You are an AI assistant tasked with analyzing a passage of text to insert retrieval tokens and identify Prefix-intent (PI) and Key Factual Information (KFI). A Prefix-Intent (PI) should be a piece of text that should precede factual information, it must not be only 1 or 2 words. Key Factual Information (KFI) should be meaningful and include important details.

Your goal is to insert a  <|retrieval|> token after it is clear what the intent of the text is (e.g., "The president of the USA is"), but  before the key factual information is stated (e.g., "Joe Biden"). Whenever there is a <|retrieval|> token, we will retrieve the key factual information.

Here is the passage you will be working with:

<passage>
requires a block-level city map for initial selections, and then a household-level map of the 100 selected blocks, rather than a household-level map of the whole city. Cluster sampling (also known as clustered sampling) generally increases the variability of sample estimates above that of simple random sampling, depending on how the clusters differ between one another as compared to the within-cluster variation. For this reason, cluster sampling requires a larger sample than SRS to achieve the same level of accuracy – but cost savings from clustering might still make this a cheaper option. Cluster sampling is commonly implemented as multistage sampling. This is a complex form of cluster sampling in which two or more levels of units are embedded one in the other. The first stage consists of constructing the clusters that will be used to sample from. In the second stage, a sample of primary units is randomly selected from each cluster (rather than using all units contained in all selected clusters). In following stages, in each of those selected clusters, additional samples of units are selected, and so on. All ultimate units (individuals, for instance) selected at the last step of this procedure are then surveyed. This technique, thus, is essentially the process of taking random subsamples of preceding random samples. Multistage sampling can substantially reduce sampling costs, where the complete population list would need to be constructed (before other sampling methods could be applied). By eliminating the work involved in describing clusters that are not selected, multistage sampling can reduce the large costs associated with traditional cluster sampling. However, each sample may not be a full representative of the whole population. Quota sampling In quota sampling, the population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. Then judgement is used to select the subjects or units from each segment based on a specified proportion. For example, an interviewer may be told to sample 200 females and 300 males between the age of 45 and 60. It is this second step which makes the technique one of non-probability sampling. In quota sampling the selection of the sample is non-random. For example, interviewers might be tempted to interview those who look most helpful. The problem is that these samples may be biased because not everyone gets a chance of selection. This random element is its greatest weakness and quota versus probability has been a matter of controversy for several years. Minimax sampling In imbalanced datasets, where the sampling ratio does not follow the population statistics, one can resample the dataset in a conservative manner called minimax sampling. The minimax sampling has its origin in Anderson minimax ratio whose value is proved to be 0.5: in a binary classification, the class-sample sizes should be chosen equally. This ratio can be proved to be minimax ratio only under the assumption of LDA classifier with Gaussian distributions. The notion of minimax sampling is recently developed for a general class of classification rules, called class-wise smart classifiers. In this case, the sampling ratio of classes is selected so that the worst case classifier error over all the possible population statistics for class prior probabilities, would be the best. Accidental sampling Accidental sampling (sometimes known as grab, convenience or opportunity sampling) is a type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, a population is selected because it is readily available and convenient. It may be through meeting the person or including a person in the sample when one meets them or chosen by finding them
</passage>

Follow these steps to complete the task:

1. Inserting retrieval tokens:
   a. Read through the text carefully.
   b. Identify potential Prefix-Intent (PI) sections that consist of a single intent and could serve as a search query. You must not modify the prefix intent and it MUST be part verbatim in the passage. It cannot be single or only a few words.
   c. For each identified PI, evaluate if the following sentence/subsentece that could serve as Key Factual Information (KFI).
   d. Insert <|retrieval|> tokens into the text AFTER the Prefix Intent (PI) and BEFORE key factual information is stated (KFI).
   e. Key Factual information should not intersect with Prefix Intent.

2. Identifying Prefix-Intent (PI) and Key Factual Information (KFI):
   a. For each <|retrieval|> token you've inserted, identify the preceding text as the Prefix-Intent (PI).
   b. Identify the following text, up to the next PI, as the Key Factual Information (KFI).
   c. Ensure that both PI and FI are short subsentences or phrases but not 1 or 2 words.

3. Insert <|start-PI|>,<|end-PI|>, <|start-KFI|>, <|end-KFI|>.
   a. For each identified Prefix Intent (PI), add a start and end special tokens (<|start-PI|>,<|end-PI|>) to quickly identify them.
   b. Do the same for the Key Factual Information (KFI) (<|start-KFI|>, <|end-KFI|>)
   c. Ensure that the very first PI in the passage is preceded by <|start-PI|>.
   d. Double-check that every PI and KFI is properly enclosed in these tags.

4. Describing ideal retrieved information:
   a. Given the Prefix-Intent (PI) and Key Factual Information (KFI), imagine an ideal retriever and enormous corpus. 
   b. Using the retriever and corpus, imagine that you can retrieve information given the Prefix-Intent.  
   c. Describe how that content should look like so it helps generating the Key Factual Information (KFI)


5. Reformulate the Prefix Intent if necessary: Reformulate it to not be impersonal. This means that if the subject it is not identified (e.g. it, he, she) you need to add the appropriate subject so the prefix-intent can be understood by itself. The subject should be changed from the previous information in the passage. Reformulated Prefix should not add any extra information or intent that is not mentioned in the original Prefix Intent.


6. Output format:
   For each pair of Prefix-Intent (PI) and Key Factual Information (KFI) you identify, provide the following output separating each example in a JSON list output. Ensure that it is actually a JSON.

   - Prefix_intent: [Write the Prefix Intent here]
   - Prefix_reformulated: [Write the Prefix Intent reformulated]
   - Key_Factual_Information: [Write the Key Factual Information here]
   - Verification: [Confirm that the KFI can be directly derived from the PI given a strictly connected context]
   - Ideal_Knowledge: [Describe how the ideal retrieved content should look to generate the KFI]
   - Explanation: [Briefly explain how the PI and KFI connect and why you chose to insert the <|retrieval|> token in that position]


7. Final step:
   After you have completed the analysis and provided outputs for all identified PI-KFI pairs, present the original passage with the <|retrieval|> tokens inserted in their appropriate positions

Here's an example of the expected output format:

Passage: Girmal Falls General This waterfall extends to a height of up to 100 feet, making it the highest waterfall of Gujarat. The picturesque beauty of this site makes it popular among visitors and people of the region alike. The water swiftly falls from a great height, creating a fog like condition that’s eye catching. The government of this state is working on many projects to make this place an ideal picnic spot and a tourist attraction. The fall comes to its best form at the time of monsoon and provides an immensely striking appearance. Some of the best natural features of Gujarat can be explored in this place. This place is a nice and refreshing retreat for any traveler.

```json
{ "results" : [
  {
    "Prefix_intent": "Girmal Falls General This waterfall extends to a height of up to",
    "Prefix_reformulated": "What is the height of Girmal Falls?",
    "Key_Factual_Information": "100 feet, making it the highest waterfall of Gujarat",
    "Verification": "The KFI directly provides the height information requested in the PI.",
    "Ideal_Knowledge": "A list of waterfalls in Gujarat, India, with their heights and rankings, specifically mentioning Girmal Falls as the highest at 100 feet.",
    "Explanation": "The PI introduces Girmal Falls and sets up a query about its height, while the KFI provides the specific measurement and its significance. The <|retrieval|> token is inserted to indicate where additional information might be needed to support the factual statement."
  },
  {
    "Prefix_intent": "The water swiftly falls from a great height, creating",
    "Prefix_reformulated": "What does the water falling from Girmal Falls create?",
    "Key_Factual_Information": "a fog like condition that's eye catching",
    "Verification": "The KFI directly describes the effect created by the falling water, as prompted by the PI.",
    "Ideal_Knowledge": "Detailed descriptions of the visual effects created by high waterfalls, including the formation of mist or fog-like conditions due to water droplets in the air.",
    "Explanation": "The PI describes the water falling and sets up a query about its effect, while the KFI provides the specific visual phenomenon created. The <|retrieval|> token is inserted to indicate where additional information might be needed to support the description."
  },
  {
    "Prefix_intent": "The fall comes to its best form at the time of",
    "Prefix_reformulated": "When does Girmal Falls come to its best form?",
    "Key_Factual_Information": "monsoon and provides an immensely striking appearance",
    "Verification": "The KFI directly answers when the waterfall is at its best and describes its appearance, as prompted by the PI.",
    "Ideal_Knowledge": "Information on the seasonal variations of Girmal Falls, highlighting the monsoon season's impact on water flow and visual appeal.",
    "Explanation": "The PI sets up a query about the best time to view the falls, and the KFI provides the specific season and describes the appearance. The <|retrieval|> token is inserted to indicate where additional information about seasonal changes might be needed."
  }],
"Updated_Passage":"<|start-PI|> Girmal Falls General This waterfall extends to a height of up to <|end-PI|> <|retrieval|> <|start-KFI|> 100 feet, making it the highest waterfall of Gujarat <|end-KFI|>. The picturesque beauty of this site makes it popular among visitors and people of the region alike. <|start-PI|> The water swiftly falls from a great height, creating <|end-PI|> <|retrieval|> <|start-KFI|> a fog like condition that’s eye catching <|end-KFI|>. The government of this state is working on many projects to make this place an ideal picnic spot and a tourist attraction. <|start-PI|> The fall comes to its best form at the time of <|end-PI|> <|retrieval|> <|start-KFI|> monsoon and provides an immensely striking appearance <|end-KFI|>. Some of the best natural features of Gujarat can be explored in this place. This place is a nice and refreshing retreat for any traveler."
}

```
8. Final check:
  a. Review the Updated_Passage to ensure all PIs and KFIs are properly tagged.
  b. Verify that the first PI in the passage starts with <|start-PI|>.
  c. Make sure there are no missing or misplaced tags.
 
Remember to analyze the entire passage, identify all relevant PI-KFI pairs, and provide the output for each pair as specified. After completing the analysis, present the original passage with the <|retrieval|> tokens inserted in their appropriate positions as part of a new key in the JSON file. Only Ouput the JSON File.