answer：Okay, I need to write a Python function called capitalize_viking_names that takes a list of Viking names and returns a new list where each name is properly capitalized. Hmm, what does properly capitalized mean here? Oh right, each word's first letter should be uppercase and the rest lowercase.So, for example, if the input is "ragnar lothbrok", the output should be "Ragnar Lothbrok". Each word is treated separately. So I need to split each name into words, capitalize each word, and then join them back together.Let me think about the steps. For each name in the input list, I'll process it as follows:1. Split the name into individual words. I can use the split() method which by default splits on whitespace.2. For each word in the split list, capitalize it. The capitalize() method in Python does exactly that: it makes the first character uppercase and the rest lowercase.3. Join the capitalized words back into a single string with spaces between them.4. Collect all these processed names into a new list and return it.Wait, but what about names with hyphens or other characters? Oh, the problem statement says each name is a string, but doesn't specify. The example given uses spaces. So I think we can assume that words are separated by spaces only.So the function can be written using a list comprehension. For each name in input_names, process it as described.Let me outline the code:def capitalize_viking_names(names): capitalized = [] for name in names: words = name.split() capitalized_words = [word.capitalize() for word in words] new_name = ' '.join(capitalized_words) capitalized.append(new_name) return capitalizedAlternatively, using a list comprehension:def capitalize_viking_names(names): return [' '.join([word.capitalize() for word in name.split()]) for name in names]Yes, that should work.Let me test this logic with the sample input.Sample input: ["ragnar lothbrok", "lagertha the shieldmaiden", "bjorn ironside"]Processing each name:First name: split into ["ragnar", "lothbrok"], capitalize each to ["Ragnar", "Lothbrok"], joined as "Ragnar Lothbrok".Second name: split into ["lagertha", "the", "shieldmaiden"], capitalize each to ["Lagertha", "The", "Shieldmaiden"], joined as "Lagertha The Shieldmaiden".Third name: split into ["bjorn", "ironside"], capitalize to ["Bjorn", "Ironsides"], joined as "Bjorn Ironside".Which matches the expected output.What about edge cases? Like a single-word name, or names with multiple spaces?For example, input like ["einar", " harald fairhair "].Processing "einar" would become "Einar"." harald fairhair " after split becomes ["harald", "fairhair"], which capitalizes to "Harald Fairhair".So the function should handle leading and trailing spaces because split() ignores them.Another test case: empty string? Well, the problem says each string is a name, so maybe it's not an issue, but the function would handle it by returning an empty string.So I think this approach should work.

answer：Okay, I need to write a Python function to analyze a list of donation records. The goal is to find the total donation amount and the number of unique donors. Hmm, let's think about how to approach this.So, each record is a dictionary with 'donor_id' and 'amount'. The function should return a tuple with the total sum and the count of unique donors.First, I'll consider the steps. For the total amount, I need to sum all the 'amount' values from each dictionary. That's straightforward—loop through each record and add the amount to a running total.For the unique donors, I need to count how many distinct 'donor_id's there are. So, I can collect all the donor_ids into a set, which automatically handles uniqueness. Then, the length of the set will give the count.Wait, but what if the list is empty? Oh right, the function should return (0.0, 0) in that case. So I need to handle that scenario.Let's outline the steps:1. Initialize total to 0.0 and a set to keep track of donor_ids.2. Iterate over each record in the donation_records list.3. For each record, add the 'amount' to total.4. Add the 'donor_id' to the set.5. After processing all records, calculate the unique donor count as the length of the set.6. Return a tuple with total and the count.Wait, but what if the list is empty? Then, the loop doesn't run, and the initial values (0.0 and 0) are correct.So, the function can be structured as follows:- Check if the donation_records is empty. If so, return (0.0, 0).- Else, process each record.But wait, even if the list is empty, the initial variables are 0.0 and 0, so perhaps no need for a separate check. Let's see:Initialize total = 0.0unique_donors = set()for record in donation_records: total += record['amount'] unique_donors.add(record['donor_id'])count = len(unique_donors)return (total, count)Yes, that should handle all cases, including empty lists.Now, let's think about possible edge cases. For example, a record with a donor_id that's not an integer? But according to the problem statement, 'donor_id' is an integer, so we don't need to handle that.Another case: multiple donations from the same donor. The set will ensure they are counted once.Testing the example given:donation_records = [ {'donor_id': 1, 'amount': 50.0}, {'donor_id': 2, 'amount': 75.5}, {'donor_id': 1, 'amount': 25.0}, {'donor_id': 3, 'amount': 100.0}]Total is 50 +75.5 +25 +100 = 250.5Unique donors are 1,2,3 → count 3. So the function should return (250.5,3), which matches the expected output.What about an empty list? The function returns (0.0, 0), which is correct.Another test case: a single record. Like [{'donor_id':5, 'amount':100.5}]. The function should return (100.5, 1).What if a donor donates multiple times, but the same donor_id? The set will only count once.So, the code seems solid.Now, writing the function.Function name: analyze_donations.Parameters: donation_records.So, code:def analyze_donations(donation_records): total = 0.0 unique_donors = set() for record in donation_records: total += record['amount'] unique_donors.add(record['donor_id']) return (total, len(unique_donors))Wait, but what if the 'amount' is not a float? Well, the problem says it's a float, so no issue.Testing this function with the example should give the correct output.Another test case: empty list. Returns (0.0, 0), which is correct.Yes, this should work.

answer：Okay, I need to write a Python function called count_danish_vowels that counts the number of Danish vowels in a given string. The vowels to consider are 'a', 'e', 'i', 'o', 'u', 'æ', 'ø', and 'å'. And it should be case-insensitive, meaning it should count both uppercase and lowercase versions.Hmm, so first, I should think about how to approach this. Maybe I can convert the entire string to lowercase (or uppercase) to make the comparison easier. That way, I don't have to worry about case sensitivity when checking each character.Wait, but in the example, the input string is "Jeg elsker at lære dansk, det er så spændende!" and the expected count is 11. Let's see: the vowels are e, e, a, æ, e, a, e, a, e, e, æ. So that's 11 vowels.So the function needs to iterate through each character in the string, check if it's one of the vowels (case-insensitive), and count it.So the steps I need to take are:1. Define the set of vowels. Let's create a string or a set containing all the lowercase Danish vowels. So vowels = {'a', 'e', 'i', 'o', 'u', 'æ', 'ø', 'å'}.2. Convert the input string to lowercase (or uppercase) so that the comparison is case-insensitive. For example, if the string has 'A' or 'E', they should be treated the same as 'a' or 'e'.Wait, but wait: in the example, the string has 'Jeg' which has 'e' as a vowel. So converting to lowercase would make it 'e', which is in the vowels set.So the plan is:- Iterate over each character in the input string.- For each character, convert it to lowercase (or uppercase) and check if it is in the set of vowels.- If it is, increment the count.Wait, but wait: in the example, the string has 'lære' which has 'æ' and 'e'. So the function should count both.So, the function can be written as:Initialize a count to 0.For each char in the input string: lower_char = char.lower() if lower_char in vowels: count +=1Return count.But wait, what about the other way around? Like, if the string has uppercase vowels, like 'A' or 'Æ', converting to lowercase would make them 'a' and 'æ', which are in the set.Yes, that should work.So, the function can be structured as follows:def count_danish_vowels(s): vowels = {'a', 'e', 'i', 'o', 'u', 'æ', 'ø', 'å'} count = 0 for char in s: if char.lower() in vowels: count +=1 return countWait, but wait: what about characters that are already lowercase? It doesn't matter because char.lower() would leave them as is.Testing this with the example:Input string: "Jeg elsker at lære dansk, det er så spændende!"Let's break down the vowels:Jeg: 'e' → count 1.elsker: 'e', 'e', 'e' → count increases by 3, total 4.at: 'a' → count 5.lære: 'æ', 'e' → count 7.dansk: 'a' → count 8.det: 'e' → 9.er: 'e' → 10.så: 'å' → 11.spændende: 'e', 'e' → count 13? Wait, wait, the example says 11. Wait, perhaps I'm misunderstanding the example.Wait the example says the expected count is 11. Let me recount.Wait, the example says: The Danish vowels are: e, e, a, æ, e, a, e, a, e, e, æ. So that's 11 vowels.Wait, perhaps I'm miscounting.Wait, let's look at the input string:"Jeg elsker at lære dansk, det er så spændende!"Breaking down each word:Jeg: 'e' → 1.elsker: 'e', 'e' → 2 more, total 3.at: 'a' → 4.lære: 'æ', 'e' → 2 more, total 6.dansk: 'a' → 7.det: 'e' → 8.er: 'e' →9.så: 'å' →10.spændende: 'e', 'e' → 12? But the example says 11.Wait, perhaps I'm missing something. Let me look again.Wait the example's breakdown says: e, e, a, æ, e, a, e, a, e, e, æ → 11.Wait, perhaps I'm not considering all the vowels correctly.Wait, let's go through each character in the input string:"Jeg elsker at lære dansk, det er så spændende!"Let's list each character and see if it's a vowel.J: no.e: yes (count 1).g: no.space: no.e: yes (2).l: no.s: no.k: no.e: yes (3).r: no.space: no.a: yes (4).t: no.space: no.l: no.æ: yes (5).r: no.e: yes (6).space: no.d: no.a: yes (7).n: no.s: no.k: no.,: no.space: no.d: no.e: yes (8).t: no.space: no.e: yes (9).r: no.space: no.s: no.å: yes (10).space: no.s: no.p: no.æ: yes (11).n: no.d: no.e: yes (12).n: no.g: no.e: yes (13).!: no.Wait, that's 13. But the example expects 11. So perhaps I'm misunderstanding the input.Wait, perhaps the example's breakdown is incorrect, or I'm miscounting.Wait, perhaps the example is correct, and I'm making a mistake in the breakdown.Wait, the example says the vowels are: e, e, a, æ, e, a, e, a, e, e, æ → 11.Looking at the input string:Jeg → 'e' → 1.elsker → 'e', 'e' → 2 more (total 3).at → 'a' →4.lære → 'æ', 'e' →5,6.dansk → 'a' →7.det → 'e' →8.er → 'e' →9.så → 'å' →10.spændende → 'e', 'e' →12.Wait, but the example's count is 11. So perhaps the function is correct, but the example is wrong? Or perhaps I'm misunderstanding the example.Alternatively, perhaps the function is correct, but the example's breakdown is wrong.Wait, perhaps the function as written counts 13, but the example expects 11. So perhaps there's a mistake in my approach.Wait, perhaps the function is including 'ø' as a vowel, but in the example, there are none. So perhaps the function is correct, but the example's breakdown is wrong.Alternatively, perhaps the function is correct, and the example's breakdown is correct, but I'm miscounting.Alternatively, perhaps I'm missing something in the function.Wait, perhaps the function is case-insensitive, but the example's breakdown is considering uppercase letters as well. But in the example, the input string is all lowercase except the first letter.Wait, perhaps I should test the function with the example.Wait, let's see: the input is "Jeg elsker at lære dansk, det er så spændende!"Let's process each character:J → lowercase is 'j' → not a vowel.e → 'e' → count 1.g → no.space → no.e → count 2.l → no.s → no.k → no.e → count 3.r → no.space → no.a → count4.t → no.space → no.l → no.æ → count5.r → no.e → count6.space → no.d → no.a → count7.n → no.s → no.k → no., → no.space → no.d → no.e → count8.t → no.space → no.e → count9.r → no.space → no.s → no.å → count10.space → no.s → no.p → no.æ → count11.n → no.d → no.e → count12.n → no.g → no.e → count13.! → no.So according to this, the count is 13. But the example expects 11.Hmm, that's a problem. So why is the example expecting 11?Wait, perhaps the example's breakdown is wrong. Or perhaps I'm misunderstanding which characters are considered vowels.Wait, perhaps the function is correct, but the example is wrong. Or perhaps I'm including some characters that shouldn't be counted.Wait, perhaps the function is counting 'ø' and 'å' as vowels, but in the example, there's only one 'å' and one 'æ' in 'spændende'?Wait, in the example, the breakdown is: e, e, a, æ, e, a, e, a, e, e, æ. So 11 vowels.Wait, perhaps the function is including some other vowels that are not in the example's breakdown.Wait, perhaps the function is including 'ø' as a vowel, but in the example, there are none. So perhaps the function is correct, but the example's breakdown is wrong.Alternatively, perhaps the example's breakdown is correct, but the function is counting some other vowels.Wait, perhaps I should re-examine the example's breakdown.In the example, the breakdown is:e, e, a, æ, e, a, e, a, e, e, æ.So that's 11 vowels.Looking back at the input string:Jeg elsker at lære dansk, det er så spændende!Breaking down the vowels:Jeg: e → 1.elsker: e, e → 2,3.at: a →4.lære: æ, e →5,6.dansk: a →7.det: e →8.er: e →9.så: å →10.spændende: e, e, e →11,12,13.Wait, that's 13.But the example says 11.Hmm, perhaps the example is wrong. Or perhaps I'm misunderstanding the problem.Alternatively, perhaps the function should not count the 'ø' and 'å' as vowels, but according to the problem statement, they are.Wait, the problem statement says the vowels are 'a', 'e', 'i', 'o', 'u', 'æ', 'ø', and 'å'. So all of these are vowels.So in the example, the function would count all of them.Wait, perhaps the example's breakdown is incorrect.Alternatively, perhaps the function is correct, and the example's breakdown is wrong.But regardless, I need to write the function as per the problem statement.So the function is as I wrote: it converts each character to lowercase, checks if it's in the set of vowels, and counts it.So the function should correctly count all the vowels, including 'ø' and 'å'.Wait, but in the example, the input string is "Jeg elsker at lære dansk, det er så spændende!".Let me count the vowels in this string.Breaking it down:Jeg → e →1.elsker → e, e →3.at → a →4.lære → æ, e →6.dansk → a →7.det → e →8.er → e →9.så → å →10.spændende → e, e, e →13.Wait, that's 13. But the example expects 11.Hmm, perhaps the function is correct, but the example's breakdown is wrong.Alternatively, perhaps the function is not considering 'ø' as a vowel, but according to the problem statement, it is.Wait, perhaps the function is correct, but the example is wrong.But regardless, the function should be written as per the problem statement.So the function is correct.Wait, perhaps the example is wrong. Or perhaps I'm miscounting.Alternatively, perhaps the function is correct, but the example's breakdown is missing some vowels.Alternatively, perhaps the function is correct, but the example's breakdown is wrong.In any case, the function as written should correctly count all the vowels, including 'ø' and 'å'.So, the code I wrote earlier should be correct.Wait, but wait: in the example, the function returns 11. So perhaps the function is not counting correctly.Wait, perhaps the function is case-sensitive. No, because we are converting each character to lowercase.Wait, perhaps the function is correct, but the example is wrong.Alternatively, perhaps the function is correct, but the example's breakdown is wrong.But regardless, the function should be written as per the problem statement.So, the function is correct.Testing it with the example:input_string = "Jeg elsker at lære dansk, det er så spændende!"The function should return 13, but the example expects 11. So perhaps there's a mistake in the example.Alternatively, perhaps the function is correct, but the example is wrong.But perhaps I'm missing something.Wait, perhaps the function is correct, but the example's breakdown is wrong.Alternatively, perhaps the function is correct, but the example's breakdown is wrong.Alternatively, perhaps the function is correct, but the example's breakdown is correct, and I'm miscounting.Wait, perhaps I should re-examine the example's breakdown.The example says: The Danish vowels are: e, e, a, æ, e, a, e, a, e, e, æ.So that's 11 vowels.Looking at the input string:Jeg → e →1.elsker → e, e →3.at → a →4.lære → æ, e →6.dansk → a →7.det → e →8.er → e →9.så → å →10.spændende → e, e →12.Wait, that's 12. But the example says 11.Wait, perhaps the 'spændende' has two 'e's, not three.Wait, 'spændende' is spelled s-p-æ-n-d-e-n-d-e.So the vowels are 'æ' and 'e' and 'e' → three vowels.So in the function, it would count three.But according to the example's breakdown, it's only counting two.Hmm, perhaps the example is wrong.Alternatively, perhaps the function is correct, but the example's breakdown is wrong.In any case, the function should be written as per the problem statement.So, the code I wrote earlier should be correct.Testing it with the example, it would return 13, but the example expects 11.So perhaps the function is correct, but the example's breakdown is wrong.Alternatively, perhaps the function is correct, but the example's breakdown is wrong.Alternatively, perhaps the function is correct, but the example's breakdown is correct, and I'm miscounting.But regardless, the function should be written as per the problem statement.So, the function is correct.Another test case: perhaps a string with all the vowels.For example, "AaEeIiOoUuÆæØøÅå" → should count 10 vowels (each pair is two letters, but each is a vowel, so 10 letters, 10 counts).Wait, no: each letter is a vowel, so the count is 10.Wait, no: the string has 10 letters, each a vowel. So the count is 10.So the function would return 10.Yes.Another test case: "Hello, World!" → 'e', 'o', 'o' → count 3.Yes.So, the function should be correct.So, the code is as follows:Define the vowels as a set containing the lowercase versions.Loop through each character in the input string, convert to lowercase, check if in vowels, count.So, the function is as written.But wait, in the example, the function returns 11, but according to my breakdown, it should return 13.So perhaps the example is wrong.Alternatively, perhaps the function is correct, but the example's breakdown is wrong.But regardless, the function should be written as per the problem statement.So, the function is correct.

answer：Okay, so I came across this interesting problem where Neznaika claims that there exist eight consecutive natural numbers such that in their prime factorization, each exponent is odd. Hmm, that sounds a bit tricky, but let me try to break it down.First, let me make sure I understand the problem correctly. We need to find eight consecutive natural numbers where each number, when factored into primes, has all exponents odd. For example, they gave two consecutive numbers: 23 and 24. Let's check those. 23 is a prime number, so its prime factorization is just 23^1, which has an odd exponent. 24 factors into 2^3 * 3^1. Both exponents, 3 and 1, are odd. So, that works for two numbers. But Neznaika is talking about eight consecutive numbers. I wonder if that's possible.Let me think about the properties required. Each number in the sequence must have all exponents in their prime factorization odd. That means each number must be a squareful number, right? Because squareful numbers have exponents at least 2 in their prime factors, but wait, actually, no. Wait, squareful numbers have exponents at least 2, but here we need exponents to be odd, which could be 1, 3, 5, etc. So, actually, each number must be square-free or have exponents that are odd. Hmm, square-free numbers have exponents exactly 1, which is odd, so they satisfy the condition. But numbers with higher exponents, like 8 = 2^3, also satisfy the condition because 3 is odd.So, in essence, each number in the eight consecutive numbers must not have any prime raised to an even power in their factorization. That is, for each prime p, if p divides the number, then the exponent of p must be odd.Now, let me think about how to approach this. Maybe it's helpful to consider the Chinese Remainder Theorem or some modular arithmetic. Or perhaps looking at the exponents in the prime factorizations and how they change as we move from one number to the next.Wait, another thought: if we can find eight consecutive numbers where each is either square-free or has exponents only odd, that would work. But how likely is that? Because in any set of consecutive numbers, some of them will be even, some odd, some multiples of primes, etc.Let me try to think about the exponents in the prime factorizations. For a number to have all exponents odd, it must not be divisible by any square number except 1. Wait, no, that's not quite right. Because a number can be divisible by a square, but the exponent of that prime must be odd. For example, 18 = 2^1 * 3^2. Here, the exponent of 2 is 1 (odd), but the exponent of 3 is 2 (even). So, 18 wouldn't satisfy the condition because one of the exponents is even. So, actually, the number must be square-free or have primes raised to odd exponents, but if a prime is squared, it would make the exponent even, which is bad. So, actually, the number must be square-free. Because if a number is not square-free, it has at least one prime squared, which would make the exponent even. Therefore, each number must be square-free.Wait, hold on, that's a key point. If a number is not square-free, it has a prime factor with exponent at least 2. If that exponent is even, then it violates the condition. If it's odd, like 3, then it's okay. So, a number can have a prime raised to an odd exponent greater than 1, but not even. So, for example, 8 = 2^3 is okay because 3 is odd, but 12 = 2^2 * 3^1 is not okay because 2 has an even exponent.Therefore, each number in the eight consecutive numbers must be either square-free or have primes raised to odd exponents. So, numbers like 8, 27, etc., are okay, but numbers like 4, 12, 18, etc., are not.So, the problem reduces to finding eight consecutive numbers where each is either square-free or has all exponents in their prime factorization odd. Hmm, that seems a bit more manageable.Let me think about how often square-free numbers occur. The density of square-free numbers is about 6/π², which is roughly 0.6, so about 60% of numbers are square-free. So, in a sequence of eight numbers, we might expect about 5 or 6 to be square-free, but we need all eight to satisfy the condition. That seems challenging.But wait, the numbers don't have to be square-free; they just have to have all exponents odd in their prime factorizations. So, numbers like 8, 16, 27, etc., are allowed because their exponents are odd. So, perhaps we can have some numbers in the sequence that are not square-free but still satisfy the exponent condition.So, maybe we can have a sequence where some numbers are squares of primes, or higher powers, as long as the exponents are odd.But let's think about the consecutive numbers. In any eight consecutive numbers, we have four even numbers. Among these, numbers like 4, 8, 12, 16, etc., are multiples of 4. Let's see: 4 is 2^2, which has an even exponent, so 4 would not satisfy the condition. 8 is 2^3, which is okay. 12 is 2^2 * 3^1, which is bad because of 2^2. 16 is 2^4, which is even exponent, so bad. 20 is 2^2 * 5^1, bad. 24 is 2^3 * 3^1, which is okay. 28 is 2^2 * 7^1, bad. 32 is 2^5, which is okay.So, in the even numbers, every multiple of 4 is bad unless it's a higher power of 2 with an odd exponent. So, 8, 24, 32, etc., are okay, but 4, 12, 16, 20, 28, etc., are bad.So, in any eight consecutive numbers, there are four even numbers. Among these, some may be multiples of 4, which are bad unless they're 8, 24, 32, etc. So, if we can arrange the eight consecutive numbers such that all the even numbers are either 8, 24, 32, etc., or square-free, then maybe it's possible.But wait, in eight consecutive numbers, there are four even numbers. Let's see, how many of them can be multiples of 4? In any eight consecutive numbers, there are four even numbers, two of which are multiples of 4, and two are congruent to 2 mod 4. So, for example, in the numbers n, n+1, ..., n+7, the even numbers are n, n+2, n+4, n+6 (assuming n is even). Among these, n and n+4 are multiples of 4, while n+2 and n+6 are 2 mod 4.So, in this case, n and n+4 must be either 8, 24, 32, etc., or square-free. Similarly, n+2 and n+6 must be square-free or have exponents odd.But let's think about the numbers n and n+4. If n is a multiple of 4, say n = 4k, then n is 4k, which is 2^2 * k. So, unless k is a multiple of 2, n will have 2^2 as a factor, which is bad. So, unless k is a multiple of 2, making n = 8m, which is 2^3 * m, which is okay if m is square-free or has exponents odd.Wait, so if n is 8m, then n is okay. Similarly, n+4 would be 8m + 4 = 4(2m + 1). So, n+4 is 4 times an odd number. So, n+4 = 2^2 * (2m + 1). So, unless (2m + 1) is 1, which would make n+4 = 4, which is bad, or (2m + 1) is a square, but wait, (2m + 1) is odd, so if it's a square, it's an odd square. But even so, 4*(odd square) would still have 2^2, which is bad. So, n+4 is problematic because it's 4 times an odd number, which is 2^2 * something, making the exponent of 2 even, which is bad.Therefore, n+4 cannot be square-free or have exponents odd, unless that something is 1, but 4*1=4 is bad. So, n+4 is always bad in this case. Therefore, if n is a multiple of 8, then n is okay, but n+4 is bad. So, that breaks the sequence.Alternatively, if n is not a multiple of 8, but a multiple of 4, then n is bad because it's 4 times something, which is 2^2 * something, so exponent of 2 is even. So, n is bad.Wait, so if n is even, then either n is a multiple of 4, which is bad, or n is 2 mod 4, which is square-free or not?If n is 2 mod 4, then n is 2 times an odd number. So, n = 2 * k, where k is odd. So, the exponent of 2 is 1, which is odd, so that's okay. But k could have even exponents in its prime factors, making n have even exponents. So, n is okay only if k is square-free or has exponents odd.Wait, so n = 2 * k, where k is square-free or has exponents odd. So, if k is square-free, then n is square-free except for the factor of 2, which is exponent 1, so n is okay. If k is not square-free, but has exponents odd, then n is okay as well.So, n being 2 mod 4 can be okay if k is square-free or has exponents odd.Similarly, n+2 would be 4 mod 4, which is 0 mod 4, so n+2 is a multiple of 4, which is bad unless it's 8, 24, etc. But n+2 is 4 mod 4, so it's 4*(m + 1), which is 4 times something. So, unless m + 1 is 2, making n+2 = 8, which is okay, otherwise, n+2 is bad.Wait, this is getting complicated. Maybe I should try to find such a sequence or prove it's impossible.Alternatively, perhaps considering the fact that in any eight consecutive numbers, there must be a multiple of 8, which is 2^3, which is okay, but also a multiple of 4, which is bad unless it's 8, 24, etc. But in eight consecutive numbers, there can be at most two multiples of 4: one multiple of 8 and another multiple of 4 but not 8. For example, in 8,9,10,11,12,13,14,15: 8 is 2^3 (okay), 12 is 2^2 * 3 (bad). So, 12 is bad.Similarly, in 24,25,...,31: 24 is 2^3 * 3 (okay), 28 is 2^2 * 7 (bad). So, again, 28 is bad.So, in any eight consecutive numbers, there will be two multiples of 4: one is 8m, which is okay, and the other is 4(2m + 1), which is bad. So, in any such sequence, one of the numbers will be bad because of the multiple of 4.Wait, unless the multiple of 4 is also a multiple of a higher power, like 16, 32, etc. Let's see: if n is 16, then n is 2^4, which is bad because exponent is even. So, 16 is bad. If n is 24, which is 2^3 * 3, which is okay. Then n+4 is 28, which is 2^2 * 7, which is bad. So, even if n is 24, which is okay, n+4 is bad.Wait, so if we have eight consecutive numbers starting at 24: 24,25,26,27,28,29,30,31.24: 2^3 * 3^1 (okay)25: 5^2 (bad, exponent 2 is even)26: 2^1 *13^1 (okay)27: 3^3 (okay)28: 2^2 *7^1 (bad)29: prime (okay)30: 2^1 *3^1 *5^1 (okay)31: prime (okay)So, in this sequence, 25 and 28 are bad. So, two bad numbers. So, that doesn't work.What if we try starting at 8: 8,9,10,11,12,13,14,15.8: 2^3 (okay)9: 3^2 (bad)10: 2^1 *5^1 (okay)11: prime (okay)12: 2^2 *3^1 (bad)13: prime (okay)14: 2^1 *7^1 (okay)15: 3^1 *5^1 (okay)Again, 9 and 12 are bad. So, two bad numbers.Hmm, seems like in any such sequence, we get at least two bad numbers because of the multiples of 4 and squares.Wait, but maybe if we can find a sequence where the multiples of 4 are also higher powers with odd exponents, and the squares are also higher powers. Let me think.Suppose we have a number that's a square, say 25 = 5^2, which is bad. But if we have 27 = 3^3, which is okay. So, if in the sequence, the square numbers are actually cubes or higher with odd exponents, that might help.But in eight consecutive numbers, how likely is that? For example, let's say we have a cube in the sequence. Let's try starting at 26: 26,27,28,29,30,31,32,33.26: 2*13 (okay)27: 3^3 (okay)28: 2^2 *7 (bad)29: prime (okay)30: 2*3*5 (okay)31: prime (okay)32: 2^5 (okay)33: 3*11 (okay)So, here, 28 is bad. So, one bad number. If we can somehow make 28 okay, but 28 is 2^2 *7, which is bad. So, unless 28 is a higher power, but 28 is not a cube or anything.Alternatively, starting at 32: 32,33,34,35,36,37,38,39.32: 2^5 (okay)33: 3*11 (okay)34: 2*17 (okay)35:5*7 (okay)36: 6^2 = 2^2 *3^2 (bad)37: prime (okay)38:2*19 (okay)39:3*13 (okay)So, 36 is bad. So, again, one bad number.Wait, so in this case, starting at 32, we have only one bad number, 36. So, maybe if we can find a sequence where only one number is bad, but the problem requires all eight to be okay. So, that's not sufficient.Wait, but maybe if we can find a sequence where the multiple of 4 is a higher power with an odd exponent, and the square is also a higher power. Let me think.For example, let's say we have a number that's both a multiple of 4 and a cube. Let's see, 64 is 4^3, which is 2^6, which is bad because exponent is even. 16 is 4^2, which is 2^4, bad. 32 is 4*8, which is 2^5, okay. So, 32 is okay.Wait, 32 is 2^5, which is okay. So, if we have a multiple of 4 that's also a higher power with an odd exponent, like 32, then it's okay. So, maybe if we can arrange the eight consecutive numbers such that the multiple of 4 is 32, and the square is also a higher power.But in eight consecutive numbers, if we have 32, then the next multiple of 4 is 36, which is 6^2, which is 2^2 *3^2, which is bad. So, 36 is bad.Alternatively, if we have 24, which is 2^3 *3, okay, and 28, which is 2^2 *7, bad.Hmm, seems challenging.Wait, another approach: maybe considering the exponents modulo 2. For each prime p, the exponent in the prime factorization of n must be odd. So, for each prime p, the exponent of p in n is odd.So, for each prime p, the exponent of p in n is odd, which is equivalent to n being a quadratic non-residue modulo p^2? Wait, not exactly. Maybe not the right approach.Alternatively, perhaps considering the multiplicative functions. The condition is that for each n in the sequence, the radical of n (the product of distinct prime factors) is equal to n divided by the largest square dividing n. But since we need all exponents to be odd, it's a bit different.Wait, actually, if all exponents are odd, then n is equal to the product of primes raised to odd exponents. So, n can be written as m^2 * k, where k is square-free. But since exponents are odd, k must be 1 or a product of primes, each appearing once. Wait, no, because if n = m^2 * k, then exponents in m^2 are even, and exponents in k are odd. So, the total exponents would be even + odd = odd. So, yes, n can be written as m^2 * k, where k is square-free.But in that case, n is square-free times a square. So, n is not necessarily square-free, but can have square factors as long as the exponents are odd.Wait, but if n is written as m^2 * k, with k square-free, then the exponents in n are even (from m^2) plus exponents in k, which are 0 or 1. So, if k has a prime p, then the exponent of p in n is 1, which is odd. If k doesn't have p, then the exponent is even. So, n is square-free times a square, which is the same as saying n is powerful? Wait, no, powerful numbers have exponents at least 2. Hmm, maybe not.Alternatively, maybe n is a square times a square-free number. So, n = a^2 * b, where b is square-free. Then, the exponents in n are even (from a^2) plus 0 or 1 (from b). So, if b has a prime p, then exponent of p in n is 1, which is odd. If b doesn't have p, then exponent is even. So, n can be written as a square times a square-free number.Therefore, for each n in our sequence, n must be of the form a^2 * b, where b is square-free.So, our problem reduces to finding eight consecutive numbers where each is of the form a^2 * b, with b square-free.Now, considering that, let's think about the numbers in the sequence. Each number must be square-free or have square factors, but with exponents odd.But in any case, each number must be square-free times a square. So, maybe we can find such a sequence.But how?Alternatively, perhaps considering the Chinese Remainder Theorem. If we can find a number n such that:n ≡ 0 mod 2^3 (so n is divisible by 8, exponent of 2 is 3, which is odd)n+1 ≡ 1 mod something, maybe square-free.Wait, but this might get too complicated.Alternatively, maybe considering that in eight consecutive numbers, we can have numbers divisible by different primes, each raised to odd exponents.But it's not clear.Wait, another thought: the numbers must not be divisible by any square number with even exponent. So, for each prime p, if p^2 divides n, then the exponent of p in n must be odd. So, n can be divisible by p^2, p^4, etc., but not p^3, p^5, etc., wait no, p^3 is okay because exponent is odd.Wait, no, p^3 is okay because exponent is odd. So, n can be divisible by p^2, p^3, p^4, etc., but if it's divisible by p^2, the exponent must be odd. So, p^2 divides n only if the exponent is odd, meaning p^3, p^5, etc.Wait, no, if p^2 divides n, then the exponent is at least 2. But for the exponent to be odd, it must be 3,5,7, etc. So, n can be divisible by p^3, p^5, etc., but not p^2, p^4, etc.Therefore, n cannot be divisible by p^2 for any prime p, unless it's divisible by p^3, p^5, etc.So, n must be square-free or have prime factors with exponents at least 3 and odd.Therefore, n cannot be divisible by p^2 unless it's divisible by p^3.So, for example, 8 is okay because it's 2^3, but 4 is bad because it's 2^2.Similarly, 18 is 2*3^2, which is bad because 3^2 is present, but 27 is 3^3, which is okay.So, in our eight consecutive numbers, we must avoid numbers divisible by p^2 unless they are divisible by p^3.Therefore, in the eight consecutive numbers, we must ensure that any number divisible by p^2 is also divisible by p^3.So, for example, if a number is divisible by 4, it must be divisible by 8. If a number is divisible by 9, it must be divisible by 27, etc.So, in our sequence, any multiple of 4 must be a multiple of 8, any multiple of 9 must be a multiple of 27, any multiple of 25 must be a multiple of 125, etc.Therefore, in eight consecutive numbers, we need to ensure that:- All multiples of 4 are multiples of 8.- All multiples of 9 are multiples of 27.- All multiples of 25 are multiples of 125.And so on for higher squares.But in eight consecutive numbers, how likely is that?Let's think about the multiples of 4. In eight consecutive numbers, there are two multiples of 4. For both of them to be multiples of 8, the starting number must be congruent to 0 mod 8 or 4 mod 8.Wait, if the starting number is 0 mod 8, then the multiples of 4 in the sequence are 0 mod 8 and 4 mod 8. But 4 mod 8 is 4, which is 2^2, which is bad unless it's 8, which it's not. So, 4 mod 8 is bad.Similarly, if the starting number is 4 mod 8, then the multiples of 4 in the sequence are 4 mod 8 and 0 mod 8. So, 4 mod 8 is bad, and 0 mod 8 is okay.Therefore, in any case, in eight consecutive numbers, one of the multiples of 4 is bad (4 mod 8), unless that number is 8 itself, but 8 is 0 mod 8, so if the sequence includes 8, then 8 is okay, but the other multiple of 4 would be 4 mod 8, which is bad unless it's 8, but it's not.Wait, for example, starting at 8: 8,9,10,11,12,13,14,15.Here, 8 is okay, 12 is bad because it's 4 mod 8 and not 8.Similarly, starting at 4: 4,5,6,7,8,9,10,11.4 is bad, 8 is okay.So, in any case, one of the multiples of 4 is bad.Therefore, in any eight consecutive numbers, there is at least one number which is a multiple of 4 but not a multiple of 8, hence bad.Therefore, it's impossible to have eight consecutive numbers where all exponents in their prime factorizations are odd.Wait, but hold on, what about numbers divisible by higher squares, like 9, 25, etc. For example, if a number is divisible by 9, it must be divisible by 27 to have an odd exponent. So, in eight consecutive numbers, if one of them is divisible by 9, it must be divisible by 27. Similarly, if divisible by 25, must be divisible by 125, etc.But in eight consecutive numbers, it's possible that none are divisible by 9 or 25, so that condition is automatically satisfied. So, the only problem is with multiples of 4.But as we saw, in any eight consecutive numbers, there is at least one multiple of 4 that is not a multiple of 8, hence bad.Therefore, it's impossible to have eight consecutive numbers where all exponents in their prime factorizations are odd.Wait, but the problem statement says that Neznaika claims such numbers exist. So, maybe I'm missing something.Wait, let me check the example they gave: 23 and 24. 23 is prime, 24 is 2^3 * 3. So, both are okay. So, two consecutive numbers. Maybe for eight, it's impossible, but for two, it's possible.But according to my reasoning, in any eight consecutive numbers, there will be at least one multiple of 4 that is not a multiple of 8, hence bad. Therefore, such a sequence cannot exist.Therefore, Neznaika is incorrect.Wait, but before concluding, let me think if there's any way around this. Maybe if the multiple of 4 is also a multiple of a higher power, like 16, 32, etc. But 16 is 2^4, which is bad because exponent is even. 32 is 2^5, which is okay. So, if the multiple of 4 is 32, which is okay, but then the other multiple of 4 would be 36, which is 4*9, which is 2^2 *3^2, which is bad.So, even if one multiple of 4 is okay, the other is bad.Therefore, in any case, one of the multiples of 4 is bad.Hence, it's impossible to have eight consecutive numbers where all exponents in their prime factorizations are odd.Therefore, Neznaika is incorrect.**Final Answer**boxed{No}

answer：Okay, I need to write a Python function to determine if a basketball player can join a prestigious team. The function takes two inputs: a list of the player's skills and a dictionary representing the rival coach's influence. The output is a boolean indicating whether the player's total score is at least 5 after considering the influence.Hmm, let's break this down. Each skill initially contributes 3 points. So for each skill in the player's list, we add 3. Then, for each skill that the rival coach influences, we subtract the corresponding value from the total.Wait, but how do I handle the influence? The rival's influence is a dictionary where the keys are skills and the values are the negative impact. So for each skill in the influence, if the player has that skill, we subtract the influence's value from the total.So the steps are:1. Calculate the initial total score by multiplying the number of skills by 3.2. For each skill in the rival_influence dictionary: a. If the skill is present in the player's skills list, subtract the influence value from the total.3. After considering all influences, check if the total is >=5. If yes, return True; else, False.Wait, but what if the same skill is in both the player's skills and the influence? Like, if the player has "shooting" and the influence also has "shooting", then we subtract that value once.So, for example, in the sample given:skills = ["shooting", "dribbling", "defense"]rival_influence = {"shooting": -2, "defense": -3}Initial score is 3*3=9.Then, for each key in rival_influence:- "shooting" is in skills, so subtract -2 (which is adding 2? Wait no, wait the value is -2, so subtracting that would be 9 - (-2) = 11? Wait no, wait no. Wait, the influence is negative. So the value is -2, so subtracting that would be adding 2. Wait, no. Wait, the influence is a negative impact. So for "shooting", the influence is -2, which means the player's shooting score is reduced by 2. So the initial is 3, subtract 2, becomes 1. So for the total, it's 3*3=9, then subtract 2 and 3, so 9-2-3=4.Wait, but in the example, the expected output is False because 4 is less than 5. Oh right, but in the example, the expected output is True? Wait, no, wait the example says the expected output is True, but wait the calculation is 9-2-3=4, which is less than 5. So the output should be False. Oh wait, the example says the output is True? Or is that a mistake?Wait, looking back at the example:The sample input has skills as ["shooting", "dribbling", "defense"], and the rival_influence is {"shooting": -2, "defense": -3}.The initial score is 3*3=9. Then, subtract 2 for shooting, and 3 for defense. So 9-2-3=4. So the total is 4, which is less than 5. So the function should return False. But the example says the expected output is True. Wait, that's conflicting. Or perhaps I'm misunderstanding the example.Wait, the example says: the expected output is True, but the explanation says the total is 4, which is less than 5. So that's a contradiction. So perhaps the example is incorrect, or perhaps I'm misunderstanding the problem.Wait, perhaps the example is wrong. Or perhaps I made a mistake in the calculation.Wait, let me re-read the example:Sample:skills = ["shooting", "dribbling", "defense"]rival_influence = {"shooting": -2, "defense": -3}Expected output: TrueExplanation: Initial score = 3*3=9, Shooting influence = -2, Defense influence = -3. Total score = 9-2-3=4, which is less than 5, so output should be False.Wait, but the expected output is True. That's conflicting. So perhaps the example is wrong, or perhaps I'm misunderstanding the problem.Wait, perhaps the initial score is 3 per skill, but the influence is applied per skill. So for each skill, if the rival influences it, subtract the influence. So for example, for "shooting", the initial is 3, subtract 2, becomes 1. For "defense", initial 3, subtract 3, becomes 0. Dribbling is 3. So total is 1+3+0=4. So less than 5, so output is False. But the example says expected output is True. So perhaps the example is wrong.Wait, perhaps the example is a typo. Or perhaps I'm misunderstanding the problem.Alternatively, perhaps the rival's influence is added, not subtracted. Because in the example, the influence is negative, so adding it would decrease the score.Wait, the problem statement says the rival's influence is a dictionary where the values are integers indicating the strength of the influence. So for example, {"shooting": -2} would mean that the coach's influence on shooting is -2, which I think means that the player's shooting score is reduced by 2.So in the sample, the initial is 9, subtract 2 and 3, total 4, which is less than 5. So the function should return False. But the example says the expected output is True. So perhaps the example is incorrect, or perhaps I'm misunderstanding the problem.Alternatively, perhaps the rival's influence is applied as a multiplier, not a subtraction. Or perhaps the initial score is the sum of the skills, and each skill is 3, but the influence is applied as a multiplier.Wait, perhaps I should read the problem statement again.The function should return True if the player's total score is at least 5 after considering the rival's influence.Each skill contributes 3 points initially. Then, the rival's influence is applied. So for each skill in the influence, if the player has that skill, subtract the influence's value.Wait, but in the example, the influence is -2 and -3. So subtracting -2 is adding 2, and subtracting -3 is adding 3. So initial 9, plus 2 and 3, total 14, which is more than 5. So output is True.Ah! That's probably the confusion. So the problem is that the influence is a negative value, but when subtracting that, it's adding to the total.Wait, let's clarify:The rival's influence is a dictionary where the values are the influence. So for a skill, the influence is subtracted from the total.So for each skill in the influence:total -= influence_valueSo for example, if the influence is -2, then total -= (-2) is total += 2.Wait, that's a key point. So the influence is a negative impact, but the way it's applied is by subtracting the influence's value. So if the influence is -2, subtracting it would add 2 to the total.So in the sample:Initial score is 9.Shooting's influence is -2: 9 - (-2) = 11.Defense's influence is -3: 11 - (-3) = 14.So total is 14, which is >=5. So function returns True.But wait, that's opposite to the initial explanation. So perhaps the example's explanation is incorrect.So the problem is that the influence is subtracted, but the influence's value is negative, so subtracting a negative is adding.So the function should:1. Calculate initial score as 3 * len(skills).2. For each skill in the rival_influence's keys: a. If the skill is in the player's skills list, subtract the influence value from the total.So, for each key in rival_influence:if skill in skills, total += abs(influence) if influence is negative, because subtracting a negative is adding.Wait, no. Let's think numerically.Suppose the influence is -2.Subtracting that from the total is total = total - (-2) = total + 2.So yes, the total increases by 2.So in the sample, the initial is 9.Shooting influence is -2: 9 - (-2) = 11.Defense influence is -3: 11 - (-3) = 14.So total is 14, which is >=5. So function returns True.But the example's explanation says the total is 4, which is wrong.So perhaps the example is incorrect. Or perhaps I'm misunderstanding the problem.Wait, perhaps the influence is applied as a multiplier. Like, for each skill, the influence is multiplied by the initial 3. Or perhaps the influence is applied per skill.Wait, the problem statement says: each skill contributes 3 points before influence. Then, the influence is applied. So for each skill in the influence, if the player has it, subtract the influence's value.So for each skill in the influence:if the player has that skill, subtract the influence value.So in the sample:Shooting is in the skills. So subtract -2: 3 - (-2) = 5.Defense is in the skills. Subtract -3: 3 - (-3) =6.Dribbling is not in the influence, so remains 3.Total is 5 +6 +3 =14.Which is >=5, so return True.So the sample's expected output is True, which aligns with this calculation.But the example's explanation says that the total is 4, which is wrong. So perhaps the example's explanation is incorrect, but the expected output is correct.So the function should calculate the initial score as 3 * len(skills), then for each skill in the influence, if present in the player's skills, subtract the influence's value.So, the steps are:1. Calculate initial_score = 3 * len(skills).2. For each skill in rival_influence: a. If skill is in skills, subtract the influence value from initial_score.3. If the resulting score is >=5, return True; else, False.So, in code:def can_join_team(skills, rival_influence): initial = 3 * len(skills) for skill, influence in rival_influence.items(): if skill in skills: initial -= influence return initial >=5Wait, but in the sample, this would give 9 - (-2) - (-3) = 9+2+3=14, which is >=5, so return True.Which is correct.Another test case: suppose skills are ["shooting"], and influence is {"shooting": -5}.Initial is 3.Subtract -5: 3 - (-5) =8 >=5: return True.Another test case: skills = ["shooting"], influence = {"shooting": -4}.Initial is 3.3 - (-4) =7 >=5: True.Another case: skills = ["shooting"], influence = {"shooting": -3}.3 - (-3) =6 >=5: True.Another case: skills = ["shooting"], influence = {"shooting": -4}.3 - (-4) =7 >=5: True.Wait, but what if the influence is positive? Like, if the influence is 2.Then, subtracting 2 from the initial.So for example, skills = ["shooting"], influence = {"shooting": 2}.Initial is 3.3 -2 =1 <5: return False.So the function correctly handles that.So the code seems correct.So the function signature is:def can_join_team(skills, rival_influence): initial = 3 * len(skills) for skill, influence in rival_influence.items(): if skill in skills: initial -= influence return initial >=5Yes, that should work.So the function is as above.

answer：Okay, I need to write a Python function that processes a list of events involving Knights and Dragons. The goal is to count the consecutive occurrences of each and return a dictionary with these counts. Hmm, let's think about how to approach this.So, the input is a list like ["Knight", "Knight", "Dragon", ...]. The output should be a dictionary where each key is "Knight" or "Dragon", and the value is a list of integers representing the consecutive counts.Let me look at the example. The input is ["Knight", "Knight", "Dragon", "Dragon", "Dragon", "Knight", "Dragon"]. The output is {"Knight": [2, 1], "Dragon": [3, 1]}. Oh right, because the first two are Knights, then three Dragons, then one Knight, then one Dragon.So the process is: iterate through the list, track the current event and count how many times it repeats consecutively. When the event changes, we add the count to the respective list and reset the count.How to implement this? I think I'll need to initialize some variables. Maybe a dictionary to hold the counts, with each key starting as an empty list. Also, I'll need a variable to track the current event and a counter.Let me outline the steps:1. Initialize the result dictionary with both "Knight" and "Dragon" as keys, each mapping to an empty list.2. Check if the input list is empty. If so, return the result.3. Set the current event to the first element, and start a counter at 1.4. Iterate through the list starting from the second element: a. For each element, if it's the same as current event, increment the counter. b. If it's different, append the counter to the current event's list in the result, then set current event to this new element and reset counter to 1.5. After the loop ends, don't forget to append the last counter to the current event's list.6. Return the result.Wait, but what if the list is empty? Then the result should be empty lists for both. But according to the problem statement, the function is given a list, but it could be empty. So I should handle that.Let me think about some test cases.Test case 1: Empty list. Output should be {"Knight": [], "Dragon": []}.Test case 2: All Knights. Like ["Knight", "Knight", "Knight"]. Then the output should be {"Knight": [3], "Dragon": []}.Test case 3: Alternating events. Like ["Knight", "Dragon", "Knight", "Dragon"]. Then each has a count of 1 each time, so "Knight": [1,1], "Dragon": [1,1].So, the plan is solid.Now, let's think about the code structure.Initialize the result:result = {"Knight": [], "Dragon": []}If the input list is empty, return result.Else:current = first elementcount = 1loop from index 1 to end: if same as current, count +=1 else: append count to result[current] current = this element count =1After loop, append count to current's list.Wait, but in the example, after the loop, the last count is added. So yes.So, code:def process_events(events): if not events: return {"Knight": [], "Dragon": []} result = {"Knight": [], "Dragon": []} current = events[0] count = 1 for event in events[1:]: if event == current: count +=1 else: result[current].append(count) current = event count =1 # After loop, add the last count result[current].append(count) return resultWait, but what if the events list is not empty, but has other strings? Like "Wizard"? According to the problem statement, each string is either "Knight" or "Dragon". So we don't need to handle other cases.Testing the example:Input: ["Knight", "Knight", "Dragon", "Dragon", "Dragon", "Knight", "Dragon"]Processing:current is "Knight", count 1.Next event is "Knight" → count 2.Next is "Dragon" → append 2 to Knight's list. Now current is Dragon, count 1.Next two events are Dragon → count 3.Next is Knight → append 3 to Dragon's list. Now current is Knight, count 1.Next is Dragon → append 1 to Knight's list. Now current is Dragon, count 1.Loop ends. Append 1 to Dragon's list.So the result is:Knight: [2,1], Dragon: [3,1], which matches the expected output.Another test case: events = ["Knight", "Knight", "Knight"]Processing:current is Knight, count 1.Next two are Knight → count 3.Loop ends, append 3 to Knight's list.Result: {"Knight": [3], "Dragon": []}.Another test case: events = ["Dragon", "Knight", "Dragon"]Processing:current is Dragon, count 1.Next is Knight → append 1 to Dragon's list. current is Knight, count 1.Next is Dragon → append 1 to Knight's list. current is Dragon, count 1.Loop ends, append 1 to Dragon's list.Result: {"Knight": [1], "Dragon": [1,1]}.Yes, that's correct.So the code should handle all these cases.Wait, but what if the events list is like ["Knight", "Knight", "Knight", "Knight"]? Then the result should be {"Knight": [4], "Dragon": []}.Yes, the code would handle that.Another edge case: events has one element. Like ["Knight"]. Then the result is {"Knight": [1], "Dragon": []}.Yes.So the code seems correct.