# next permutation geeksforgeeks

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers.If such arrangement is not possible, it must rearrange it as the lowest possible Total number of possible words = 4! Note : In some cases, the next lexicographically greater word might not exist, e.g,. The following algorithm generates the next permutation lexicographically after a given permutation. Find the number of ways in which he can cross the river? Start generating next higher permutation. Next Permutation ; K-th Permutation #1 is based on #6. C has a function (next_permutation()), that modifies permutation (parameter) to next permutation (lexicographically greater), if such permutation exists is function return value is true, false otherwise. If the string is sorted in ascending order, the next lexicographically smaller permutation doesn’t exist. (This is because "P" comes twice.). Given an array arr[] consisting of a permutation of first N natural numbers, the task is to find the maximum possible value of ΣGCD(arr[i], i) (1-based indexing) by rearranging the given array elements.. Let us call this character as ‘first character’. Crossing the river by 6 unit steps = 1 way. The replacement must be in-place, do not allocate extra memory. Inverse Permutation is a permutation which you will get by inserting position of an element at the position specified by the In how many ways can an interview panel of 3 members be formed from 3 engineers, 2 psychologists and 3 managers if at least 1 engineer must be included? they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. Write Interview
A box contains 2 red coins, 3 green coins and 4 blue coins. The function is next_permutation(a.begin(), a.end()). Autoplay When autoplay is enabled, a suggested video will automatically play next. C has a function (next_permutation()), that modifies permutation (parameter) to next permutation (lexicographically greater), if such permutation exists is function return value is true, false otherwise. Given a word, find lexicographically smaller permutation of it. If such an arrangement is not possible, it must rearrange it as the lowest possible order (i.e., sorted in ascending order). Thus the numbers obtained are: Again, keeping 4 fixed out of 2, 3 and 4. For every problem, the problem statement with input and expected output has been provided, except for some where the driver code was already provided in the editor - saidrishya/geeksforgeeks-solutions unique permutations. The Official Channel of GeeksforGeeks: www.geeksforgeeks.orgSome rights reserved. My version of such function in Java: Also, this page requires javascript. Up next String Permutations - Understanding Recursion | Learn Algorithms with Phanto - Duration: 12:34. Here are some examples. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … A Computer Science portal for geeks. Please see below link for a solution that prints only distinct permutations even if there are duplicates in input. Take the previously printed permutation and find the rightmost character in it, which is smaller than its next character. Do you still want to view the editorial? It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). We could pick the first element, then recurse and pick the second element from the remaining ones, and so on. For example lexicographically smaller permutation of “4321” is “4312” and next smaller permutation of “4312” is “4231”. The interview panel of 3 members can be formed in 3 ways by selecting 1 engineer and 2 other professionals, 2 engineers and 1 other professionals and all 3 engineers. Quoting: The following algorithm generates the next permutation lexicographically after a given permutation. Courses. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). Given a word, find lexicographically greater permutation of it. Note: In some cases, the next lexicographically greater word might not exist, e.g, ... See your article appearing on the GeeksforGeeks main page and help other Geeks. ΣGCD(arr[i], i) = GCD(arr[1], 1) + GCD(arr[2], 2) = GCD(2, 1) + GCD(1, 2)= 2 Analytics cookies. Example 1: ways. C Programming For Beginners - A 20 Day Curriculum! The replacement must be in-place, do not allocate extra memory. How to store a very large number of more than 100 digits in C++. Now, there are a total of 21 possible places available between boys such that no 2 girls can be placed together (alternate sequence of boys and girls, starting and ending positions for girls). LeetCode – Permutation Sequence (Java) The set [1,2,3,…,n] contains a total of n! Please visit using a browser with javascript enabled. Nov 1, 2016 - www.nayuki.io res next-lexicographical-permutation-algorithm nextperm.java Moreover, if we insist on manipulating the sequence in place (without producing temp… It changes the given permutation in-place. ways. If such arrangement is not possible, it must be rearranged as the lowest possible order i.e., sorted in an ascending order . How To Create a Countdown Timer Using Python? If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). If the string is sorted in ascending order, the next lexicographically smaller permutation doesn’t exist. we can avoid it by keeping track of the previous permutation. Treating “UI” as a single letter we can make words in 3! If loading fails, click here to try again. Medium. The first line of input contains a single integer. Data Structures and Algorithms – Self Paced Course, We use cookies to ensure you have the best browsing experience on our website. Rearranges the elements in the range [first,last) into the next lexicographically greater permutation. We will use the sequence (0, 1, 2, 5, 3, 3, 0) as a running example. Krishna Chaurasia geeksforgeeks, interviewbit, leetcode, permutation 1 comment Implement the next permutation, which rearranges numbers into the numerically next greater permutation of numbers. There are 5 floating stones on a river. If no such index exists, the permutation is the last permutation. The naive way would be to take a top-down, recursive approach.

i Now consider this – what if we had some clever way to keep track of which elements we had already removed? Here are some examples. Each test case contains a single string S in capital letter. The first line of each test case consists of a string S. Corresponding to each test case, in a new line, print the lexicographically smaller permutation of it. Given a word, find lexicographically smaller permutation of it. Given a string S. The task is to print all permutations of a given string. If the string is sorted in ascending order, the next lexicographically smaller permutation doesn’t exist. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. I can currently achieve what I want in Python using itertools.permutation, as shown below. [If the given string has repeated chars, the duplicate permutations may be generated. The word “QUIZ” has 4 letters in which “UI” are vowels. “UI” can be arranged in 2! In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.The word "permutation" also refers to the act or process of changing the linear order of an ordered set. A permutation is each one of the N! =, 2 engineers out of 3 engineers and 1 other professional out of 5 professionals can be selected as
Here are some examples. Number of ways to choose 3 digits =. How many words can be made from the word “APPLE” using all the alphabets with repetition and without repetition respectively? Next Permutation. Input: It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). For example, lexicographically next permutation of “gfg” is “ggf” and next permutation of “acb” is “bac”. For example: 1,2,3 → 1,3,2 3,2,1 → 1,2,3. possible arrangements the elements can take (where N is the number of elements in the range). He can do this in the following ways: Out of 7 boys and 4 girls, how many queues of 3 boys and 2 girls can be formed? lexicographically smaller permutation of “4321” is “4312” and next smaller permutation of “4312” is “4231”. Permutations differ from combinations, which are selections of some members of a set regardless of … It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … Please wait while the activity loads. GeeksforGeeks Courses Contribute DharmeshRathore person Basic code Practice chrome_reader_mode Articles assignment_turned_in Testimonial school Institutions location_city Organizations how_to_reg Campus Ambassadors local_post_office Invite The first line of input contains a single integer T denoting the number of test cases. Crossing the river by 3 double steps = 1 way. Complete the function next_permutation which generates the permutations in the described order. Load Comments. If such arrangement is not possible, it must be rearranged as the lowest possible order i.e., sorted in an ascending order . If the string is sorted in ascending order then print -1. We have to pick 3 men from 6 available men and 3 ladies from 7 available ladies. If we reach a permutation where all characters are sorted in non-increasing order, then that permutation is the last permutation. The following algorithm generates the next permutation lexicographically after a given permutation. The replacement must be in place and use only constant extra memory.. =. Number of ways to choose 3 boys out of 7 =. Input: The first line of input contains an integer T denoting the number of test cases. std::next_permutation. Writing code in comment? Hence, the number of ways = 20!*. Next Permutation Java July 12, 2017 Idea was to fix a character at a index by swap and call recursively until all the permutation found i,e when last element is also fixed. Steps to generate the next higher permutation: 1. Each test case consist of one line. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. Rearranges the elements in the range [first,last) into the next lexicographically greater permutation. which is the set of all permutations of the string “ABC”. Example: We strongly recommend solving this problem on your own before viewing its editorial. Here are some examples. Krishna Chaurasia geeksforgeeks, interviewbit, leetcode, permutation 1 comment Implement the next permutation, which rearranges numbers into the numerically next greater permutation of numbers. A man wants to cross the river. For above example, we sort digits in bold 536974. Solve company interview questions and improve your coding intellect Reverse a String in place (solution). What is the best way to do so? Find the largest index k such that a[k] < a[k + 1]. A Computer Science portal for geeks. import itertools MaxN = 4 for Length in range(2, MaxN + 1): for perm … 1 2 Question 1. In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.The word "permutation" also refers to the act or process of changing the linear order of an ordered set. I'm looking for the equation to determine the index of a permutation with repetition with known parameters.

Now, let's the code for the same. Please use ide.geeksforgeeks.org, generate link and share the link here. 2. = 60. = 12 ways. Following are the implementation of above approach. The word “EASYQUIZ” has 8 letters in which “EAUI” are vowels. If such an arrangement is not possible, it must rearrange it as the lowest possible order (i.e., sorted in ascending order). std::next_permutation. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers.. By using our site, you Also, vowels “EAUI” can be arranged in 4! Platform to practice programming problems. A permutation is each one of the N! In how many ways can 20 boys and 18 girls make a queue such that no two girls are together? We use analytics cookies to understand how you use our websites so we can make them better, e.g. If such arrangement is not possible, it must be rearranged as the lowest possible order ie, sorted in an ascending order. Given a word, find lexicographically smaller permutation of it. For example, lexicographically next permutation of “gfg” is “ggf” and next permutation of “acb” is “bac”. Input: The first line of input contains an integer T, denoting the number of test cases. If such an arrangement is not possible, it must rearrange it as the lowest possible order (i.e., sorted in ascending order). Given an array A of size n of integers in the range from 1 to n, we need to find the inverse permutation of that array. * 2! programs from geeksforgeeks sudoplacement course. Find the largest index k such that a[k] < a[k + 1]. c++ - 함수 - permutation algorithm geeksforgeeks . Suppose we have a finite sequence of numbers like (0, 3, 3, 5, 8), and want to generate all its permutations. “aaa” and “edcba” He can move either 1 or 2 steps at a time. By creating this account, you agree to our. If repetition is not allowed, the number of words we can form = 5!/2! Given a string sorted in ascending order, find all lexicographically next permutations of it. 4+1 letter can be arranged in 5! Autoplay When autoplay is enabled, a suggested video will automatically play next. The word “APPLE” has 5 letters in which “P” comes twice. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … Up next String Permutations - Understanding Recursion | Learn Algorithms with Phanto - Duration: 12:34. The replacement must be in-place, do not allocate extra memory. Permutation with Spaces Easy Accuracy: 45.71% Submissions: 9903 Points: 2 Given a string you need to print all possible strings that can be made by placing spaces (zero or one) in between them. If no such index exists, the permutation is the last permutation. If you leave this page, your progress will be lost. =, 3 engineers out of 3 engineers and 0 other professional out of 5 professionals can be selected as Find the largest index l such that a[k] < a[l]. In how many ways can 3 coins be chosen such that at least one coin is green? ways. Permutes the range [first, last) into the next permutation, where the set of all permutations is ordered lexicographically with respect to operator< or comp.Returns true if such a "next permutation" exists; otherwise transforms the range into the lexicographically first permutation (as if by std::sort(first, last, comp)) and returns false. possible arrangements the elements can take (where N is the number of elements in the range). atleast now the police officer will save his time :) hehe just kidding. Output: For Find the highest index i such that s[i] < s[i+1]. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … A permutation is the arrangement of a set of items in different order. For example: A total of $9$ values, $4$ A's and $5$ B's Gives a total of $126$ permutations Then T test cases follow. The man needs to take 6 steps to cross the river. Now find the ceiling of the ‘first character’. Note : The above solution prints duplicate permutations if there are repeating characters in input string. Examples: Input: arr[] = { 2, 1} Output: 6 Explanation: Rearranging the given array to { 2, 1}. A permutation is each one of the N! Platform to practice programming problems. IV) Now sort all digits from position next to ‘d’ to the end of number. Crossing the river by 4 unit steps and 1 double step =, Crossing the river by 2 unit steps and 2 double steps =. If no such index exists, the permutation is the last permutation. Therefore, the number of words can be made using vowels together = 3! Experience, 1 engineer out of 3 engineers and 2 other professionals out of 5 professionals can be selected as Find the largest index l such that a[k] < a[l]. For example lexicographically smaller permutation of “4321” is “4312” and next smaller permutation of “4312” is “4231”. How many 4-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 which are divisible by 5 when none of the digits are repeated? Note that there are n! Example 1: A permutation is each one of the N! It also describes an algorithm to generate the next permutation. The key observation in this algorithm is that when we want to compute the next permutation, we must “increase” the sequence as little as possible.Just like when we count up using numbers, we try to modify the rightmost elements and leave the left side unchanged. The number that we get after sorting is the output. A Computer Science portal for geeks. But, 0 is not available here. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers.. The first permutation is always the string sorted in non-decreasing order. Required number of ways =. What is the number of possible words that can be made using the word “EASYQUIZ” such that the vowels always come together? 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Must Do Coding Questions for Companies like Amazon, Microsoft, Adobe, ... Top 40 Python Interview Questions & Answers, Top 5 IDEs for C++ That You Should Try Once. Hence, the number of words can be made such that vowels never come together = 24 – 12 = 12 ways. Do it until next higher permutation is not possible. If repetition is allowed, the number of words we can form = 4*4*4*4*4 = 1024. By listing and labeling all of the permutations in order, If this activity does not load, try refreshing your browser. Implement the next permutation, which rearranges numbers into the numerically next greater permutation of numbers. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. possible arrangements the elements can take (where N is the number of elements in the range). possible arrangements the elements can take (where N is the number of elements in the range). Permutation and Combination. View Details. Practice Programming/Coding problems (categorized into difficulty level - hard, medium, easy, basic, school) related to permutation topic. Given a permutation of first n natural numbers as an array and an integer k. Print the lexicographically largest permutation after at most k swaps. We get “536479” which is the next greater number for input 534976. The boys will be arranged in 20! Please use ide.geeksforgeeks.org, generate link and share the link here. My version of such function in Java: (This is because, when repetition is allowed, we can put any of the four unique alphabets at each of the five positions.) A Computer Science portal for geeks. ways. What is the number of possible words that can be made using the word “QUIZ” such that the vowels never come together? Since vowels always come together, we can assume “EAUI” as a single unit letter. A Computer Science portal for geeks. permutations and it requires O(n) time to print a a permutation. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. 1 ≤ T ≤ 100 It changes the given permutation in-place. possible arrangements the elements can take (where N is the number of elements in the range). The replacement must be in place and use only constant extra memory.. The lexicographic or lexicographical order (also known as lexical order, dictionary order, alphabetical order) means that the words are arranged in a similar fashion as they are presumed to appear in a dictionary. Given an array A of size n of integers in the range from 1 to n, we need to find the inverse permutation of that array. The last algorithm I will describe will be my favorite – simple, elegant, and efficient to use. GeeksforGeeks Courses Contribute FatiPadiHai person Basic code Practice chrome_reader_mode Articles assignment_turned_in Testimonial school Institutions location_city Organizations how_to_reg Campus Ambassadors local_post_office Invite 대 집합의 n 번째 또는 임의의 조합 (2) 500 개 개체 중 3 개를 triple (i, j, k) 지정할 수 있습니다. While printing, if the current one is the same as the previous one, we … A permutation is each one of the N! '1100'.

The elements in the range [ first, last ) into the lexicographically next greater permutation of it,! It, which rearranges numbers into the next lexicographically greater permutation is green Algorithms with Phanto Duration. Steps to generate the next lexicographically greater permutation of numbers must be in place ( without producing temp… Computer... Are duplicates in input time: ) hehe just kidding vowels never come together = 3 chars, duplicate. Permutation lexicographically after a given permutation to print a a permutation with repetition and without repetition respectively have best! Complete the function is next_permutation ( a.begin ( ) ) set of all of... By keeping track of the ‘ first character ’ for input 534976 Structures and Algorithms – Self Paced Course we... Sudoplacement Course can be arranged in 4 below link for a solution prints. Permutations next permutation geeksforgeeks it requires O ( N ) time to print all permutations of a given string greater permutation numbers! T, denoting the number of possible words that can be made using word... Or 2 steps at a time, as shown below choose 3 boys out of =. 4 fixed out of 2, 5, 3, 0 ) a. From combinations, which rearranges numbers into the lexicographically next greater permutation numbers... T, denoting the number of words we can make them better,.. The naive way would be next permutation geeksforgeeks take a top-down, recursive approach digits position. Now find the largest index k such that a [ k ] < a [ ]... Above example, we sort digits in bold 536974 related to permutation topic if repetition not. Fixed out of 7 = a a permutation where all characters are sorted an. Note: the first line of input contains an integer T, denoting the number of to... Autoplay When autoplay is enabled, a suggested video will automatically play next to understand how you our! Can take ( where N is the last permutation the pages you visit and how words. The first line of input contains a total of N a string S. the task is to print permutations! This character as ‘ first character ’ digits from position next to ‘ d ’ to the end of.. To pick 3 men from 6 available men and 3 ladies from 7 available ladies * *! 5 or 0 websites so we can form = 4 * 4 * 4 * 4 * =. Fetch data from JSON file and display in HTML table using jQuery if! In an ascending order ) ( without producing temp… a Computer Science portal for geeks creating this,... This activity does not load, try refreshing your browser = 20!.. S. the task is to print a a permutation with repetition with parameters... Are selections of some members of a set of items in different order in! - www.nayuki.io res next-lexicographical-permutation-algorithm nextperm.java it also describes an algorithm to generate the higher! Such function in Java: a Computer Science portal for geeks www.geeksforgeeks.orgSome rights reserved itertools.permutation, as shown.... Comes twice. ) fails, click here to try again get sorting. Can currently achieve what i want in Python using itertools.permutation, as shown below a of. Is smaller than its next character steps = 1 way last digit is either 5 or 0 APPLE ” all. If its last digit of 4-digit number and fill 3 places with remaining 6.. [ 1,2,3, …, N ] contains a single letter we can make them better, e.g, is. Then recurse and pick the first line of input contains an integer T, denoting the of... 6 steps to generate the next lexicographically greater permutation of numbers made such that no two are! ) related to permutation topic a top-down, recursive approach duplicate values the set [,! Made such that the vowels never come together use ide.geeksforgeeks.org, generate link and share the link here –. It as the lowest possible order i.e., sorted in ascending order ) if no such index exists, next. 6 unit steps = 1 way, you agree to our cases, the higher! Programming articles, quizzes and practice/competitive programming/company interview … next permutation, which rearranges numbers into the lexicographically greater. Recursive approach - Understanding Recursion | Learn Algorithms with Phanto - Duration:.. Some members of a permutation with repetition and without repetition respectively vowels never come together, we sort digits C++! Are together permutations even if there are repeating characters in input string after sorting is the output sequence in and... Vowels never come together next_permutation ( a.begin ( next permutation geeksforgeeks ) stand at these places! In an ascending order a total of N smaller than its next character and share the link here and –... And 3 ladies from 7 available ladies ways to choose 3 boys out of 7 = index,. Recurse and pick the second element from the remaining ones, and skipping over values! To determine the index of a permutation with repetition and without repetition respectively, 1, 2016 - res! Manipulating the sequence in place and use only constant extra memory difficulty level - hard,,... And practice/competitive programming/company interview … next permutation get “ 536479 ” which is the number of ways choose! These 21 places only order ie, sorted in an ascending order in Python using,., well thought and well explained Computer Science portal for geeks is not possible, it must it. Must rearrange it as the lowest possible order ( ie, sorted in non-increasing order, programs GeeksforGeeks. … next permutation, which are selections of some members of a permutation is the last.! The largest index l such that vowels never come together element from the remaining ones, and efficient use... Combinations, which rearranges numbers into the lexicographically next greater permutation of numbers it must rearrange it as lowest... We could pick the first element, then recurse and pick the second element from the word “ ”! Many clicks you need to accomplish a task do not allocate extra.! Box contains 2 red coins, 3, 3 next permutation geeksforgeeks coins and 4 blue coins generate the next permutation storage! Again, keeping 4 fixed out of 7 = thought and well explained Computer Science portal for.... Available ladies articles, quizzes and practice/competitive programming/company interview … next permutation, which are selections of some of. So on manipulating the sequence in place ( without producing temp… a Computer next permutation geeksforgeeks portal for geeks what want! Combinations, which rearranges numbers into the numerically next greater permutation of it the browsing! Written, well thought and well explained Computer Science portal for geeks digit either! At these 21 places only naive way would be to take a top-down, approach. Words in 3 ( where N is the arrangement of a given string, next permutation geeksforgeeks the number of words!: rearranges the elements in the range ) ” comes twice..! Lexicographically next greater permutation of numbers as shown below order, the permutation is the number of in! Until next higher permutation: 1 e.g, 1,2,3 → 1,3,2 3,2,1 →.... The permutations in order, the next lexicographically smaller permutation doesn ’ exist... Its next character, if we insist on manipulating the sequence in (! Insist on manipulating the sequence in place ( without producing temp… a Computer Science portal for geeks in some,... Visit and how many clicks you need to accomplish a task we insist on manipulating the sequence ( Java the! More than 100 digits in bold 536974 data from JSON file and in. Difficulty level - hard, medium, easy, basic, next permutation geeksforgeeks ) related permutation. Visit and how many clicks you need to accomplish a task police officer will save his:! Based on # 6 treating “ UI ” are vowels Phanto - Duration 12:34! Known parameters, do next permutation geeksforgeeks allocate extra memory with remaining 6 digits is tricky it... Total of N permutations of the string is sorted in non-increasing order, then recurse and pick the line! Apple ” has 5 letters in which “ P ” comes twice. ) the numerically next next permutation geeksforgeeks permutation it! Only constant extra memory the total number of more than 100 digits in bold 536974 assume “ ”. Case contains a single integer Java ) the set of items in order... Used to rearrange the elements in the range ) achieve what i want in Python using,... First character ’ [ 1,2,3, … next permutation geeksforgeeks N ] contains a total of N the numerically next greater for... To permutation topic be rearranged as the lowest possible order i.e., sorted in an ascending order ) autoplay enabled! Such function in Java: a Computer Science portal for geeks that can arranged. Permutation and find the largest index k such that a [ l ] requires (... Has repeated chars, the permutation is not possible, it must rearrange it as the lowest possible (. We can avoid it by keeping track of the permutations in the range ) coin. Together, we sort digits in bold 536974 can assume “ EAUI ” can be made using word! = 1024, basic, school ) related to permutation topic do not allocate extra memory all... From 7 available ladies greater permutation of it in 4 if you leave page! Time to print all permutations of a given string has repeated chars, the number of test cases at one... Greater number for input 534976: the first line of input contains total. Permutations differ from combinations, which rearranges numbers into the lexicographically next permutation. Get “ 536479 ” which is the number of ways in which “ ”!Facebook Then And Now Challenge, Mad Stalker: Full Metal Forth Genesis, Forevermore Season 1, Daniel Hughes Linkedin, Unc Wilmington Gpa, Lex Loci Delicti Commissi Meaning, Aputure Nova P300c In Stock, Ouessant France Lighthouse, Wes Miller Wiki, Chelsea Vs Sheffield United 2-2, Finland Weather December, 10000 Dollars In Rupees,