Chef has an array 𝐴A of size 𝑁N. He wants to make a permutation†† using this array.Find whether there exists an array 𝐵B consisting of 𝑁N non-negative integers, such that the array 𝐶C constructed as 𝐶𝑖=𝐴𝑖+𝐵𝑖C i​ =A i​ +B i​ is a permutation.†† A permutation of size 𝑁N is an array of 𝑁N distinct elements in the range [1,𝑁][1,N]. For example, [4,2,1,3][4,2,1,3] is a permutation of size 44, while [3,2,2,1][3,2,2,1] and [1,3,4][1,3,4] are not.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case consists of 𝑁N - the size of the array 𝐴AThe next line contains 𝑁N space-separated integers - 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ - the elements of array 𝐴A.Output FormatFor each test case, output YES if there exists an array 𝐵B such that array 𝐶C constructed as 𝐶𝑖=𝐴𝑖+𝐵𝑖C i​ =A i​ +B i​ is a permutation, otherwise output NO.You may print each character of the string in uppercase or lowercase (for example, the strings YES, yEs, yes, and yeS will all be treated as identical).Constraints1≤𝑇≤1001≤T≤1001≤𝑁≤1001≤N≤1001≤𝐴𝑖≤𝑁1≤A i​ ≤NSample 1:InputOutput454 1 3 2 152 4 3 4 21161 1 1 1 6 6YESNOYESNOExplanation:Test case 11 : Consider 𝐵=[0,4,0,0,0]B=[0,4,0,0,0]. The corresponding array 𝐶C becomes [4,5,3,2,1][4,5,3,2,1], which is a permutation. Some other possible values of 𝐵B for which 𝐶C is a permutation are [1,0,1,1,1][1,0,1,1,1] and [1,3,0,0,0][1,3,0,0,0].Test case 22 : It can be proven that no valid array 𝐵B exists.

Make PermutationChef has an array 𝐴A of size 𝑁N. He wants to make a permutation†† using this array.Find whether there exists an array 𝐵B consisting of 𝑁N non-negative integers, such that the array 𝐶C constructed as 𝐶𝑖=𝐴𝑖+𝐵𝑖C i​ =A i​ +B i​ is a permutation.†† A permutation of size 𝑁N is an array of 𝑁N distinct elements in the range [1,𝑁][1,N]. For example, [4,2,1,3][4,2,1,3] is a permutation of size 44, while [3,2,2,1][3,2,2,1] and [1,3,4][1,3,4] are not.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case consists of 𝑁N - the size of the array 𝐴AThe next line contains 𝑁N space-separated integers - 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ - the elements of array 𝐴A.Output FormatFor each test case, output YES if there exists an array 𝐵B such that array 𝐶C constructed as 𝐶𝑖=𝐴𝑖+𝐵𝑖C i​ =A i​ +B i​ is a permutation, otherwise output NO.You may print each character of the string in uppercase or lowercase (for example, the strings YES, yEs, yes, and yeS will all be treated as identical).Constraints1≤𝑇≤1001≤T≤1001≤𝑁≤1001≤N≤1001≤𝐴𝑖≤𝑁1≤A i​ ≤NSample 1:InputOutput454 1 3 2 152 4 3 4 21161 1 1 1 6 6YESNOYESNOExplanation:Test case 11 : Consider 𝐵=[0,4,0,0,0]B=[0,4,0,0,0]. The corresponding array 𝐶C becomes [4,5,3,2,1][4,5,3,2,1], which is a permutation. Some other possible values of 𝐵B for which 𝐶C is a permutation are [1,0,1,1,1][1,0,1,1,1] and [1,3,0,0,0][1,3,0,0,0].Test case 22 : It can be proven that no valid array 𝐵B exists.

Chef has a sequence of 𝑁N integers, 𝐴1,𝐴2,...,𝐴𝑁A 1​ ,A 2​ ,...,A N​ . He likes this sequence if it contains a subsequence of 𝑀M integers, 𝐵1,𝐵2,...,𝐵𝑀B 1​ ,B 2​ ,...,B M​ within it. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.You will be given a sequence of 𝑁N integers, 𝐴1,𝐴2,...,𝐴𝑁A 1​ ,A 2​ ,...,A N​ followed by another sequence of 𝑀M integers, 𝐵1,𝐵2,...,𝐵𝑀B 1​ ,B 2​ ,...,B M​ . Given these, you have to tell whether Chef likes the sequence of 𝑁N integers(𝐴1,𝐴2,...,𝐴𝑁A 1​ ,A 2​ ,...,A N​ ) or not.Formally, output "Yes" if∃𝑖𝑑𝑥1,𝑖𝑑𝑥2,...,𝑖𝑑𝑥𝑀∣1≤𝑖𝑑𝑥1<𝑖𝑑𝑥2<...<𝑖𝑑𝑥𝑀≤𝑁∃idx 1​ ,idx 2​ ,...,idx M​ ∣1≤idx 1​ <idx 2​ <...<idx M​ ≤N and 𝐴𝑖𝑑𝑥𝑖=𝐵𝑖∀𝑖,1≤𝑖≤𝑀A idx i​ ​ =B i​ ∀i,1≤i≤MOtherwise output "No". Note that the quotes are for clarity.InputThe first line contains a single integer, 𝑇T.𝑇T test cases follow where each test case contains four lines:The first line of a test case contains a single integer 𝑁NThe second line of the test case contains 𝑁N space separated integers, 𝐴1,𝐴2,...,𝐴𝑁A 1​ ,A 2​ ,...,A N​ The third line of the test case contains a single integer 𝑀M.The fourth line contains 𝑀M space separated integers, 𝐵1,𝐵2,...,𝐵𝑀B 1​ ,B 2​ ,...,B M​ Symbols have usual meanings as described in the statement.OutputFor each test case, output a single line containing the output. Output is "Yes" if Chef likes the sequence 𝐴A. Output is "No" if Chef dislikes the sequence 𝐴A.Constraints1≤𝑇≤1001≤T≤1001≤𝑁≤1031≤N≤10 3 1≤𝑀≤1031≤M≤10 3 1≤𝐴𝑖,𝐵𝑖≤1091≤A i​ ,B i​ ≤10 9 Sample Input3 6 1 2 3 4 5 6 3 2 3 4 6 22 5 6 33 1 4 2 4 15 4 1 3 4 2 2 1 2Sample OutputYes No YesExplanation:In sample test case 11, the sequence 1,2,3,4,5,61,2,3,4,5,6 contains the subsequence 2,3,42,3,4. The subsequence is present at indices 1,2,31,2,3 of the original sequence. Hence, 1,2,3,4,5,61,2,3,4,5,6 is a sequence which Chef likes it. Therefore, we output "Yes".In sample test case 22, the subsequence 4,154,15 is not present in sequence 22,5,6,33,1,422,5,6,33,1,4. Hence, we output "No".In sample test case 33, the sequence 1,3,4,21,3,4,2 contains the subsequence 1,21,2. The subsequence is present at indices 0,30,3. Therefore, we output "Yes".

Maximum Distance PermutationsDefine the distance between 22 permutations†† 𝐴A and 𝐵B, each of length 𝑁N, as the minimum value of ∣𝐴𝑖−𝐵𝑖∣‡∣A i​ −B i​ ∣ ‡ for 1≤𝑖≤𝑁1≤i≤N.Find a pair of permutations of length 𝑁N which have the maximum possible distance among all pairs of permutations of length 𝑁N.†† A permutation of length 𝑁N is an array of 𝑁N distinct elements which are all in the range [1,𝑁][1,N]. For example, [2,3,1,4][2,3,1,4] is a permutation of length 44 whereas [2,4,3][2,4,3] and [1,1,2][1,1,2] are not.‡‡ ∣𝑋∣∣X∣ denotes the absolute value of 𝑋X. For example, ∣−5∣=∣5∣=5∣−5∣=∣5∣=5.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a single integer 𝑁N - the length of the permutations.Output FormatFor each test case, output 22 lines.The first line containing 𝑁N space-separated integers - 𝐴1,𝐴2,𝐴3,…,𝐴𝑁A 1​ ,A 2​ ,A 3​ ,…,A N​ , denoting the permutation 𝐴A.The second line containing 𝑁N space-separated integers - 𝐵1,𝐵2,𝐵3,…,𝐵𝑁B 1​ ,B 2​ ,B 3​ ,…,B N​ , denoting the permutation 𝐵B.The permutations 𝐴A and 𝐵B must have the maximum distance possible. If multiple answers are possible, all will be accepted.Constraints1≤𝑇≤1001≤T≤1001≤𝑁≤1001≤N≤100Sample 1:InputOutput3123111 22 11 2 33 1 2Explanation:Test case 1 : There is only one possible permutation of length 𝑁N, and thus only one possible pair, which has distance 00.Test case 2 : The permutations [1,2][1,2] and [2,1][2,1] have a distance of 11. This can be shown to be the maximum possible distance.

Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order. Example 1:Input: nums = [1,2,3]Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]Example 2:Input: nums = [0,1]Output: [[0,1],[1,0]]Example 3:Input: nums = [1]Output: [[1]] Constraints:1 <= nums.length <= 6-10 <= nums[i] <= 10All the integers of nums are unique.

Chef defines a pair of positive integers (𝑎,𝑏)(a,b) to be a Oneful PairOneful Pair, if𝑎+𝑏+(𝑎⋅𝑏)=111a+b+(a⋅b)=111For example, (1,55)(1,55) is a Oneful PairOneful Pair, since 1+55+(1⋅55)=56+55=1111+55+(1⋅55)=56+55=111.But (1,56)(1,56) is not a Oneful PairOneful Pair, since 1+56+(1⋅56)=57+56=113≠1111+56+(1⋅56)=57+56=113=111.Which of these pairs are Oneful PairOneful Pair?