Investment Rating - The investment rating for the company is "Maintain Buy" [6] Core Views - The company is a leading player in the casting industry, benefiting from the high growth and large-scale development of wind power installations [4] - The company's revenue for 2024 is reported at 4.696 billion yuan, a year-on-year increase of 0.87%, while the net profit attributable to shareholders is 624 million yuan, up 29.55% year-on-year [1][4] - The company is expected to see an increase in shipment volume in 2025 due to the rise in wind power installations, with a projected revenue of 6.333 billion yuan [5] Financial Performance Summary - In 2024, the company achieved a gross margin of 17.34%, a decrease of 1.33 percentage points year-on-year, while the net margin improved to 13.11%, an increase of 2.83 percentage points [1] - The company reported a gross margin of 15.53% in Q1 2025, down 6.24 percentage points year-on-year, with a net margin of 9.03%, down 3.25 percentage points [1] - The company’s net profit for 2025 is projected to be 784 million yuan, with a year-on-year growth rate of 25.7% [5] Market and Product Development Summary - The company is focusing on the development of large-scale wind turbine components, which are expected to enhance efficiency and reduce the cost of electricity generation [3] - The company has established a production capacity of 700,000 tons for casting and 420,000 tons for precision machining, allowing for flexible adjustments in production [2] - The company is expanding its market presence in high-end alloy steel and is actively developing large die-casting machines for the new energy vehicle sector [3] Profit Forecast - The company is expected to achieve net profits of 784 million yuan, 912 million yuan, and 1.048 billion yuan for the years 2025, 2026, and 2027 respectively, with corresponding P/E ratios of 16.3, 14.0, and 12.2 [4]

Quantitative Models and Construction 1. Model Name: Timing Radar Six-Factor Framework - **Model Construction Idea**: The equity market is influenced by multiple dimensions. This model selects 21 indicators from six perspectives: liquidity, economic fundamentals, valuation, capital flows, technical trends, and crowding. These are summarized into four categories: "Valuation Cost-Effectiveness," "Macro Fundamentals," "Capital & Trend," and "Crowding & Reversal," generating a comprehensive timing score within the range of [-1, 1][1][6][8] - **Model Construction Process**: - The 21 indicators are grouped into six dimensions, and their scores are aggregated into four broader categories. - The final timing score is calculated as a weighted average of these categories, normalized to the range of [-1, 1][1][6][8] - **Model Evaluation**: The model provides a comprehensive and multi-dimensional view of market timing, integrating macroeconomic, technical, and sentiment factors[1][6] --- Quantitative Factors and Construction 1. Factor Name: Monetary Direction Factor - **Factor Construction Idea**: This factor aims to determine the direction of monetary policy by analyzing changes in central bank policy rates and short-term market rates over the past 90 days[12] - **Factor Construction Process**: - Calculate the average change in central bank policy rates and short-term market rates over the past 90 days - If the factor value > 0, monetary policy is deemed accommodative; if < 0, it is deemed tight[12] - **Factor Evaluation**: Effectively captures the directional bias of monetary policy[12] 2. Factor Name: Monetary Strength Factor - **Factor Construction Idea**: Based on the "interest rate corridor" concept, this factor measures the deviation of short-term market rates from policy rates[15] - **Factor Construction Process**: - Compute the deviation as: $ \text{Deviation} = \frac{\text{DR007}}{\text{7-Year Reverse Repo Rate}} - 1 $ - Smooth and normalize the deviation using z-scores - Assign scores based on thresholds: <-1.5 SD indicates a loose environment (score = 1), >1.5 SD indicates a tight environment (score = -1)[15] - **Factor Evaluation**: Provides a quantitative measure of liquidity conditions in the short-term market[15] 3. Factor Name: Credit Direction Factor - **Factor Construction Idea**: Measures the transmission of credit from banks to the real economy using long-term loan data[18] - **Factor Construction Process**: - Calculate the year-over-year growth of long-term loans over the past 12 months - Compare the current value to its level three months ago - If the factor is rising, assign a score of 1; if falling, assign a score of -1[18] - **Factor Evaluation**: Captures the directional trend of credit expansion or contraction[18] 4. Factor Name: Credit Strength Factor - **Factor Construction Idea**: Measures whether credit data significantly exceeds or falls short of expectations[20] - **Factor Construction Process**: - Compute the z-score of the difference between actual and expected new RMB loans: $ \text{Credit Strength Factor} = \frac{\text{Actual Loans} - \text{Expected Median}}{\text{Expected Standard Deviation}} $ - Assign scores based on thresholds: >1.5 SD indicates a strong credit environment (score = 1), <-1.5 SD indicates a weak credit environment (score = -1)[20] - **Factor Evaluation**: Quantifies the surprise element in credit data[20] 5. Factor Name: Growth Direction Factor - **Factor Construction Idea**: Based on PMI data, this factor identifies the directional trend of economic growth[21] - **Factor Construction Process**: - Compute the year-over-year change in the 12-month moving average of PMI data - Compare the current value to its level three months ago - If the factor is rising, assign a score of 1; if falling, assign a score of -1[21] - **Factor Evaluation**: Tracks the momentum of economic growth effectively[21] 6. Factor Name: Growth Strength Factor - **Factor Construction Idea**: Measures whether economic growth data significantly exceeds or falls short of expectations[25] - **Factor Construction Process**: - Compute the z-score of the difference between actual and expected PMI values: $ \text{Growth Strength Factor} = \frac{\text{Actual PMI} - \text{Expected Median}}{\text{Expected Standard Deviation}} $ - Assign scores based on thresholds: >1.5 SD indicates strong growth (score = 1), <-1.5 SD indicates weak growth (score = -1)[25] - **Factor Evaluation**: Captures the surprise element in economic growth data[25] 7. Factor Name: Inflation Direction Factor - **Factor Construction Idea**: Reflects the impact of inflation trends on monetary policy and equity markets[26] - **Factor Construction Process**: - Compute the weighted average of smoothed CPI and raw PPI year-over-year changes: $ \text{Inflation Direction Factor} = 0.5 \times \text{CPI} + 0.5 \times \text{PPI} $ - Compare the current value to its level three months ago - If the factor is falling, assign a score of 1; if rising, assign a score of -1[26] - **Factor Evaluation**: Provides insights into the inflationary environment and its implications for monetary policy[26] 8. Factor Name: Inflation Strength Factor - **Factor Construction Idea**: Measures whether inflation data significantly exceeds or falls short of expectations[29] - **Factor Construction Process**: - Compute the z-score of the difference between actual and expected CPI and PPI values: $ \text{Inflation Strength Factor} = \frac{\text{CPI Difference} + \text{PPI Difference}}{2} $ - Assign scores based on thresholds: <-1.5 SD indicates low inflation (score = 1), >1.5 SD indicates high inflation (score = -1)[29] - **Factor Evaluation**: Quantifies the surprise element in inflation data[29] --- Factor Backtesting Results 1. Monetary Direction Factor - Current Score: 1[12] 2. Monetary Strength Factor - Current Score: -1[16] 3. Credit Direction Factor - Current Score: -1[18] 4. Credit Strength Factor - Current Score: 1[20] 5. Growth Direction Factor - Current Score: 1[21] 6. Growth Strength Factor - Current Score: 0[25] 7. Inflation Direction Factor - Current Score: 1[26] 8. Inflation Strength Factor - Current Score: 1[29]

证券研究报告 | 金融工程 gszqdatemark 2025 05 11 年 月 日 量化周报 市场可逢低布局 市场可逢低布局。本周（5.6-5.9），大盘震荡上行，上证指数全周收涨 1.92%。在此背景下，大部分指数迎来了一波 30 分钟级别回调。当下我 们认为，经历了贸易战的冲击后，市场的底部区间已然探明。短期市场到 了选择方向的时候：1、一方面大部分规模指数和行业的的日线级别下跌 只走了 1 浪结构，日线下跌结构不够充分；2、另一方面经历了近期的震 荡上行后，很多指数和板块马上要形成新的日线级别上涨，比如上证 50、 纺服、轻工、汽车等板块。未来，不论哪种情况出现，投资者都可逢低布 局，因为即便是继续日线级别下跌，空间和时间都有限。中期来看，上证 指数、上证 50、沪深 300、中证 500、深证成指、创业板指、科创 50 纷 纷确认周线级别上涨，而且在日线上只走出了 1 浪结构，中期牛市刚刚开 始；此外，已有 21 个行业处于周线级别上涨中，且 8 个行业周线上涨只 走了 1 浪结构，因此我们认为本轮牛市刚刚开始，而且还是个普涨格局。 中期对于投资者而言，仍然可以逆势布局。 A 股景气指数观察。截至 ...

1. Report Industry Investment Rating No relevant content provided. 2. Core View of the Report - The current loose funds have not been fully reflected in the bond market. The bond market is expected to develop from short - term to long - term, with the curve likely to first show a bullish steepening and then a bullish flattening. The overall interest rate downward trend remains unchanged [3][5][24] 3. Summary by Related Content Market Performance - This week, funds were loose, and the short - end trend was significantly stronger than the long - end. After the holiday, the R001 and R007 dropped to 1.52% and 1.58% respectively, driving the short - term interest rates to decline significantly. The 1 - year AAA certificate of deposit (CD) dropped 7.5bps to 1.66% this week. Short - term interest rates and short - term credit also decreased significantly. The 10 - year and 30 - year treasury bonds rose slightly by 1.1bps and 1.9bps to 1.64% and 1.84% respectively [1][8] Reasons for Loose Funds - Seasonally, funds are loose in the first and middle of May. The central bank announced a 0.5 - percentage - point reserve requirement ratio cut this week, releasing about 1 trillion yuan in liquidity. Even if considering the maturity of MLF (125 billion yuan) and repurchase (90 billion yuan) this month and assuming a half - volume continuation, the net capital injection from the reserve requirement ratio cut and repurchase is still over 50 billion yuan. Calculated with the March money multiplier of 8.65, it can support about 4.3 trillion yuan in financing demand. Since the social financing scale in May last year was only 2 trillion yuan, the current loose funds situation will remain until before the end - of - quarter impact [2][9] Impact on the Bond Market Quantity Perspective - As the capital price drops, the spreads between CDs, short - term credit, etc., and funds have turned positive, meaning that leveraging can effectively increase returns. Although the current leverage level has rebounded, it is not significantly higher than previous years. The daily trading volume of inter - bank pledged repurchase on May 9 was about 6.5 trillion yuan, basically the same as the same period last year [3][12] Price Perspective - Short - term interest rates still have room to decline further. The 1 - year CD is expected to drop to around 1.6%. Based on the average spread of about 9.5bps between the 1 - year AAA CD and overnight funds in the past year, if the overnight interest rate stabilizes at around 1.5% and the R007 at around 1.6%, the 1 - year AAA CD rate may be around 1.6%. Currently, the CD rate has dropped to 1.66% [3][13] Short - Term Bond Interest Rates - The 1 - year treasury bond and 1 - year AAA medium - term note are expected to drop to around 1.2% and 1.6% respectively. The spread between the 1 - year AAA CD and the 1 - year treasury bond has narrowed to 24bps, the lowest since 2023. If the spread returns to the average level of about 42bps since 2023, a 1.6% CD rate may correspond to a 1.2% 1 - year treasury bond rate. Credit bonds and CD rates are basically the same, so as the CD rate drops to around 1.6%, the same - maturity high - grade credit bonds are also expected to reach the corresponding level [4][19] Long - Term Bond Interest Rates - The decline in short - term interest rates will protect long - term interest rates and promote a significant recovery in the credit bond curve slope. If the 2 - year treasury bond drops to around 1.2%, combined with the average spread of 44bps between the 10 - year and 2 - year treasury bonds since 2023, the corresponding 10 - year treasury bond will be around 1.64%, indicating limited adjustment pressure on long - term bonds. The decline in short - term bond interest rates will bring better investment opportunities for 3 - 5 - year interest - rate bonds and 3 - 5 - year secondary perpetual bonds. The spread between the 5 - year and 1 - year AAA - secondary capital bonds has rebounded to around 20bps, more than 20bps higher than the low point in February, and the long - end allocation value of secondary perpetual bonds is emerging [4][21] Market Outlook - The bond market is expected to develop from short - term to long - term. The loose funds protect the short - end. The current CD rate is higher than the capital price, allowing leveraging to allocate CDs to increase returns. The spread between CDs and short - term treasury bonds has reached a low in recent years, making short - term treasury bonds more cost - effective than CDs for bank self - operated funds. The market leverage is also expected to gradually recover. The decline in short - term interest rates will increase the term spread, protect long - term interest rates, and enhance the allocation cost - effectiveness of 3 - 5 - year interest - rate bonds and credit bonds, gradually realizing the trend of the bond market first showing a bullish steepening and then a bullish flattening [5][24]

Investment Rating - The report maintains a "Buy" rating for key companies in the construction and decoration industry, indicating a positive outlook for their stock performance relative to the benchmark index [7][26]. Core Insights - The China Securities Regulatory Commission (CSRC) has released a plan to promote high-quality development of public funds, which includes linking fund manager compensation to performance benchmarks. This is expected to drive fund managers to align their portfolios more closely with benchmarks, creating structural investment opportunities in the market [2][20]. - Based on 2024 annual report data, it is estimated that active equity funds will need to increase their allocation to the CSI 300 index by 303.6 billion yuan. The construction sector is currently underrepresented in these funds, with a holding ratio of only 0.71% [3][6]. - The report identifies a potential increase in funding for the construction sector amounting to 21.8 billion yuan, which represents approximately 6.5% of the free float market capitalization of construction stocks in the CSI 300 index [6][26]. Summary by Sections Investment Recommendations - Key companies recommended for significant capital allocation include: - China State Construction Engineering Corporation: 6.6 billion yuan - China Railway Group: 3.3 billion yuan - China Power Construction Group: 2.3 billion yuan - China Railway Construction Corporation: 2.1 billion yuan - China Communications Construction Company: 1.8 billion yuan - China Energy Engineering Corporation: 1.6 billion yuan - China National Chemical Corporation: 1.6 billion yuan - Sichuan Road and Bridge Group: 1.3 billion yuan - China Metallurgical Group Corporation: 1.2 billion yuan [7][26]. Industry Dynamics - The construction and decoration sector has shown a weekly increase of 1.99%, ranking 16th among 31 A-share industries. The sector's performance is compared to the Shanghai Composite Index and CSI 300 Index, which saw minimal changes [14][20]. - The report highlights the potential for structural changes in fund holdings due to the new compensation policies, which may lead to increased investment in the construction sector [2][20]. Market Analysis - Active equity funds are categorized into four types, with a total of 8,141 funds managing 5.95 trillion yuan. Among these, 4,020 funds include the CSI 300 index in their benchmarks, with an average weight of 61% [3][21]. - The report provides detailed calculations on how the allocation adjustments will impact the construction sector, estimating a total of 218 billion yuan in additional funding [6][25].

Investment Rating - The industry maintains a rating of "Buy" for key companies such as Anta Sports, Tabo, and Bosideng, with a recommendation to focus on high-quality brands and companies with strong fundamentals [5][10][28]. Core Insights - Puma's Q1 2025 performance met expectations, with revenue growth of 0.1% year-on-year to €2.076 billion, while net profit saw a significant decline of 99.5% to €500,000 due to global economic fluctuations, particularly in the US and China [1][15]. - The report emphasizes the resilience of the sportswear sector, projecting a revenue growth of 4.4% and a net profit decline of only 0.6% for key apparel companies in 2024, with a stronger recovery anticipated in 2025 [4][26]. - The DTC (Direct-to-Consumer) business showed robust growth, with a 12% increase in revenue to €550 million, while wholesale revenue declined by 3.6% [3][20]. Summary by Sections Puma's Q1 2025 Performance - Revenue increased by 0.1% to €2.076 billion, with a slight decline in gross margin by 0.6 percentage points to 47% [1][15]. - Operating profit fell by 63.7% to €6 million, and net profit dropped by 99.5% to €500,000, attributed to economic volatility [1][15]. - Inventory rose by 16.3% to €2.08 billion, mainly due to increased in-transit stock [1][15]. Regional and Business Model Analysis - EMEA region revenue grew by 5.1% to €890 million, while the Americas saw a decline of 2.7% to €750 million, primarily due to a 11.1% drop in North America [2][20]. - The Asia-Pacific region experienced a 4.7% decline to €430 million, with a notable 17.7% drop in Greater China [2][20]. - The company is adapting to US tariff issues by optimizing product sourcing and reallocating production [2][20]. DTC and Wholesale Business Performance - DTC revenue increased by 12% to €550 million, with e-commerce growing by 17.3% and self-operated retail stores by 8.9% [3][20]. - Wholesale revenue decreased by 3.6% to €1.53 billion, driven by weak demand in the US and China [3][20]. Industry Outlook - The report suggests focusing on brands with solid fundamentals and anticipating a recovery in 2025, with the sportswear sector expected to benefit from government policies and increased consumer participation in sports [4][26]. - Recommendations include companies like Anta Sports, Tabo, and Bosideng, which are projected to have strong earnings growth and attractive valuations [28][29].

Investment Rating - The report maintains an "Increase" rating for the banking sector [5] Core Insights - The report highlights that by the end of 2024, the bond investments of 42 listed banks significantly contributed to their performance, particularly due to the continuous decline in bond market interest rates, with a cumulative drop of 88 basis points in the 10-year government bond yield [1] - The report emphasizes the substantial floating profits accumulated in the FV-OCI financial assets due to fair value changes, which banks have utilized to support their performance through timely disposals of financial assets [1][4] - The report identifies that the floating profits from FV-OCI assets are particularly significant for certain city commercial banks and rural commercial banks, with some banks showing floating profit to profit ratios exceeding 100% [2][3] Summary by Sections 1. FV-OCI Floating Profit Situation - State-owned banks dominate the floating profit scale, with China Construction Bank and Agricultural Bank of China exceeding 50 billion yuan in floating profits by the end of 2024 [1] - City and rural commercial banks show high ratios of FV-OCI floating profits to profits, with Lanzhou Bank reaching 126.9% [2] - The contribution of FV-OCI floating profits to core Tier 1 capital is significant for several city and rural commercial banks, with notable increases year-on-year [3] 2. Financial Asset Disposal Income Situation - In 2024, listed banks disposed of AC financial assets generating a total income of 50.29 billion yuan, an increase of 82.5% year-on-year, and FV-OCI financial assets generating 85.36 billion yuan, an increase of 134.4% year-on-year, leading to a total disposal income of 135.6 billion yuan [4][8] - The report notes that while the disposal income is significant, it does not imply a substantial increase in the scale of asset disposals, as the gains are influenced by the declining interest rates in the bond market [4] 3. Sector Outlook - The report suggests that while short-term impacts from tariff policies may affect exports, long-term domestic policies aimed at stabilizing real estate, promoting consumption, and enhancing social welfare are expected to support economic growth [9] - The banking sector is anticipated to benefit from policy catalysts, with specific banks like Ningbo Bank, Postal Savings Bank, and China Merchants Bank highlighted as potential investment opportunities [9]

Investment Rating - The report maintains an "Increase" rating for the media industry, indicating a positive outlook for the sector [4]. Core Insights - The media sector has shown resilience with a 1.39% increase in the index from May 6 to May 9, 2025, driven by market momentum. The report highlights optimism towards AI applications, IP monetization, and mergers and acquisitions as key growth areas for 2025 [1][8]. - AI applications are expected to focus on new investment mappings and data tracking for mature applications, particularly in the multimodal industry direction. Companies with IP advantages and full industry chain potential are seen as having monetization opportunities, especially in trendy toys and film content [1][17]. - The report emphasizes the importance of state-owned enterprises in the media sector, particularly in light of the State-owned Assets Supervision and Administration Commission's focus on market capitalization assessments for state-owned enterprises [1]. Summary by Sections Market Overview - The media sector index increased by 1.39% during the week of May 6-9, 2025, with the top-performing sectors being defense and military (6.44%), communication (5.43%), and banking (3.98%) [8][10]. - The report identifies the top five gainers in the media sector: Baotong Technology (24.7%), Huicheng Technology (16.2%), Shengxunda (12.2%), Zhongqingbao (10.4%), and Huawen Group (9.3%) [11]. Subsector Insights - Key focus areas include resource integration expectations with companies like Zhongshi Media, Guoxin Culture, and Guangxi Broadcasting. AI-related companies such as Rongxin Culture and Aofei Entertainment are also highlighted [17]. - In the gaming sector, companies with strong certainty like Shenzhou Taiyue and Kaiying Network are recommended for attention, along with Perfect World and ST Huatuo [17]. - The report also notes significant interest in Hong Kong stocks, particularly Alibaba, Tencent, and Pop Mart, as well as educational leaders like New Oriental and regional leaders with strong earnings elasticity [17]. Key Events Review - Tencent launched the HunyuanCustom video model, which excels in character consistency and multimodal input, achieving industry-leading performance in various metrics [19]. - Lightricks introduced the LTX Video model, boasting 130 billion parameters and a 30-fold improvement in video generation quality compared to existing models, operable on consumer-grade GPUs [19]. Subsector Data Tracking - The report provides insights into the gaming market, highlighting popular upcoming games and their expected performance [20]. - The domestic film market's weekly box office reached approximately 508 million yuan, with top films including "Dumpling Queen" and "Hunting Gold Game" [21]. - The report tracks viewership for series and variety shows, noting the top-ranking series and their respective platforms [25][26].

Investment Rating - The report maintains a "Buy" rating for key companies in the environmental sector, including High Energy Environment and Huicheng Environmental [6][7]. Core Insights - The environmental industry is experiencing a transformation driven by deepening pollution prevention measures and low-carbon investments, with a focus on green development [1]. - The macroeconomic environment is favorable, with historically low interest rates, making high-dividend and growth-oriented assets attractive [2]. - The report highlights the importance of the newly proposed sustainable disclosure standards for enterprises, which aim to enhance transparency regarding climate-related risks and opportunities [10][20]. Summary by Sections Industry Investment Rating - The report recommends "Buy" for companies such as Huicheng Environmental, High Energy Environment, and Hongcheng Environment, indicating strong growth potential and favorable market conditions [6][7]. Industry Performance - The environmental sector outperformed the market, with a weekly increase of 3.32%, surpassing the Shanghai Composite Index by 1.40% and the ChiNext Index by 0.05% [3][35]. - Key sub-sectors showed positive growth, particularly monitoring (5.65%) and waste treatment (3.24%) [3]. Policy Developments - The Ministry of Finance issued a draft for the "Sustainable Disclosure Standards No. 1 - Climate," which outlines how companies should disclose climate-related risks and impacts [10][20]. - The Guangxi Autonomous Region's plan for air pollution prevention emphasizes strict control measures and accountability for pollution management [21][32]. Market Trends - The report notes that the environmental sector's valuation and institutional holdings are at historical lows, suggesting a potential for continued rebound [33]. - Companies like High Energy Environment and Huicheng Environmental are positioned to benefit from increased demand for waste treatment and recycling solutions [36]. Key Company Highlights - High Energy Environment is focusing on hazardous waste resource utilization and has a strong project pipeline, which is expected to accelerate revenue growth [36]. - Huicheng Environmental is advancing in the hazardous waste sector with significant projects and innovative technologies for plastic recycling, indicating robust growth prospects [36].

Investment Rating - The report indicates a positive outlook for the pet industry, highlighting its rapid growth and potential investment opportunities [1][15][17]. Core Insights - The pet industry is experiencing significant growth, with exhibition space increasing from 42,000 square meters in 2021 to 100,000 square meters by 2025, representing a 138% growth [1][15]. - The number of exhibitors has surged from 400 in 2021 to 1,200 by 2025, marking a 200% increase [1][15]. - The first day of the event saw a 43% increase in attendees compared to the previous year, with a new procurement event attracting over 120 exhibitors and 3,262 high-quality buyers [1][15]. - The transaction volume during the two-day professional visitor day exceeded 35 million yuan, a 175% increase year-on-year [1][15]. - The report emphasizes the importance of new product iterations in driving industry upgrades, with over 300 exclusive new products launched this year [2][16]. Summary by Sections Livestock Farming - The average price for lean pigs is 14.73 yuan/kg, down 0.3% from last week, indicating a relatively low valuation in the market [3][17]. - The average price for white feather chickens is 7.45 yuan/kg, down 0.4%, while chicken product prices remain stable at 8.9 yuan/kg [3][17]. - The report suggests focusing on leading companies with cost-effective growth potential, such as Muyuan Foods and Wens Foodstuff Group [3][17]. Agricultural Products - The approval of genetically modified varieties is set to enter commercial sales, with potential for significant growth in the sector [3][17]. - The report highlights the investment potential in the agricultural sector, particularly in companies that can leverage procurement and scale advantages [3][17]. Market Trends - The agricultural sector has underperformed the broader market by 1 percentage point this week, with a 1% increase in the agricultural sector overall [8][12]. - The report notes a 3.87% increase in the fishery sector, indicating a positive trend in that area [12][8].