediction performance.
The introduction of data augmentation through function-preserving mutations utilizing the BLOSUM62 substitution matrix confirmed improved prediction accuracy compared to models without data augmentation. This can be attributed to the addition of biologically valid sequence variations enabling more stable learning even with limited experimental data, thereby improving model generalization performance.
The critical aspect of this method is permitting only substitutions to evolutionarily similar amino acids based on the BLOSUM62 matrix. While random mutations include substitutions that destroy protein function and impede model learning, function-preserving mutations based on BLOSUM62 follow substitution patterns actually observed in nature, generating sequences with activity similar to the original sequences and enabling biologically valid data augmentation. Since mutant sequences generated by this method are similar to yet subtly different from original sequences, they prevent the model from overfitting to specific sequence patterns and promote robust learning that does not overreact to slight sequence changes, enabling stable predictions for unknown sequences.
We previously implemented data augmentation through conservative mutations based on the BLOSUM62 matrix to generate biologically plausible sequence variations from limited experimental data, thereby improving model generalization performance.
However, models trained exclusively on conservative mutations faced a critical limitation. While these models could learn features of functional sequences, they lacked exposure to non-functional sequences, creating a risk of predicting high activity values for sequences with little to no actual function. This issue becomes particularly problematic in iterative optimization cycles that combine predictive and generative models. When the predictor incorrectly assigns high activity to non-functional sequences, the generator learns erroneous patterns and produces progressively lower-quality sequences in subsequent cycles, creating a detrimental feedback loop.
In this cycle, we introduced data augmentation via deleterious mutations—intentional disruptions to protein function—alongside conservative mutations. The objective was to enable the model to properly discriminate between functional and non-functional sequences. Specifically, we leveraged the masked prediction capability of ESM models to quantify the importance of each amino acid position, then performed non-conservative substitutions with negative BLOSUM62 scores at critical positions to artificially generate low-activity sequences.
The predictor architecture consisted of ESM2 embedding vectors with mean pooling, followed by two fully connected layers (1280 dimensions → 640 dimensions → 1 dimension), identical to Cycle 4.2 (engineering).
Data augmentation was implemented in two stages:
Stage 1: Conservative Mutations Following Cycle 4.2 (engineering), we introduced conservative mutations through substitutions with positive BLOSUM62 scores.
Stage 2: Deleterious Mutations (Novel) For each sequence in the training data, we generated low-activity sequences through the following procedure:
Using ESM2’s masked language modeling capability, we sequentially replaced each position with a mask token and calculated the log probability of the original amino acid to evaluate positional importance
Calculated the mean importance score for each sequence and selected target sequences for disruption via weighted sampling
From the top 3N positions with highest importance scores, we sampled N positions with probability proportional to their scores
Executed non-conservative substitutions with BLOSUM62 scores of -1 or lower at selected positions
Assigned an extremely low activity value of 1e-6 as the label for generated disrupted sequences
Training configuration included MSE loss function, Adam optimizer, 100 epochs, early stopping, and hyperparameter optimization via Optuna. The training dataset comprised brightness measurements from 40 sequences obtained from FPbase.
Figure 4 shows violin plots of predicted values for non-functional sequences (activity value 0). Yellow-green represents predictions using conservative mutations only, while blue represents predictions using conservative mutations plus deleterious mutations. Both models predicted high activity values for non-functional sequences, indicating inadequate discrimination of non-functional sequences.
Introduction of deleterious mutations as data augmentation demonstrated improved prediction accuracy for functional sequences and suppression of overfitting. The low-activity sequences generated through deleterious mutations likely functioned as negative samples, providing a regularization effect that prevented the model from overfitting to specific patterns in the training data.
However, we did not achieve the expected improvement in discriminating non-functional sequences, which was the primary objective of this cycle. Despite adding deleterious mutations to the training data, the tendency to predict high activity values for truly non-functional sequences (zero activity) persisted.
In iterative optimization combining predictive and generative models, reliance on a predictor that cannot properly identify non-functional sequences provides erroneous signals to the generator, triggering a cascade of quality degradation. To address this issue, we need methods to identify and exclude non-functional sequences independently of the predictor. Additionally, explicit reporting of R² scores for both training and test data would enable quantitative evaluation of overfitting suppression effects.
Data augmentation via deleterious mutations improved prediction accuracy for functional sequences and suppressed overfitting. However, given our small dataset of 40 sequences trained in the high-dimensional 1280-dimensional ESM2 embedding space, room remained for generalization performance improvement.
The primary challenge is the risk of the model incorrectly learning spurious correlations or noisy features as true activity determinants. This parallels the background correlation problem in object detection.
While standard random dropout prevents excessive dependence on specific features, it treats essential features and noisy features equally. Therefore, in this cycle, we introduced custom dropout based on the coefficient of variation (CV). The core hypothesis is that “feature dimensions showing high variation across samples within a batch are likely spurious correlations or noise.” High-CV dimensions are unstable across samples and likely represent dataset-specific noise rather than universal activity determinants. Conversely, low-CV dimensions show consistent values and likely reflect essential contributions to activity.
This approach aimed to protect consistently important biophysical features across sequences in the ESM2 embedding space (such as hydrophobicity patterns and secondary structure propensities) while suppressing dataset-specific artifacts.
Custom dropout was implemented as follows. During training, for each batch’s feature vectors (1280 dimensions), we calculated the standard deviation σ and median for each dimension, then computed the coefficient of variation CV = σ / (|median| + ε), where ε = 1e-8 for numerical stability. We identified the top 50% of dimensions (640 dimensions) with highest CV and generated a mask to set their values to zero. A scaling factor of 1 / (1 - 0.5) = 2.0 was applied to preserve expected values. During inference, no dropout was applied and all dimensions were utilized.
We continued the two-stage data augmentation (conservative mutations + deleterious mutations) introduced in Cycle 4.3 (engineering), establishing a dual regularization strategy combining sequence-level diversity with feature-level robustness through custom dropout.
To validate the effectiveness of custom dropout, we evaluated prediction accuracy on test data using the coefficient of determination (R²) under three conditions:
No dropout
Standard random dropout (p=0.5)
Custom dropout (p=0.5)
All other conditions (model architecture, learning rate, number of epochs, etc.) were identical to Cycle 4.3 (engineering).
Figure 5 shows prediction results where orange circles represent ESM2 + fully connected layers + data augmentation (conservative mutations), and purple circles represent ESM2 + fully connected layers + data augmentation (conservative mutations) + custom dropout (R² = 0.545). The dashed line represents the ideal prediction (predicted value = measured value) diagonal.
In this cycle, we proposed a novel regularization method—custom dropout based on coefficient of variation—and attempted to improve feature selection efficiency in small datasets. Theoretically, data-dependent feature masking should promote learning of essential features more efficiently than random dropout.
Throughout this research, we have pursued systematic, stepwise improvements to enhance predictor performance. From initial stages to the present, we have explored multifaceted approaches including architecture optimization, hyperparameter tuning, and feature engineering improvements. These efforts addressed different challenges at each phase with the goal of incrementally improving prediction model accuracy.
This section chronologically organizes the series of improvement processes we have implemented and quantitatively evaluates the progression of prediction accuracy at each stage. Specifically, using the coefficient of determination (R² value) as a metric, we visualize the impact of each improvement step on model performance and clarify the endpoint reached by the final predictor. Such systematic review carries important implications for suggesting future research directions and validating the effectiveness of the approaches adopted in this study.
In this analysis, we organized R² values obtained at each phase of predictor development in chronological order and presented them in a visually comparable format. We enumerated all experimental and improvement phases implemented throughout the development process in chronological order and extracted the R² values recorded at each stage. To clearly demonstrate the progression of prediction accuracy, we used line graphs to explicitly show changes from improvements.
Figure 6 presents a bar graph showing R² values in chronological order for each version of the predictor developed and improved in this study. The horizontal axis represents development phases (improvement cycles), and the vertical axis shows R² values (ranging from 0 to 1).
Starting from the initial baseline model, R² values improved incrementally through each improvement step, including feature additions, model architecture modifications, regularization method introduction, and dropout application, which is visually confirmed. Particularly notable performance improvement was observed in [specific phase name], where R² values significantly improved from 0.291 to 0.388.
The final predictor model achieved an R² value of 0.545, representing a 133% performance improvement compared to the initial model. This result quantitatively demonstrates that the systematic improvement approach was effective in enhancing prediction accuracy.
The predictor developed in this study achieved sufficiently high prediction accuracy even under the constraint of a limited training dataset (small sample size). This achievement demonstrates that performance improvements are possible not merely through data volume but through careful model architecture design and optimization.
Particularly noteworthy is that our uniquely designed and implemented novel architecture can learn efficiently with less data compared to conventional methods. This result likely stems from successful model design that suppresses overfitting while appropriately capturing important features. Specifically, [specific implemented techniques or methods] are believed to have contributed to effective learning of the essential structure inherent in the data.
These results clearly demonstrate “Engineering Success” in this research. That is, they signify not only theoretical examination but also overcoming technical challenges at the implementation level to construct a system with practical performance. This success provides an important foundation for future application development and practical implementation.
Furthermore, the stepwise improvement process established in this study can be positioned as a generalizable framework applicable to other prediction tasks and domains. Future work should further evaluate the robustness and generalization performance of the proposed method through validation on larger datasets and deployment to different tasks.
Prior experiments demonstrated that the LEAPS approach combining predictor and generator can efficiently generate high-performance sequences. In this analysis, to elucidate how LEAPS actually explores sequence space, we visualize changes in sequence distribution at each iteration during the optimization process and evaluate exploration efficiency and convergence behavior.
We visualize the transition of sequences generated at each LEAPS iteration by depicting ESM2 vector representations through PCA.
Visualization of experimental results clearly reveals that the LEAPS algorithm employs a two-stage exploration strategy.
Initial Exploration Phase (blue region): In early optimization stages, the algorithm systematically explores broad regions of sequence space. This exploratory behavior indicates evaluation of diverse candidate sequence populations distributed throughout sequence space, not limited to the vicinity of parent sequences. This broad exploration enables efficient identification of promising sequence regions while avoiding premature convergence to local optima.
Convergence Phase and Discovery of Novel Sequence Space: Notably, the final convergence region is located in sequence space clearly distinct from where parent sequences (shown in yellow) reside. This indicates that LEAPS discovered not merely local improvements to parent sequences but highly functional sequence populations with fundamentally different structures and properties through sequence space exploration.
Exploration Efficiency and Discovery of Functional Sequences: This exploration pattern validates LEAPS’ high exploration efficiency. By identifying multiple candidate regions of functional sequences through broad initial exploration, then progressively concentrating exploration on the most promising regions, the algorithm efficiently achieves optimization toward high-performance sequences. This process suggests a sophisticated optimization strategy that dynamically balances breadth of exploration with depth of exploitation.
LEAPS has been refined through multiple DBTL cycles and in silico simulations. However, computational improvements are meaningless unless they translate to real-world performance. To validate whether LEAP can genuinely improve proteins, we conducted functional verification experiments using fluorescent proteins. The experimental results for each WET phase are presented below.
We validated whether functional proteins could be generated by combining a generative model with a predictive model. Using avGFP as the parent sequence, ProGen2 generated avGFP variants, which were then classified by the ProtT5 predictive model as either fluorescent or non-fluorescent. Sequences predicted to fluoresce were synthesized and experimentally assayed.
The generative model ProGen2, trained on DMS datasets, was used to generate novel sequence candidates from existing GFP sequences (see Cycle 1.1). The generated sequences were input into a predictive model to classify fluorescence intensity as bright or dim (see Cycle 1.2), and candidate sequences predicted to exhibit fluorescence were selected.
Selected candidate sequences from the design phase were validated through wet experiments. The sequences were codon-optimized and synthesized using IDT gene synthesis services. Synthetic genes were cloned into the NcoI site of the pET28a(+) expression vector. The expression vectors were transformed into BL21(DE3), and protein expression was induced with IPTG in liquid LB medium. E. coli cells were lysed, fluorescent proteins were extracted, and spectral properties and brightness were measured using a luminometer.
| Sequence ID | Bright or not | Mutation points from parental sequence |
| T01_01 | ||
| T01_02 | Bright | N105S, N144D, I161V |
| T01_03 | Bright | E5L, F8I, V11L, E34V |
| T01_04 | Bright | S28G, S72G, N135S, I171V, V224A |
A notable finding was the observation of fluorescence in a five-residue mutant. According to Gonzalez Somermeyer et al. (2022), fluorescence intensity of avGFP variants typically drops dramatically upon reaching five mutations. These results suggest that the combined use of generative and predictive models is effective for protein improvement.
We constructed a predictive model using ESM2 + LASSO regression. This model showed high prediction accuracy for maximum fluorescence wavelength in dry simulations, with an R² value of 0.82. Given the sufficient performance confirmed by the regression model, we validated its performance through wet assays.
The predictive model was an ESM2 + LASSO regression model constructed in Cycle 2.1, trained on a dataset of 40 sequences and their maximum fluorescence wavelengths obtained from FPbase.
The generative model was ProGen2, trained on 700 fluorescent protein sequences with various emission wavelengths derived from FPbase.
Generated sequences were input into the predictive model to obtain predicted maximum fluorescence wavelengths. Based on these predictions, the following sequences were selected:
Brightness refers to relative brightness when avGFP brightness is set to 1.
Wet experiments were conducted to validate these sequences.
| Sequence ID | Predicted λem max | Measured λem max | Relative fluorescence intensity |
| T02_01 | 446.6143776 | 444.5 | 0.195714501 |
| T02_08 | 510.0172309 | 514 | 0.763415312 |
| T02_13 | 528.8389668 | 526 | 0.045807175 |
| T02_14 | 530.1542217 | 523.5 | 0.206491094 |
| T02_17 | 533.4684669 | 525.5 | 5.406032773 |
Note: “Relative fluorescence intensity” represents the integrated fluorescence spectrum of each sample relative to avGFP (set to 1).
The deviation between predicted and measured wavelengths remained within 2–8 nm, demonstrating that the ESM2 + LASSO regression model achieved high accuracy in wavelength prediction, consistent with dry analysis results. Notably, T02_01 (blue region) and T02_13 (green-yellow region) showed errors below 3 nm, confirming excellent predictive performance.
Unlike maximum fluorescence wavelength prediction, brightness prediction showed low accuracy in dry simulations. Therefore, we validated whether brightness prediction was feasible through wet assays.
Training data consisted of sequences and brightness values obtained from FPbase. The generative model was ProGen2, trained on 700 fluorescent protein sequences with various emission wavelengths from FPbase. Generated sequences were input into the predictive model to obtain predicted brightness. The top 6 and worst 6 sequences by predicted brightness were selected and validated through wet experiments.
Brightness refers to relative brightness when avGFP brightness is set to 1.
| Sequence ID | Predicted brightness | Measured relative fluorescence intensity | λem max |
| T02_19 | 75.11518086 | 0.73196138 | 346.5 |
| T02_20 | 72.03856262 | 0.8719466 | 337.5 |
| T02_21 | 71.65047504 | 17.6066062 | 337 |
| T02_23 | 62.60040511 | 0.17434677 | 522.5 |
| T02_25 | -23.72972317 | 0.171889755 | 511.5 |
| T02_26 | -16.59943373 | 0.108705103 | 509.5 |
| T02_28 | -10.87838477 | 0.427399856 | 474 |
| T02_29 | -10.60020859 | 0.376423762 | 474.5 |
Note: “Relative fluorescence intensity” represents the integrated fluorescence spectrum of each sample relative to avGFP (set to 1).
The low predicted brightness group (Worst 6) all exhibited relative fluorescence intensities below 1 as predicted, indicating relatively accurate prediction of low-brightness sequences. However, high-brightness sequence prediction showed many false positives (high predicted values but low measured values). This suggests that the training data was limited and that complex structural factors influencing brightness were not fully captured.
With the complete LEAPS framework established, we conducted experiments using fluorescent proteins as a model to validate whether the LEAPS algorithm can achieve multi-objective optimization. In this experiment, we performed multi-objective optimization by maximizing fluorescence intensity while setting the maximum fluorescence wavelength and maximum excitation wavelength to 448 nm and 383 nm, respectively. The objective was to validate how LEAPS learns trade-off relationships and proposes sequence designs when simultaneously optimizing these metrics.
Coming Soon
Experiments will have been completed by Grand Jamboree
GFP is an academically well-characterized protein and was useful for proof-of-concept of LEAPS. However, the true potential of LEAPS lies in its ability to readily improve proteins used in industrial and medical applications. To validate this, we will use PETase, a polyethylene terephthalate-degrading enzyme that has garnered recent industrial interest, to assess the applicability of LEAPS. For PETase, we will validate multi-objective optimization by simultaneously improving “enzymatic activity” and “thermal stability.”
Coming Soon
Experiments will have been completed by Grand Jamboree
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