Quantitative Models and Construction Methods Model Name: DFQ-FactorGCL - **Model Construction Idea**: Based on hypergraph convolutional neural networks and temporal residual contrastive learning for stock return prediction[6] - **Model Construction Process**: The model uses hypergraph convolutional neural networks to capture complex relationships between stocks and temporal residual contrastive learning to enhance prediction accuracy[6] - **Model Evaluation**: The model is effective in capturing stock trends and improving prediction accuracy[6] Model Name: Neural ODE - **Model Construction Idea**: Reconstructing time series dynamic systems for deep learning factor mining[6] - **Model Construction Process**: The model uses ordinary differential equations to model the continuous dynamics of stock prices, allowing for more accurate factor extraction[6] - **Model Evaluation**: The model provides a novel approach to factor mining, improving the robustness and accuracy of predictions[6] Model Name: DFQ-FactorVAE-pro - **Model Construction Idea**: Incorporating feature selection and environmental variable modules into the FactorVAE model[6] - **Model Construction Process**: The model uses variational autoencoders with additional modules for feature selection and environmental variables to enhance stock selection[6] - **Model Evaluation**: The model improves stock selection by considering more comprehensive factors and environmental variables[6] Quantitative Factors and Construction Methods Factor Name: Beta - **Factor Construction Idea**: Bayesian compressed market Beta[16] - **Factor Construction Process**: The factor is constructed by compressing the market Beta using Bayesian methods to capture market sensitivity[16] - **Factor Evaluation**: The factor is effective in identifying stocks with high market sensitivity[12] Factor Name: Volatility - **Factor Construction Idea**: Average logarithmic turnover rate over the past 243 days[16] - **Factor Construction Process**: The factor is calculated using the average logarithmic turnover rate and its regression with the market turnover rate over the past 243 days[16] - **Factor Evaluation**: The factor captures the demand for high volatility assets[12] Factor Name: Liquidity - **Factor Construction Idea**: Average logarithmic turnover rate over the past 243 days[16] - **Factor Construction Process**: The factor is calculated using the average logarithmic turnover rate and its regression with the market turnover rate over the past 243 days[16] - **Factor Evaluation**: The factor indicates the demand for high liquidity assets[12] Factor Name: Value - **Factor Construction Idea**: Book-to-market ratio (BP) and earnings yield (EP)[16] - **Factor Construction Process**: The factor is calculated using the book-to-market ratio and earnings yield[16] - **Factor Evaluation**: The factor shows limited recognition of value investment strategies[12] Factor Name: Growth - **Factor Construction Idea**: State-owned enterprise stock proportion[16] - **Factor Construction Process**: The factor is calculated using the proportion of state-owned enterprise stocks[16] - **Factor Evaluation**: The factor indicates the market's attention to state-owned enterprise stocks[12] Factor Name: Cubic Size - **Factor Construction Idea**: Market capitalization power term[16] - **Factor Construction Process**: The factor is calculated using the market capitalization power term[16] - **Factor Evaluation**: The factor shows the market's reduced attention to micro-cap stocks[12] Factor Name: Trend - **Factor Construction Idea**: EWMA with different half-lives[18] - **Factor Construction Process**: The factor is calculated using EWMA with half-lives of 20, 120, and 240 days, standard volatility, FF3 specific volatility, range, and maximum and minimum returns over the past 243 days[18] - **Factor Evaluation**: The factor indicates the market's reduced preference for trend investment strategies[12] Factor Name: Certainty - **Factor Construction Idea**: Sales growth, institutional holding percentage, net asset growth, analyst coverage, and listing days[18] - **Factor Construction Process**: The factor is calculated using sales growth, institutional holding percentage, net asset growth, analyst coverage, and listing days[18] - **Factor Evaluation**: The factor shows the market's reduced confidence in certainty investment strategies[12] Factor Performance Monitoring Performance in Different Index Spaces - **CSI 300 Index**: Factors like expected PEG, DELTAROE, and single-quarter EP performed well, while three-month reversal and one-month volatility performed poorly[7][24][26] - **CSI 500 Index**: Factors like one-year momentum and expected ROE change performed well, while three-month reversal and three-month institutional coverage performed poorly[7][28][30] - **CSI 800 Index**: Factors like expected ROE change and DELTAROE performed well, while one-month volatility and three-month reversal performed poorly[7][32][34] - **CSI 1000 Index**: Factors like DELTAROA and single-quarter net profit growth performed well, while public holding market value and standardized unexpected revenue performed poorly[7][36][37] - **CNI 2000 Index**: Factors like non-liquidity impact and expected PEG performed well, while public holding market value and one-month volatility performed poorly[7][39][41] - **ChiNext Index**: Factors like three-month earnings adjustment and single-quarter EP performed well, while expected net profit change and expected ROE change performed poorly[7][43][45] - **CSI All Index**: Factors like one-month UMR and one-month reversal performed well, while one-month volatility and three-month volatility performed poorly[7][47][50] Factor Backtesting Results CSI 300 Index - **Expected PEG**: 0.75% (recent week), 2.07% (recent month), 7.23% (year-to-date), 5.96% (annualized)[24] - **DELTAROE**: 0.73% (recent week), 2.19% (recent month), 7.91% (year-to-date), 5.07% (annualized)[24] - **Single-quarter EP**: 0.71% (recent week), 0.96% (recent month), 5.93% (year-to-date), 7.58% (annualized)[24] CSI 500 Index - **One-year momentum**: 0.84% (recent week), 2.33% (recent month), 3.83% (year-to-date), 3.00% (annualized)[28] - **Expected ROE change**: 0.76% (recent week), 0.28% (recent month), 6.15% (year-to-date), 7.67% (annualized)[28] - **Three-month UMR**: 0.74% (recent week), -0.38% (recent month), 0.29% (year-to-date), -1.06% (annualized)[28] CSI 800 Index - **Expected ROE change**: 0.93% (recent week), 1.76% (recent month), 2.27% (year-to-date), -3.20% (annualized)[32] - **Expected PEG**: 0.83% (recent week), 2.60% (recent month), 10.99% (year-to-date), 10.96% (annualized)[32] - **DELTAROE**: 0.79% (recent week), 2.64% (recent month), 11.60% (year-to-date), 8.99% (annualized)[32] CSI 1000 Index - **DELTAROA**: 0.63% (recent week), 1.57% (recent month), 8.06% (year-to-date), 15.10% (annualized)[36] - **Single-quarter net profit growth**: 0.57% (recent week), 1.03% (recent month), 8.04% (year-to-date), 10.77% (annualized)[36] - **One-month UMR**: 0.47% (recent week), -0.92% (recent month), 1.13% (year-to-date), -3.13% (annualized)[36] CNI 2000 Index - **Non-liquidity impact**: 1.26% (recent week), 1.99% (recent month), 12.11% (year-to-date), 21.51% (annualized)[39] - **Expected PEG**: 0.54% (recent week), 0.32% (recent month), 10.32% (year-to-date), 36.23% (annualized)[39] - **Three-month institutional coverage**: 0.54% (recent week), 4.56% (recent month), 5.41% (year-to-date), -1.19% (annualized)[39] ChiNext Index - **Three-month earnings adjustment**: 0.66% (recent week), 0.53% (recent month), -12.72% (year-to-date), -28.10% (annualized)[43] - **Single-quarter EP**: 0.66% (recent week), 0.69% (recent month), 2.90% (year-to-date), 24.70% (annualized)[43] - **PB_ROE rank difference**: 0.61% (recent week), -0.26% (

Quantitative Factor and Model Analysis Quantitative Models and Construction 1. **Model Name**: GAN_GRU Model **Model Construction Idea**: The GAN_GRU model combines Generative Adversarial Networks (GAN) for generating realistic price-volume sequential features and Gated Recurrent Units (GRU) for encoding these sequential features into predictive signals for stock selection [2][9]. **Model Construction Process**: - **GRU Component**: - Input features include 18 price-volume features such as closing price, opening price, turnover, and turnover rate [10][13]. - Training data consists of the past 400 trading days' features, sampled every 5 trading days, forming a 40x18 feature matrix to predict the cumulative return over the next 20 trading days [14]. - Data preprocessing includes outlier removal and standardization at both time-series and cross-sectional levels [14]. - The GRU network consists of two layers (GRU(128, 128)) followed by an MLP (256, 64, 64), with the final output being the predicted return (pRet) [18]. - **GAN Component**: - The generator (G) uses an LSTM model to preserve the sequential nature of the input features, while the discriminator (D) employs a CNN to process the two-dimensional price-volume feature "images" [29][32]. - The generator's loss function is: $$ L_{G} = -\mathbb{E}_{z\sim P_{z}(z)}[\log(D(G(z)))] $$ where \( z \) represents random noise, \( G(z) \) is the generated data, and \( D(G(z)) \) is the discriminator's output probability [20][21]. - The discriminator's loss function is: $$ L_{D} = -\mathbb{E}_{x\sim P_{data}(x)}[\log D(x)] - \mathbb{E}_{z\sim P_{z}(z)}[\log(1-D(G(z)))] $$ where \( x \) is real data, \( D(x) \) is the discriminator's output for real data, and \( D(G(z)) \) is the output for generated data [23][25]. - Training alternates between updating the discriminator and generator parameters until convergence [26]. **Model Evaluation**: The GAN_GRU model effectively captures both sequential and cross-sectional price-volume features, leveraging the strengths of GANs and GRUs for stock selection [2][9][29]. --- Quantitative Factors and Construction 1. **Factor Name**: GAN_GRU Factor **Factor Construction Idea**: The GAN_GRU factor is derived from the GAN_GRU model's output, representing the encoded price-volume sequential features as a stock selection signal [2][9]. **Factor Construction Process**: - The factor is derived from the predicted return (pRet) output of the GAN_GRU model [18]. - The factor undergoes industry and market capitalization neutralization, followed by standardization [18]. **Factor Evaluation**: The GAN_GRU factor demonstrates strong predictive power across various industries, with consistent performance in both IC and excess returns [36][40]. --- Model Backtest Results 1. **GAN_GRU Model**: - **IC Mean**: 11.54% - **ICIR**: 0.89 - **Turnover Rate**: 0.83 - **Recent IC**: 8.34% - **1-Year IC Mean**: 11.09% - **Annualized Return**: 37.71% - **Annualized Volatility**: 24.95% - **IR**: 1.56 - **Max Drawdown**: 27.29% - **Annualized Excess Return**: 24.95% [36][37]. --- Factor Backtest Results 1. **GAN_GRU Factor**: - **IC Mean**: 11.54% - **ICIR**: 0.89 - **Turnover Rate**: 0.83 - **Recent IC**: 8.34% - **1-Year IC Mean**: 11.09% - **Annualized Return**: 37.71% - **Annualized Volatility**: 24.95% - **IR**: 1.56 - **Max Drawdown**: 27.29% - **Annualized Excess Return**: 24.95% [36][37].

Quantitative Factors and Construction Methods Factor Name: Liquidity - **Construction Idea**: Measures the market's preference for high-liquidity assets, reflecting the demand for stocks with higher turnover rates [9][14] - **Construction Process**: - **TO**: Average logarithmic turnover rate over the past 243 trading days - **Liquidity Beta**: Regression of individual stock turnover rates against market turnover rates over the past 243 trading days [14] - **Evaluation**: Demonstrated the highest positive return among style factors in the recent week, indicating a significant increase in demand for high-liquidity assets [9] - **Performance**: Weekly return of 5.44%, monthly return of 13.08%, and annualized return of 33.79% over the past year [11] Factor Name: Volatility - **Construction Idea**: Captures the market's preference for high-volatility stocks, reflecting risk appetite [9][14] - **Construction Process**: - **Stdvol**: Standard deviation of daily returns over the past 243 trading days - **Ivff**: Fama-French 3-factor idiosyncratic volatility over the past 243 trading days - **Range**: Difference between the highest and lowest prices over the past 243 trading days - **MaxRet_6**: Average return of the six highest daily returns over the past 243 trading days - **MinRet_6**: Average return of the six lowest daily returns over the past 243 trading days [14] - **Evaluation**: Showed a significant improvement in weekly performance, reflecting increased market risk appetite [9] - **Performance**: Weekly return of 5.03%, monthly return of 12.37%, and annualized return of 25.55% over the past year [11] Factor Name: Beta - **Construction Idea**: Represents the market's preference for high-beta stocks, indicating sensitivity to market movements [9][14] - **Construction Process**: Bayesian shrinkage of market beta [14] - **Evaluation**: Significant weekly performance improvement, indicating a strong preference for high-beta stocks [9] - **Performance**: Weekly return of 4.28%, monthly return of 12.51%, and annualized return of 33.02% over the past year [11] Factor Name: Growth - **Construction Idea**: Measures the market's preference for growth-oriented stocks, focusing on financial growth metrics [9][14] - **Construction Process**: - **Delta ROE**: Average change in ROE over the past three years - **Sales Growth**: 3-year compound growth rate of TTM sales revenue - **Na Growth**: 3-year compound growth rate of TTM net assets [14] - **Evaluation**: Improved weekly performance, reflecting increased market interest in growth stocks [9] - **Performance**: Weekly return of 1.65%, monthly return of 0.77%, and annualized return of 1.32% over the past year [11] Factor Name: Certainty - **Construction Idea**: Reflects the market's preference for stocks with higher predictability and stability [10][14] - **Construction Process**: - **Instholder Pct**: Proportion of holdings by mutual funds - **Cov**: Analyst coverage adjusted for market capitalization - **Listdays**: Number of days since the stock's listing [14] - **Evaluation**: Experienced a significant decline in weekly performance, indicating reduced confidence in certainty-based strategies [10] - **Performance**: Weekly return of -3.99%, monthly return of -9.10%, and annualized return of -17.07% over the past year [11] Factor Name: Value - **Construction Idea**: Measures the market's preference for undervalued stocks based on valuation metrics [10][14] - **Construction Process**: - **BP**: Book-to-price ratio - **EP**: Earnings yield [14] - **Evaluation**: Significant decline in weekly performance, reflecting reduced market interest in value-based strategies [10] - **Performance**: Weekly return of -4.75%, monthly return of -8.10%, and annualized return of -16.96% over the past year [11] Factor Name: Size - **Construction Idea**: Captures the market's preference for small-cap stocks [10][14] - **Construction Process**: Logarithm of total market capitalization [14] - **Evaluation**: Experienced the largest decline among style factors, indicating reduced market interest in small-cap stocks [10] - **Performance**: Weekly return of -5.96%, monthly return of -12.84%, and annualized return of -54.81% over the past year [11] --- Factor Backtesting Results Weekly Performance - **Liquidity**: 5.44% - **Volatility**: 5.03% - **Beta**: 4.28% - **Growth**: 1.65% - **Certainty**: -3.99% - **Value**: -4.75% - **Size**: -5.96% [11] Monthly Performance - **Liquidity**: 13.08% - **Volatility**: 12.37% - **Beta**: 12.51% - **Growth**: 0.77% - **Certainty**: -9.10% - **Value**: -8.10% - **Size**: -12.84% [11] Annualized Performance (Past Year) - **Liquidity**: 33.79% - **Volatility**: 25.55% - **Beta**: 33.02% - **Growth**: 1.32% - **Certainty**: -17.07% - **Value**: -16.96% - **Size**: -54.81% [11]

Quantitative Models and Factor Analysis Quantitative Factors and Construction Methods - **Factor Name**: Non-liquidity Shock **Construction Idea**: Measures the impact of illiquidity on stock returns **Construction Process**: Calculated as the average absolute daily return over the past 20 trading days divided by the corresponding daily trading volume[6][16][19] **Evaluation**: Demonstrated strong performance across multiple indices, indicating its effectiveness in capturing illiquidity effects[6][19][21] - **Factor Name**: Six-Month UMR **Construction Idea**: Captures momentum adjusted for risk over a six-month window **Construction Process**: Risk-adjusted momentum is calculated using a six-month rolling window, incorporating volatility adjustments[6][16][19] **Evaluation**: Consistently performed well in recent periods, showing robustness across different market conditions[6][19][21] - **Factor Name**: One-Year UMR **Construction Idea**: Similar to Six-Month UMR but uses a one-year window for risk-adjusted momentum **Construction Process**: Momentum is adjusted for risk using a one-year rolling window, factoring in volatility[6][16][19] **Evaluation**: Effective in capturing long-term momentum trends, though performance varies by index[6][19][21] - **Factor Name**: Three-Month Volatility **Construction Idea**: Measures short-term price fluctuations **Construction Process**: Calculated as the standard deviation of daily returns over the past 60 trading days[6][16][19] **Evaluation**: Demonstrated strong negative correlation with returns, indicating its utility in identifying high-risk assets[6][19][21] - **Factor Name**: One-Month Turnover **Construction Idea**: Reflects trading activity and liquidity over a short period **Construction Process**: Average daily turnover rate over the past 20 trading days[6][16][19] **Evaluation**: Effective in capturing liquidity dynamics, though performance varies across indices[6][19][21] Factor Backtesting Results - **Non-liquidity Shock**: - Recent Week: 0.58% (HS300), 0.91% (CSI500), 0.93% (CSI800), 0.87% (CSI1000), 1.14% (CSI All)[19][23][27][31][42] - Recent Month: 0.31% (HS300), 0.64% (CSI500), 0.77% (CSI800), 2.40% (CSI1000), 1.33% (CSI All)[19][23][27][31][42] - **Six-Month UMR**: - Recent Week: 0.54% (HS300), -0.09% (CSI500), 0.57% (CSI800), 0.73% (CSI1000), 0.73% (CSI All)[19][23][27][31][42] - Recent Month: 1.53% (HS300), 2.09% (CSI500), 2.35% (CSI800), 3.49% (CSI1000), 3.85% (CSI All)[19][23][27][31][42] - **One-Year UMR**: - Recent Week: 0.46% (HS300), 0.06% (CSI500), 0.88% (CSI800), 0.52% (CSI1000), 0.76% (CSI All)[19][23][27][31][42] - Recent Month: 1.15% (HS300), 2.19% (CSI500), 2.50% (CSI800), 2.85% (CSI1000), 3.74% (CSI All)[19][23][27][31][42] - **Three-Month Volatility**: - Recent Week: 0.24% (HS300), 0.78% (CSI500), 0.59% (CSI800), 0.65% (CSI1000), 0.86% (CSI All)[19][23][27][31][42] - Recent Month: 0.84% (HS300), 3.24% (CSI500), 2.17% (CSI800), 3.63% (CSI1000), 3.60% (CSI All)[19][23][27][31][42] - **One-Month Turnover**: - Recent Week: -0.05% (HS300), 0.48% (CSI500), 0.04% (CSI800), 0.57% (CSI1000), 0.50% (CSI All)[19][23][27][31][42] - Recent Month: 0.19% (HS300), 2.47% (CSI500), 0.19% (CSI800), 3.87% (CSI1000), 1.65% (CSI All)[19][23][27][31][42] Quantitative Model Construction - **Model Name**: Maximized Factor Exposure Portfolio (MFE) **Construction Idea**: Optimizes portfolio weights to maximize exposure to a single factor while controlling for constraints **Construction Process**: - Objective Function: Maximize $f^T w$, where $f$ is the factor value and $w$ is the weight vector - Constraints: Include style exposure, industry deviation, stock weight limits, turnover, and full investment constraints - Formula: $\begin{array}{ll}max&f^{T}w\\ s.t.&s_{l}\leq X(w-w_{b})\leq s_{h}\\ &h_{l}\leq H(w-w_{b})\leq h_{h}\\ &w_{l}\leq w-w_{b}\leq w_{h}\\ &b_{l}\leq B_{b}w\leq b_{h}\\ &0\leq w\leq l\\ &1^{T}w=1\\ &\Sigma|w-w_{0}|\leq to_{h}\end{array}$[57][58][61] **Evaluation**: Provides a robust framework for testing factor effectiveness under realistic constraints[57][58][61] Model Backtesting Results - **MFE Portfolio**: - Demonstrated strong performance in capturing factor-specific returns while adhering to constraints such as turnover and industry exposure[57][58][61]

Quantitative Models and Construction Methods Factor: 3-Month Earnings Revision - **Construction Idea**: Measures the upward or downward revisions in earnings estimates over the past three months, reflecting changes in analysts' expectations[6][23][42] - **Construction Process**: Calculated as the difference between the number of upward and downward revisions in earnings estimates over the last three months, normalized by the total number of estimates[19][42] - **Evaluation**: Demonstrates strong performance in multiple index universes, indicating its effectiveness in capturing short-term earnings momentum[6][23][42] Factor: UMR (Up-Market Ratio) - **Construction Idea**: Captures momentum by analyzing risk-adjusted returns over different time windows (1 month, 3 months, 6 months, 1 year)[6][19][42] - **Construction Process**: - **1-Month UMR**: Risk-adjusted momentum over a 1-month window - **3-Month UMR**: Risk-adjusted momentum over a 3-month window - **6-Month UMR**: Risk-adjusted momentum over a 6-month window - **1-Year UMR**: Risk-adjusted momentum over a 12-month window[19][42] - **Evaluation**: Consistently performs well across multiple index universes, particularly in capturing medium-term momentum trends[6][23][42] Factor: EPTTM (Earnings-to-Price Trailing Twelve Months) - **Construction Idea**: A valuation factor that measures the earnings yield based on trailing twelve months' earnings[19][42] - **Construction Process**: Calculated as the ratio of trailing twelve months' earnings to the current market price[19][42] - **Evaluation**: Shows strong performance in certain index universes, particularly in value-oriented strategies[6][23][42] Factor: DeltaROE - **Construction Idea**: Measures the change in return on equity (ROE) over a specific period, reflecting improvements or deteriorations in profitability[19][42] - **Construction Process**: Calculated as the difference in ROE between the current period and the same period in the previous year[19][42] - **Evaluation**: Effective in identifying companies with improving profitability trends[6][23][42] Factor: Analyst Coverage (3-Month) - **Construction Idea**: Tracks the number of analysts covering a stock over the past three months, reflecting market attention and sentiment[19][42] - **Construction Process**: Count of unique analysts issuing reports on a stock in the last three months[19][42] - **Evaluation**: Performs well in identifying stocks with increasing market interest[6][23][42] --- Factor Backtesting Results 3-Month Earnings Revision - **Recent 1 Week**: 1.94% (China Securities All Index)[43] - **Recent 1 Month**: 0.82% (China Securities All Index)[43] - **Year-to-Date**: 2.50% (China Securities All Index)[43] UMR (Up-Market Ratio) - **1-Month UMR**: - **Recent 1 Week**: 1.30% (China Securities All Index)[43] - **Recent 1 Month**: 2.57% (China Securities All Index)[43] - **Year-to-Date**: 3.85% (China Securities All Index)[43] - **3-Month UMR**: - **Recent 1 Week**: 0.75% (China Securities All Index)[43] - **Recent 1 Month**: 2.14% (China Securities All Index)[43] - **Year-to-Date**: 2.48% (China Securities All Index)[43] - **6-Month UMR**: - **Recent 1 Week**: 0.72% (China Securities All Index)[43] - **Recent 1 Month**: 4.19% (China Securities All Index)[43] - **Year-to-Date**: 1.12% (China Securities All Index)[43] - **1-Year UMR**: - **Recent 1 Week**: 0.74% (China Securities All Index)[43] - **Recent 1 Month**: 3.92% (China Securities All Index)[43] - **Year-to-Date**: 0.80% (China Securities All Index)[43] EPTTM - **Recent 1 Week**: 0.83% (China Securities All Index)[43] - **Recent 1 Month**: 3.70% (China Securities All Index)[43] - **Year-to-Date**: -0.22% (China Securities All Index)[43] DeltaROE - **Recent 1 Week**: 0.19% (China Securities All Index)[43] - **Recent 1 Month**: -0.31% (China Securities All Index)[43] - **Year-to-Date**: 1.66% (China Securities All Index)[43] Analyst Coverage (3-Month) - **Recent 1 Week**: 1.86% (China Securities All Index)[43] - **Recent 1 Month**: 2.24% (China Securities All Index)[43] - **Year-to-Date**: 4.89% (China Securities All Index)[43] --- MFE Portfolio Construction - **Construction Method**: - Maximizes single-factor exposure while controlling for industry, style, and stock-specific deviations relative to the benchmark index[56][57][59] - Constraints include: - Style exposure limits - Industry exposure limits - Stock weight deviation limits - Turnover limits[56][57][59] - **Optimization Model**: $\begin{array}{ll}max&f^{T}w\\ s.t.&s_{l}\leq X(w-w_{b})\leq s_{h}\\ &h_{l}\leq H(w-w_{b})\leq h_{h}\\ &w_{l}\leq w-w_{b}\leq w_{h}\\ &b_{l}\leq B_{b}w\leq b_{h}\\ &0\leq w\leq l\\ &1^{T}w=1\\ &\Sigma|w-w_{0}|\leq to_{h}\end{array}$[56][57] - **Evaluation**: Effective in isolating factor performance under realistic portfolio constraints[56][57][60]