Respan Dataset Explorer

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\noindent A group of 16 people will be partitioned into 4 indistinguishable 4-person committees. Each committee will have one chairperson and one secretary. The number of different ways to make these assignments can be written as \(3^r M\), where \(r\) and \(M\) are positive integers and \(M\) is not divisible by 3. What is \(r\)?

\end{document}
\

To solve this problem, we need to calculate the total number of ways to partition 16 people into four indistinguishable 4-person committees, each with a chairperson and a secretary. This calculation involves combinatorial analysis and prime factorization to find the power of 3 in the final expression.

**1. Partitioning into Committees:**

Since the committees are indistinguishable, the number of ways to partition the 16 people into four committees of four is given by:

\[
\text{Number of ways} = \frac{16!}{4! \, 4! \, 4! \, 4! \times 4!}
\]

Here, the denominator includes an extra \(4!\) to account for the indistinguishability of the committees.

**2. Assigning Chairperson and Secretary in Each Committee:**

For each committee, we need to assign a chairperson and a secretary:

- Number of ways to choose a chairperson: 4 choices.
- Number of ways to choose a secretary (after choosing the chairperson): 3 choices.
- Total ways per committee: \(4 \times 3 = 12\).

Since there are four committees, the total number of ways for all committees is \(12^4\).

**3. Total Number of Ways:**

Combining both steps:

\[
\text{Total ways} = \frac{16!}{(4!)^4 \times 4!} \times 12^4
\]

**4. Prime Factorization to Find the Power of 3:**

We need to express the total number of ways in the form \(3^r M\), where \(M\) is not divisible by 3.

First, factorize each term to find the exponents of 3:

- \(16!\) contains exponents of primes up to 16. The exponent of 3 in \(16!\) is calculated using Legendre's formula:

\[
\nu_3(16!) = \left\lfloor \frac{16}{3} \right\rfloor + \left\lfloor \frac{16}{9} \right\rfloor = 5 + 1 = 6
\]

- \((4!)^4 = (24)^4 = (2^3 \times 3)^4 = 2^{12} \times 3^4\)
- \(4! = 24 = 2^3 \times 3\)
- \(12^4 = (2^2 \times 3)^4 = 2^8 \times 3^4\)

Now, combine the exponents of 3:

- Numerator exponent: \(6 ( \text{from } 16!) + 4 ( \text{from } 12^4) = 10\)
- Denominator exponent: \(4 ( \text{from } (24)^4) + 1 ( \text{from } 4!) = 5\)

Subtracting the exponents in the denominator from the numerator:

\[
r = 10 - 5 = 5
\]

Therefore, the exponent \(r\) is 5.

**Answer:** \(5\)

System: You are an expert Named Entity Recognition (NER) system. Label all identifiable entities, abstract concepts, and meaningful ideas in the provided input text, emphasizing relevance to the financial domain.

Ensure the following:
Label All Meaningful Entities: Identify every meaningful entity related to financial analysis, economic dynamics, or market contexts.
Define New Concepts as Needed: Introduce and define entity types for abstract financial concepts or industry-specific terms not typically found in standard NER tasks.
Provide an Exhaustive Entity List: Include every relevant label mentioned in the input text.

Answer in the following format:
<entity from the text> | <entity concept> | <description of entity group/concept>,
<entity from the text> | <entity concept> | <description of entity group/concept>,
...

Here is an Example : 
Input: 
Lawmakers continue to try to police social media use among teens — but Meta, parent company to Facebook, Instagram, and Threads, is pushing another group of companies to do the security work. Meta is expected to announce a proposal on Nov. 15 that will push for tech giants like Google and Apple to carry a bigger burden in keeping teenagers off of potentially harmful platforms. Meta's vision is that these companies, which manage app stores such as the Apple App Store and Google Play Store, require parental approval for teenagers aged 13 to 15 to download applications, according to a report by The Washington Post.

Output:
Lawmakers | Regulatory agents | Individuals or groups responsible for creating and enacting laws, often influencing economic and regulatory environments.  
social media | Digital Channel | Online media channels for content sharing and user interaction, particularly influential in advertising and consumer engagement.
Meta | Company | Parent company of Facebook, Instagram, and Threads, involved in social media and technology sectors.  
Facebook | Company | Social media platform owned by Meta, significant player in digital advertising and social media markets.  
Instagram | Company | Photo and video sharing social media platform owned by Meta, influential in marketing and consumer engagement.  
Threads | Company | Social media platform owned by Meta, contributing to the digital communication landscape.  
Nov. 15 | Date | Specific date relevant for financial or regulatory announcements, potentially impacting market perceptions. 
tech giants | Major Companies | Entities that hold substantial market power in the technology sector. 
Google | Company | Technology company known for its search engine and digital services, significant in advertising and app distribution.  
Apple | Company | Technology company known for its hardware and software products, influential in consumer technology and app distribution.  
bigger burden | Operational Challenge | heightened difficulties or obstacles impacting a company’s operations, often resulting in resource strain or inefficiencies.
Apple App Store | Platform | Digital distribution platform for applications on Apple devices, relevant for app market dynamics.  
Google Play Store | Platform | Digital distribution platform for applications on Android devices, important for app market dynamics.  
Parental approval | Concept | Regulatory measure proposed to manage access to applications by minors, impacting technology and social media usage.  
The Washington Post | Newspaper | News outlet providing reports and analysis, influential in shaping public opinion and regulatory discourse.
User: KEY POINTS: On average, premiums are set to rise by more than 50% for people getting health coverage through a marketplace plan. The American Rescue Plan Act, which was signed into law in March 2021, removed — for two years — the income cap for eligibility (400%) of the federal poverty level. Of the 14.5 million people enrolled in marketplace plans, 13 million receive subsidies of varying amounts to reduce what they pay in premiums. If you get your health insurance through the government Health Insurance Marketplace, you may want to brace for higher premiums next year. Unless Congress takes action, enhanced premium subsidies — technically, tax credits — that have been in place for 2021 and 2022 will disappear after this year. The change would affect 13
Assistant:

premiums | Financial Term | Regular payments made for health insurance coverage, relevant to financial planning and household budgeting.
marketplace plan | Health Insurance Type | Health coverage plans available through the government Health Insurance Marketplace, impacting personal finances.
American Rescue Plan Act | Legislation | Law signed in March 2021 aimed at providing economic relief post-pandemic, substantial in healthcare and economic policy contexts.
income cap | Financial Threshold | Limit on earnings for eligibility of financial benefits, relevant to financial assistance programs.
federal poverty level | Economic Measure | Standardized income measure used to determine financial assistance eligibility, significant in socioeconomic analysis.
subsidies | Financial Assistance | Financial support provided to reduce costs, crucial in the context of healthcare affordability.
Health Insurance Marketplace | Platform | Government-established exchange for purchasing health insurance, affecting insurance market dynamics and consumer choice.
Congress | Legislative Body | The national legislative body tasked with enacting laws, influential in policy making and economic regulation.
enhanced premium subsidies | Financial Assistance | Increased financial support for health insurance premiums, tied to economic policy and legislation.
tax credits | Tax Concept | Deductions from the total amount of money a taxpayer owes, significant in financial planning and government policy.

System: You are an expert Named Entity Recognition (NER) system. Label all identifiable entities, abstract concepts, and meaningful ideas in the provided input text, emphasizing relevance to the financial domain.

Ensure the following:
Label All Meaningful Entities: Identify every meaningful entity related to financial analysis, economic dynamics, or market contexts.
Define New Concepts as Needed: Introduce and define entity types for abstract financial concepts or industry-specific terms not typically found in standard NER tasks.
Provide an Exhaustive Entity List: Include every relevant label mentioned in the input text.

Answer in the following format:
<entity from the text> | <entity concept> | <description of entity group/concept>,
<entity from the text> | <entity concept> | <description of entity group/concept>,
...

Here is an Example : 
Input: 
Lawmakers continue to try to police social media use among teens — but Meta, parent company to Facebook, Instagram, and Threads, is pushing another group of companies to do the security work. Meta is expected to announce a proposal on Nov. 15 that will push for tech giants like Google and Apple to carry a bigger burden in keeping teenagers off of potentially harmful platforms. Meta's vision is that these companies, which manage app stores such as the Apple App Store and Google Play Store, require parental approval for teenagers aged 13 to 15 to download applications, according to a report by The Washington Post.

Output:
Lawmakers | Regulatory agents | Individuals or groups responsible for creating and enacting laws, often influencing economic and regulatory environments.  
social media | Digital Channel | Online media channels for content sharing and user interaction, particularly influential in advertising and consumer engagement.
Meta | Company | Parent company of Facebook, Instagram, and Threads, involved in social media and technology sectors.  
Facebook | Company | Social media platform owned by Meta, significant player in digital advertising and social media markets.  
Instagram | Company | Photo and video sharing social media platform owned by Meta, influential in marketing and consumer engagement.  
Threads | Company | Social media platform owned by Meta, contributing to the digital communication landscape.  
Nov. 15 | Date | Specific date relevant for financial or regulatory announcements, potentially impacting market perceptions. 
tech giants | Major Companies | Entities that hold substantial market power in the technology sector. 
Google | Company | Technology company known for its search engine and digital services, significant in advertising and app distribution.  
Apple | Company | Technology company known for its hardware and software products, influential in consumer technology and app distribution.  
bigger burden | Operational Challenge | heightened difficulties or obstacles impacting a company’s operations, often resulting in resource strain or inefficiencies.
Apple App Store | Platform | Digital distribution platform for applications on Apple devices, relevant for app market dynamics.  
Google Play Store | Platform | Digital distribution platform for applications on Android devices, important for app market dynamics.  
Parental approval | Concept | Regulatory measure proposed to manage access to applications by minors, impacting technology and social media usage.  
The Washington Post | Newspaper | News outlet providing reports and analysis, influential in shaping public opinion and regulatory discourse.
User: KEY POINTS: Germany has proposed new legislation to allow British SMEs to become German. Around 10,000 German-based businesses are registered under British rules. The new legislation was adopted by Germany’s cabinet on Wednesday. Germany is planning to allow thousands of small businesses registered under British rules to convert to being German firms after Brexit. The draft bill, seen by CNBC and put forward by the Federal Ministry of Justice and Consumer Protection, was adopted by the German government Wednesday. If passed through the German parliament, amendments could be made to the country's Transformation Act, affecting around 10,000 small to medium-sized businesses. Under EU freedoms, those businesses were able to register their firms under British rules despite being based in Germany. Reasons for this were that it was considered
Assistant:

Germany | Country | European nation, key player in EU economic policies and legislation.  
legislation | Legal Framework | A proposed or enacted law or body of laws, significant in shaping economic and business environments.  
British SMEs | Business Entity | Small and Medium-sized Enterprises based in the United Kingdom, important for the economy due to their contribution to employment and GDP.  
German-based businesses | Business Entity | Companies operating in Germany, significant for local economic activity and employment.  
British rules | Regulatory Framework | Legal and operational standards set by the United Kingdom, impacting businesses registered under its jurisdiction.  
Germany’s cabinet | Government Body | Executive governing body of Germany responsible for policy-making and legislation proposals.  
Brexit | Political Event | The United Kingdom's withdrawal from the European Union, impacting trade, regulatory, and economic frameworks.  
Federal Ministry of Justice and Consumer Protection | Government Body | German government ministry responsible for legal affairs, influencing regulatory changes and consumer rights.  
German government | Government Entity | The federal governing body of Germany, responsible for enacting laws and managing national affairs.  
German parliament | Government Body | Legislative body of Germany, responsible for passing laws and shaping national legislation.  
Transformation Act | Legal Framework | German legal statute governing corporate transformations, influencing business structuring and operations.  
EU freedoms | Legal Principle | Rights and privileges within the European Union that facilitate cross-border business operations and mobility.  
CNBC | Media Outlet | Business news network providing financial and economic analyses, influencing public and investment perceptions.

System: You are an expert Named Entity Recognition (NER) system. Label all identifiable entities, abstract concepts, and meaningful ideas in the provided input text, emphasizing relevance to the financial domain.

Ensure the following:
Label All Meaningful Entities: Identify every meaningful entity related to financial analysis, economic dynamics, or market contexts.
Define New Concepts as Needed: Introduce and define entity types for abstract financial concepts or industry-specific terms not typically found in standard NER tasks.
Provide an Exhaustive Entity List: Include every relevant label mentioned in the input text.

Answer in the following format:
<entity from the text> | <entity concept> | <description of entity group/concept>,
<entity from the text> | <entity concept> | <description of entity group/concept>,
...

Here is an Example : 
Input: 
Lawmakers continue to try to police social media use among teens — but Meta, parent company to Facebook, Instagram, and Threads, is pushing another group of companies to do the security work. Meta is expected to announce a proposal on Nov. 15 that will push for tech giants like Google and Apple to carry a bigger burden in keeping teenagers off of potentially harmful platforms. Meta's vision is that these companies, which manage app stores such as the Apple App Store and Google Play Store, require parental approval for teenagers aged 13 to 15 to download applications, according to a report by The Washington Post.

Output:
Lawmakers | Regulatory agents | Individuals or groups responsible for creating and enacting laws, often influencing economic and regulatory environments.  
social media | Digital Channel | Online media channels for content sharing and user interaction, particularly influential in advertising and consumer engagement.
Meta | Company | Parent company of Facebook, Instagram, and Threads, involved in social media and technology sectors.  
Facebook | Company | Social media platform owned by Meta, significant player in digital advertising and social media markets.  
Instagram | Company | Photo and video sharing social media platform owned by Meta, influential in marketing and consumer engagement.  
Threads | Company | Social media platform owned by Meta, contributing to the digital communication landscape.  
Nov. 15 | Date | Specific date relevant for financial or regulatory announcements, potentially impacting market perceptions. 
tech giants | Major Companies | Entities that hold substantial market power in the technology sector. 
Google | Company | Technology company known for its search engine and digital services, significant in advertising and app distribution.  
Apple | Company | Technology company known for its hardware and software products, influential in consumer technology and app distribution.  
bigger burden | Operational Challenge | heightened difficulties or obstacles impacting a company’s operations, often resulting in resource strain or inefficiencies.
Apple App Store | Platform | Digital distribution platform for applications on Apple devices, relevant for app market dynamics.  
Google Play Store | Platform | Digital distribution platform for applications on Android devices, important for app market dynamics.  
Parental approval | Concept | Regulatory measure proposed to manage access to applications by minors, impacting technology and social media usage.  
The Washington Post | Newspaper | News outlet providing reports and analysis, influential in shaping public opinion and regulatory discourse.
User: KEY POINTS: More Americans are planning to move this year due to the flexible work from home lifestyle that the Covid-19 pandemic has ushered in, market researcher The NPD Group said. Twenty percent more consumers are planning to move this year compared with the prior year. Consumers are relocating for a variety of reasons during the pandemic such as lowering their cost of living or being closer to family, NPD Group said. Sales of moving supplies and services have shot up during this time. More Americans are planning to move this year due to the flexible work from home lifestyle that the Covid-19 pandemic has ushered in, market researcher The NPD Group said in a recent blog post. Nearly 20% of people in the country are working from
Assistant:

More Americans | Demographic Group | Population segment within the United States experiencing changes in living arrangements due to economic and social factors.  
flexible work from home lifestyle | Trend | An emerging work arrangement allowing employees to perform their jobs outside traditional office settings, significantly impacting housing and labor markets.  
Covid-19 pandemic | Health Event | Global pandemic that has drastically influenced economic dynamics, social behaviors, and policy decisions.  
The NPD Group | Market Research Firm | Organization specializing in market research, providing insights into consumer behaviors and trends.  
Twenty percent more consumers | Statistical Data | Quantitative measure indicating a significant increase in the number of consumers planning to move compared to the previous year.  
cost of living | Economic Factor | The amount of money needed to sustain a certain standard of living, often influencing relocation decisions.  
Sales of moving supplies and services | Economic Indicator | Measure indicating increased economic activity in the moving industry, correlating with relocation trends.  
blog post | Digital Publication | Online form of communication used by organizations to share information and insights, impacting public understanding and investor perceptions.  
relocating | Activity | The act of moving to a different place, often for economic, social, or personal reasons, impacting real estate and labor markets.  
pandemic | Concept | Refers to the widespread outbreak of a disease, affecting economic activities and lifestyle changes globally.

System: You are an expert Named Entity Recognition (NER) system. Label all identifiable entities, abstract concepts, and meaningful ideas in the provided input text, emphasizing relevance to the financial domain.

Ensure the following:
Label All Meaningful Entities: Identify every meaningful entity related to financial analysis, economic dynamics, or market contexts.
Define New Concepts as Needed: Introduce and define entity types for abstract financial concepts or industry-specific terms not typically found in standard NER tasks.
Provide an Exhaustive Entity List: Include every relevant label mentioned in the input text.

Answer in the following format:
<entity from the text> | <entity concept> | <description of entity group/concept>,
<entity from the text> | <entity concept> | <description of entity group/concept>,
...

Here is an Example : 
Input: 
Lawmakers continue to try to police social media use among teens — but Meta, parent company to Facebook, Instagram, and Threads, is pushing another group of companies to do the security work. Meta is expected to announce a proposal on Nov. 15 that will push for tech giants like Google and Apple to carry a bigger burden in keeping teenagers off of potentially harmful platforms. Meta's vision is that these companies, which manage app stores such as the Apple App Store and Google Play Store, require parental approval for teenagers aged 13 to 15 to download applications, according to a report by The Washington Post.

Output:
Lawmakers | Regulatory agents | Individuals or groups responsible for creating and enacting laws, often influencing economic and regulatory environments.  
social media | Digital Channel | Online media channels for content sharing and user interaction, particularly influential in advertising and consumer engagement.
Meta | Company | Parent company of Facebook, Instagram, and Threads, involved in social media and technology sectors.  
Facebook | Company | Social media platform owned by Meta, significant player in digital advertising and social media markets.  
Instagram | Company | Photo and video sharing social media platform owned by Meta, influential in marketing and consumer engagement.  
Threads | Company | Social media platform owned by Meta, contributing to the digital communication landscape.  
Nov. 15 | Date | Specific date relevant for financial or regulatory announcements, potentially impacting market perceptions. 
tech giants | Major Companies | Entities that hold substantial market power in the technology sector. 
Google | Company | Technology company known for its search engine and digital services, significant in advertising and app distribution.  
Apple | Company | Technology company known for its hardware and software products, influential in consumer technology and app distribution.  
bigger burden | Operational Challenge | heightened difficulties or obstacles impacting a company’s operations, often resulting in resource strain or inefficiencies.
Apple App Store | Platform | Digital distribution platform for applications on Apple devices, relevant for app market dynamics.  
Google Play Store | Platform | Digital distribution platform for applications on Android devices, important for app market dynamics.  
Parental approval | Concept | Regulatory measure proposed to manage access to applications by minors, impacting technology and social media usage.  
The Washington Post | Newspaper | News outlet providing reports and analysis, influential in shaping public opinion and regulatory discourse.
User: KEY POINTS: Monday - Friday, 6:00 - 7:00 PM ET The stock of Advanced Micro Devices, a semiconductor company going up against Intel and Nvidia, could be just the right pick for those worried about a slowdown, CNBC's Jim Cramer says. "AMD is part of the tech company renaissance," the "Mad Money" host argues. While many of the market's semiconductor stocks slid into Tuesday's close, CNBC's noticed one key player prevail: the stock of Advanced Micro Devices , which has rallied an astounding 192 percent just in 2018. "Many of the semiconductor stocks were down today, but not this one," the " Mad Money " host said. "Why? End markets." A leader in chips — a colloquial term for high-power computer processors — for personal computers, video gaming,
Assistant:

Monday - Friday, 6:00 - 7:00 PM ET | Timeframe | Specific period relevant for market trading or financial program broadcasts, potentially impacting stock analyses or investor actions.
Advanced Micro Devices | Company | Semiconductor company competing with Intel and Nvidia, significant in tech industry and stock market performance.
semiconductor | Industry Sector | Industry segment related to computer hardware, particularly important in technology and electronic devices markets.
Intel | Company | Major player in the semiconductor industry, competing with companies like AMD and Nvidia.
Nvidia | Company | Leading company in graphics processing unit (GPU) technology, competing in the semiconductor market.
slowdown | Economic Condition | Period or phase of reduced economic activity or growth, affecting investment and company performance.
CNBC | Media Outlet | Television channel specializing in business and financial news, influential in investor sentiment and market analyses.
Jim Cramer | Person | Financial analyst and host of CNBC's "Mad Money," influential in stock market opinions and investment strategies.
tech company renaissance | Industry Trend | Revival or significant growth period in the technology industry, affecting stock valuations and market perceptions.
Mad Money | TV Show | Television program on CNBC focused on financial advice and stock market tips, hosted by Jim Cramer.
stock | Financial Instrument | Type of security representing ownership in a company, crucial for investment and financial market operations.
192 percent | Performance Metric | Indicator of stock growth, representing a significant increase in stock value, impacting investor decisions.
2018 | Year | Specific timeframe for financial performance and historical market context.
end markets | Market Segment | Final demand sectors for semiconductor products, influencing company sales and stock performance.
chips | Product Category | High-power computer processors used in devices such as personal computers and video gaming consoles.

You are a database expert and SQL optimizer. You will be given a SQL query and its rewritten variant. The rewritten query improves performance upon the original while maintaining equivalence. Your task is to create a new pair of original and rewritten queries that invoke a similar rewrite.

[ORIGINAL QUERY]```select case when (select count(*) from store_sales where ss_quantity between 1 and 20) > 1071 then (select avg(ss_ext_tax) from store_sales where ss_quantity between 1 and 20) else (select avg(ss_net_paid_inc_tax) from store_sales where ss_quantity between 1 and 20) end bucket1,case when (select count(*) from store_sales where ss_quantity between 21 and 40) > 39161 then (select avg(ss_ext_tax) from store_sales where ss_quantity between 21 and 40) else (select avg(ss_net_paid_inc_tax) from store_sales where ss_quantity between 21 and 40) end bucket2,case when (select count(*) from store_sales where ss_quantity between 41 and 60) > 29434 then (select avg(ss_ext_tax) from store_sales where ss_quantity between 41 and 60) else (select avg(ss_net_paid_inc_tax) from store_sales where ss_quantity between 41 and 60) end bucket3,case when (select count(*) from store_sales where ss_quantity between 61 and 80) > 6568 then (select avg(ss_ext_tax) from store_sales where ss_quantity between 61 and 80) else (select avg(ss_net_paid_inc_tax) from store_sales where ss_quantity between 61 and 80) end bucket4,case when (select count(*) from store_sales where ss_quantity between 81 and 100) > 21216 then (select avg(ss_ext_tax) from store_sales where ss_quantity between 81 and 100) else (select avg(ss_net_paid_inc_tax) from store_sales where ss_quantity between 81 and 100) end bucket5 from reason where r_reason_sk = 1 ;```

[REWRITTEN QUERY]```WITH bucket AS ( SELECT CASE WHEN ss_quantity BETWEEN 1 AND 20 THEN 1 WHEN ss_quantity BETWEEN 21 AND 40 THEN 2 WHEN ss_quantity BETWEEN 41 AND 60 THEN 3 WHEN ss_quantity BETWEEN 61 AND 80 THEN 4 WHEN ss_quantity BETWEEN 81 AND 100 THEN 5 END AS quantity_range, COUNT(*) AS cnt, AVG(ss_ext_tax) AS avg_ext_tax, AVG(ss_net_paid_inc_tax) AS avg_net_paid_inc_tax FROM store_sales GROUP BY CASE WHEN ss_quantity BETWEEN 1 AND 20 THEN 1 WHEN ss_quantity BETWEEN 21 AND 40 THEN 2 WHEN ss_quantity BETWEEN 41 AND 60 THEN 3 WHEN ss_quantity BETWEEN 61 AND 80 THEN 4 WHEN ss_quantity BETWEEN 81 AND 100 THEN 5 END ) SELECT CASE WHEN b1.cnt > 1071 THEN b1.avg_ext_tax ELSE b1.avg_net_paid_inc_tax END AS bucket1, CASE WHEN b2.cnt > 39161 THEN b2.avg_ext_tax ELSE b2.avg_net_paid_inc_tax END AS bucket2, CASE WHEN b3.cnt > 29434 THEN b3.avg_ext_tax ELSE b3.avg_net_paid_inc_tax END AS bucket3, CASE WHEN b4.cnt > 6568 THEN b4.avg_ext_tax ELSE b4.avg_net_paid_inc_tax END AS bucket4, CASE WHEN b5.cnt > 21216 THEN b5.avg_ext_tax ELSE b5.avg_net_paid_inc_tax END AS bucket5 FROM (SELECT * FROM bucket WHERE quantity_range = 1) b1, (SELECT * FROM bucket WHERE quantity_range = 2) b2, (SELECT * FROM bucket WHERE quantity_range = 3) b3, (SELECT * FROM bucket WHERE quantity_range = 4) b4, (SELECT * FROM bucket WHERE quantity_range = 5) b5, reason WHERE r_reason_sk = 1;```

Now, consider the TPC-DS schema and create a new original and equivalent rewritten query pair such that the rewrite operation is similar to the provided demonstration.Keep the following points in mind while creating the new query pair:
1. The original query must not have any CTEs.
2. The original query must make use of the following fact tables: ['store_returns', 'catalog_returns', 'store_sales']. Below is the join graph for these fact tables:
    ['store_returns(sr_hdemo_sk) references household_demographics(hd_demo_sk);', 'store_returns(sr_store_sk) references store(s_store_sk);', 'store_returns(sr_addr_sk) references customer_address(ca_address_sk);']
    ['catalog_returns(cr_warehouse_sk) references warehouse(w_warehouse_sk);', 'catalog_returns(cr_returned_time_sk) references time_dim(t_time_sk);', 'catalog_returns(cr_item_sk) references item(i_item_sk);']
    ['store_sales(ss_item_sk) references item(i_item_sk);', 'store_sales(ss_promo_sk) references promotion(p_promo_sk);', 'store_sales(ss_sold_time_sk) references time_dim(t_time_sk);']
6. The original query must employ 2 joins.
7. The original query must employ the following aggregate functions: ['min', 'count'].
8. The original query must employ the following operators in its WHERE clause: ['count'].
9. The rewritten query must be equivalent to the original query, and must follow a similar rewrite pattern as in the given example. Enclose the original and rewritten queries within ``` and ```.

Sure, here's a new pair of original and rewritten queries based on the requirements and using a similar rewrite pattern as demonstrated:

[ORIGINAL QUERY]
```sql
SELECT 
  CASE 
    WHEN (SELECT COUNT(*) FROM store_sales WHERE ss_sold_date BETWEEN '2023-01-01' AND '2023-06-30') > 5000 
    THEN (SELECT MIN(sr_return_amt) FROM store_returns JOIN store_sales ON store_returns.sr_item_sk = store_sales.ss_item_sk WHERE store_returns.sr_return_amt > 50) 
    ELSE (SELECT MIN(cr_return_amt) FROM catalog_returns JOIN store_sales ON catalog_returns.cr_item_sk = store_sales.ss_item_sk WHERE catalog_returns.cr_return_amt > 50) 
  END AS return_analysis
FROM store
WHERE s_store_sk = 3;
```

[REWRITTEN QUERY]
```sql
WITH sales_data AS (
  SELECT 
    COUNT(*) AS sales_cnt, 
    MIN(sr_return_amt) AS min_store_return_amt, 
    MIN(cr_return_amt) AS min_catalog_return_amt
  FROM store_sales 
  LEFT JOIN store_returns ON store_sales.ss_item_sk = store_returns.sr_item_sk AND store_returns.sr_return_amt > 50
  LEFT JOIN catalog_returns ON store_sales.ss_item_sk = catalog_returns.cr_item_sk AND catalog_returns.cr_return_amt > 50
  WHERE ss_sold_date BETWEEN '2023-01-01' AND '2023-06-30'
)
SELECT 
  CASE 
    WHEN sales_cnt > 5000 
    THEN min_store_return_amt 
    ELSE min_catalog_return_amt 
  END AS return_analysis
FROM sales_data, store
WHERE s_store_sk = 3;
```

**Explanation:**
1. **Fact Tables Used:** 'store_sales', 'store_returns', 'catalog_returns'
2. **Joins:** 
   - `store_returns.sr_item_sk` with `store_sales.ss_item_sk`
   - `catalog_returns.cr_item_sk` with `store_sales.ss_item_sk`
3. **Aggregate Functions:** `MIN` and `COUNT`
4. **Operators in WHERE Clause:** `COUNT`
5. **Pattern Rewrites:**
   - The original query makes repeated use of subqueries to determine counts and mins whereas the rewritten query consolidates this logic using a CTE.
   - The rewritten query achieves efficiency by computing aggregations using a single pass over the data, similar to the provided example.

System: You are an expert Named Entity Recognition (NER) system. Label all identifiable entities, abstract concepts, and meaningful ideas in the provided input text, emphasizing relevance to the financial domain.

Ensure the following:
Label All Meaningful Entities: Identify every meaningful entity related to financial analysis, economic dynamics, or market contexts.
Define New Concepts as Needed: Introduce and define entity types for abstract financial concepts or industry-specific terms not typically found in standard NER tasks.
Provide an Exhaustive Entity List: Include every relevant label mentioned in the input text.

Answer in the following format:
<entity from the text> | <entity concept> | <description of entity group/concept>,
<entity from the text> | <entity concept> | <description of entity group/concept>,
...

Here is an Example : 
Input: 
Lawmakers continue to try to police social media use among teens — but Meta, parent company to Facebook, Instagram, and Threads, is pushing another group of companies to do the security work. Meta is expected to announce a proposal on Nov. 15 that will push for tech giants like Google and Apple to carry a bigger burden in keeping teenagers off of potentially harmful platforms. Meta's vision is that these companies, which manage app stores such as the Apple App Store and Google Play Store, require parental approval for teenagers aged 13 to 15 to download applications, according to a report by The Washington Post.

Output:
Lawmakers | Regulatory agents | Individuals or groups responsible for creating and enacting laws, often influencing economic and regulatory environments.  
social media | Digital Channel | Online media channels for content sharing and user interaction, particularly influential in advertising and consumer engagement.
Meta | Company | Parent company of Facebook, Instagram, and Threads, involved in social media and technology sectors.  
Facebook | Company | Social media platform owned by Meta, significant player in digital advertising and social media markets.  
Instagram | Company | Photo and video sharing social media platform owned by Meta, influential in marketing and consumer engagement.  
Threads | Company | Social media platform owned by Meta, contributing to the digital communication landscape.  
Nov. 15 | Date | Specific date relevant for financial or regulatory announcements, potentially impacting market perceptions. 
tech giants | Major Companies | Entities that hold substantial market power in the technology sector. 
Google | Company | Technology company known for its search engine and digital services, significant in advertising and app distribution.  
Apple | Company | Technology company known for its hardware and software products, influential in consumer technology and app distribution.  
bigger burden | Operational Challenge | heightened difficulties or obstacles impacting a company’s operations, often resulting in resource strain or inefficiencies.
Apple App Store | Platform | Digital distribution platform for applications on Apple devices, relevant for app market dynamics.  
Google Play Store | Platform | Digital distribution platform for applications on Android devices, important for app market dynamics.  
Parental approval | Concept | Regulatory measure proposed to manage access to applications by minors, impacting technology and social media usage.  
The Washington Post | Newspaper | News outlet providing reports and analysis, influential in shaping public opinion and regulatory discourse.
User: TITLE: Economic Profile Governor: Ron DeSantis, Republican Population: 22,244,823 GDP growth (Q1 2023): 3.50% Unemployment rate (May 2023): 2.60% Top corporate tax rate: 5.50% Top individual income tax rate: None Gasoline tax: 61.95 cents/gallon Bond rating (Moody's/S&P): Aaa, Stable/AAA, Stable Economic profile sources: U.S. Census Bureau, U.S. Bureau of Economic Analysis, U.S. Bureau of Labor Statistics, Federation of Tax Administrators, American Petroleum Institute (including 18.40 cent/gallon federal tax), Moody's Investor Service, S&P Global Market Intelligence TITLE: More In Top States for Business 2023
Assistant:

Ron DeSantis | Person | Governor of the state, influencing economic and political decisions.
Republican | Political Party | Political affiliation of the governor, potentially impacting fiscal and regulatory policies.
Population | Demographic Metric | Total number of individuals in the area, relevant for market size and economic analysis.
22,244,823 | Population Figure | Specific population count, influencing market potential and labor force size.
GDP growth (Q1 2023) | Economic Indicator | Measure of economic performance and expansion during a specific period.
3.50% | Growth Rate | Specific percentage of GDP growth, indicating economic health and activity level.
Unemployment rate (May 2023) | Employment Metric | Measure of labor market conditions, reflecting employment levels.
2.60% | Unemployment Rate | Specific percentage of the labor force that is unemployed, indicating economic stability and labor market health.
Top corporate tax rate | Tax Metric | Highest rate of taxation imposed on corporate profits, affecting business decisions and investment.
5.50% | Tax Percentage | Specific rate of corporate taxation, influencing business environment and economic policy.
Top individual income tax rate | Tax Metric | Highest rate of taxation on individual earnings, impacting disposable income and consumption.
None | Tax Rate | Indication of no individual income tax, influencing individual financial decisions and attractiveness for residency.
Gasoline tax | Tax Metric | Tax imposed on gasoline, affecting transportation costs and consumer behavior.
61.95 cents/gallon | Tax Amount | Specific amount of gasoline tax, impacting fuel prices and economic activity.
Bond rating (Moody's/S&P) | Financial Metric | Assessment of creditworthiness by rating agencies, influencing borrowing costs and investment attractiveness.
Aaa, Stable/AAA, Stable | Credit Ratings | Specific credit ratings, indicating strong financial health and low risk.
U.S. Census Bureau | Information Source | Organization providing demographic data, relevant for population and economic studies.
U.S. Bureau of Economic Analysis | Information Source | Agency supplying economic data, including GDP and other indicators.
U.S. Bureau of Labor Statistics | Information Source | Provider of labor market data, including unemployment rates.
Federation of Tax Administrators | Information Source | Organization offering information on tax systems and policies.
American Petroleum Institute | Information Source | Provider of data on petroleum and gasoline, relevant for energy economics.
18.40 cent/gallon federal tax | Tax Detail | Specific federal tax on gasoline, part of overall fuel taxation, affecting transportation costs.
Moody's Investor Service | Rating Agency | Firm providing credit ratings, analysis, and financial risk assessments.
S&P Global Market Intelligence | Rating Agency | Company offering credit ratings and financial analysis, influencing investment decisions.
Top States for Business 2023 | Business Ranking | Evaluation or ranking of regions based on business climate and economic performance.

(In the school literature clubroom...)

Monika: "And... there! Everything's all set up for today's meeting. Now we just need Natsuki."

Sayori: "I hope she's not too late this time. I really want to hear her thoughts on that new manga!"

Yuri: "She can be a bit... particular, but I think we'll have a productive meeting once she arrives. The atmosphere is already quite nice."

Monika: "You're right, Yuri. The lighting we adjusted makes such a difference. It feels cozy and inviting."

Sayori: "Yeah! It’s like we’re in our own little world. Just us and the stories we love!"

Yuri: "And speaking of stories, I brought a few poems to share today. I think they’ll complement the manga discussions nicely."

Monika: "That sounds wonderful, Yuri! I can’t wait to hear them. And maybe we can even write a little together later."

Sayori: "Ooh, that sounds fun! I love writing with all of you. It's always a blast!" (gently rubs her belly) "Oh! And guess who can't wait to hear the new poems!"

Yuri: "Is that your stomach talking, Sayori? You must be really looking forward to the meeting!"

Sayori: "Hehe, well, it’s not just my stomach! I’m excited about the poems, too! But I could definitely use a snack while we read."

Monika: "I think we have some snacks in the back. Should I go grab them while we wait for Natsuki?"

Sayori: "Yes, please! A little treat would make everything even better!"

Yuri: "I don't mind waiting as long as we have a chance to enjoy each other's company and creativity. By the way, what type of poems did you bring, Yuri?"

Yuri: "They're a mix, really. Some are inspired by nature, while others explore emotions and relationships. I thought they might spark some interesting discussions."

Sayori: "Ooh, that sounds lovely! I can't wait to hear them. I always find poetry so beautiful, especially when it connects to our own experiences."

Monika: "Absolutely. It's fascinating how different styles can evoke various feelings. I think it complements our discussions about manga perfectly."

(Just then, the door swings open, and Natsuki rushes in.)

Natsuki: "Sorry I’m late! I got caught up with my baking, and then I almost lost track of time! Did I miss anything important?"

Sayori: "Nope! We were just talking about what we’re going to share today!"

Natsuki: "Good! Because I brought a few things to show too! And you guys better not say anything bad about them!"

Monika: "Of course not! We want to hear your thoughts. Besides, we’re all friends here, right?"

Natsuki: (smirking) "Yeah, yeah. Just you wait! You're going to love my picks!"

Yuri: "I’m looking forward to it, Natsuki. Let’s all dive in together!"

Sayori: "Yay! Now everything's perfect! I can’t wait to hear the poems and manga!" 

Natsuki: "Alright, let’s get started then! Who’s going first?"

(In the school literature clubroom...)

Monika: "And... there! Everything's all set up for today's meeting. Now we just need Natsuki."

Sayori: "I hope she's not too late this time. I really want to hear her thoughts on that new manga!"

Yuri: "She can be a bit... particular, but I think we'll have a productive meeting once she arrives. The atmosphere is already quite nice."

Monika: "You're right, Yuri. The lighting we adjusted makes such a difference. It feels cozy and inviting."

Sayori: "Yeah! It’s like we’re in our own little world. Just us and the stories we love!"

Yuri: "And speaking of stories, I brought a few poems to share today. I think they’ll complement the manga discussions nicely."

Monika: "That sounds wonderful, Yuri! I can’t wait to hear them. And maybe we can even write a little together later."

Sayori: "Ooh, that sounds fun! I love writing with all of you. It's always a blast!" (gently rubs her belly) "Oh! And guess who can't wait to hear the new poems!"

Monika: (laughs softly) "I think we all know who's excited! You're the best, Sayori."

Yuri: (smiling) "I’m glad my poems are something you look forward to. Writing can sometimes feel isolating, but sharing it makes it so much more meaningful."

Sayori: "Exactly! It’s like we’re all part of each other's stories. And that makes everything so special!"

Monika: "And speaking of stories, I had an idea. What if we each brought in our favorite manga or a novel that really touched us? It could be a fun way to express ourselves!"

Yuri: "I love that idea, Monika. It allows us to explore not just the stories themselves but also the emotions they evoke in us."

Sayori: "Yes! Let’s do it! I’m sure Natsuki will have plenty of suggestions too. She always has the best recommendations for manga!"

Monika: "Exactly! It's so lively when everyone shares their diverse tastes. It creates a nice dynamic."

Sayori: "I wonder what Natsuki's been reading lately! Maybe she found something new that's super cute and fun!"

Yuri: "Or perhaps something with a deeper theme that challenges conventional storytelling. Natsuki has a knack for finding unique gems, despite her sometimes rough exterior." 

Monika: "True! It’s always fascinating to see how differently we all interpret stories and what resonates with each of us. I can’t wait for her to join us."

Sayori: "Speaking of joining, I just realized I forgot to ask Natsuki to bring snacks! She always has the best treats!" 

Monika: "Maybe we should send her a message? It might be what’s keeping her from arriving."

Sayori: "Great idea! I’ll shoot her a text!" (pulls out her phone)

Yuri: "While we wait, how about we share our own thoughts on the manga we read this week? It might help pass the time."

Monika: "I love that idea! Let’s get started then." 

Just then, the door swings open and Natsuki rushes in, a bit flushed and holding a bag. 

Natsuki: "Sorry, I’m late! You won’t believe the new manga I just found! And I brought sweets!" 

Sayori: "Yay! You’re just in time, Natsuki!" 

Monika: "Perfect timing! Let’s dive into our discussions!" 

Natsuki: "Alright, but only if I get to go first! I have so much to say!" 

The group bursts into laughter, excitedly gathering around as Natsuki takes her seat, her energy contagious.

Three different pairs of shoes are placed in a row so that no left shoe is next to a right shoe from a different pair. In how many ways can these six shoes be lined up?

To solve this problem, we need to count the number of permutations of the six shoes (each distinguishable) such that no left shoe is next to a right shoe from a different pair. 

**Understanding the Constraints:**

- We have three pairs of shoes: A (A_L, A_R), B (B_L, B_R), and C (C_L, C_R).
- Forbidden adjacents are any pair where a left shoe is immediately next to a right shoe from a different pair.
- There are six such forbidden adjacent pairs:
  - f₁: (A_L, B_R)
  - f₂: (A_L, C_R)
  - f₃: (B_L, A_R)
  - f₄: (B_L, C_R)
  - f₅: (C_L, A_R)
  - f₆: (C_L, B_R)

**Using Inclusion-Exclusion Principle:**

1. **Total Permutations without Restrictions:** There are 6! = 720 total permutations of the six shoes.

2. **Counting Permutations with Forbidden Adjacents:**
   - For each forbidden pair fᵢ, the number of permutations where that pair appears is 5! = 120, because we treat the pair as a single entity.
   - Sum of permutations with any one forbidden adjacency:
     - S₁ = 6 forbidden pairs * 120 permutations each = 720.

3. **Subtracting Overlaps:**
   - Some permutations contain more than one forbidden adjacency.
   - For pairs of forbidden adjacents involving disjoint items (no shoe appears in both pairs), the number of permutations where both adjacents occur is 4! = 24.
   - There are 9 such disjoint pairs.
   - Sum of permutations where two forbidden adjacents occur:
     - S₂ = 9 pairs * 24 permutations each = 216.

4. **Adding Back Triple Overlaps:**
   - For triples where all forbidden adjacents involve disjoint items, the number of permutations where all three adjacents occur is 3! = 6.
   - There are 2 such triples.
   - Sum of permutations where three forbidden adjacents occur:
     - S₃ = 2 triples * 6 permutations each = 12.

5. **Applying Inclusion-Exclusion Formula:**
   - Total permutations with at least one forbidden adjacency:
     - |T| = S₁ - S₂ + S₃ = 720 - 216 + 12 = 516.
   - Permutations with no forbidden adjacents:
     - N = Total permutations - |T| = 720 - 516 = 204.

**Conclusion:**

The number of ways to line up the six shoes without any left shoe being next to a right shoe from a different pair is **204**.

\(\boxed{204}\)