You are given two integer arrays: array a𝑎 of length n𝑛 and array b𝑏 of length n+1𝑛+1.You can perform the following operations any number of times in any order:choose any element of the array a𝑎 and increase it by 11;choose any element of the array a𝑎 and decrease it by 11;choose any element of the array a𝑎, copy it and append the copy to the end of the array a𝑎.Your task is to calculate the minimum number of aforementioned operations (possibly zero) required to transform the array a𝑎 into the array b𝑏. It can be shown that under the constraints of the problem, it is always possible.InputThe first line contains a single integer t𝑡 (1≤t≤1041≤𝑡≤104) — the number of test cases.Each test case consists of three lines:the first line contains a single integer n𝑛 (1≤n≤2⋅1051≤𝑛≤2⋅105);the second line contains n𝑛 integers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛 (1≤ai≤1091≤𝑎𝑖≤109);the third line contains n+1𝑛+1 integers b1,b2,…,bn+1𝑏1,𝑏2,…,𝑏𝑛+1 (1≤bi≤1091≤𝑏𝑖≤109).Additional constraint on the input: the sum of n𝑛 over all test cases doesn't exceed 2⋅1052⋅105.OutputFor each test case, print a single integer — the minimum number of operations (possibly zero) required to transform the array a𝑎 into the array b𝑏.ExampleinputCopy3121 323 33 3 344 2 1 22 1 5 2 3outputCopy318NoteIn the first example, you can transform a𝑎 into b𝑏 as follows: [2]→[2,2]→[1,2]→[1,3][2]→[2,2]→[1,2]→[1,3].

You are given two arrays of integers a1,a2,…,an and b1,b2,…,bn. Before applying any operations, you can reorder the elements of each array as you wish. Then, in one operation, you will perform both of the following actions, if the arrays are not empty:1. Choose any element from array a and remove it (all remaining elements are shifted to a new array a)2. Choose any element from array b and remove it (all remaining elements are shifted to a new array b)Let k be the final size of both arrays. Find the minimum number of operations required to satisfy ai less than bi.Input Format2 (size of arrays a & b)1 1 (array a)3 2 (array b)Constraintsall inputs are positive integersOutput Format0 (number of minimum operations)Sample Input 041 5 1 53 8 3 3Sample Output 01Submissions: 5Max Score: 10Difficulty: MediumRate This Challenge: More Python 31n = int(input

Given an array of N integers containing only 0 or 1. You can do the following operations on the array:swap elements at two indiceschoose one index and change its value from 0 to 1 or vice-versa.You have to do the minimum number of the above operations such that the final array is non-decreasing.Note Consider 1 based Array-indexing

You are given an array 𝐴A containing 𝑁N integers.Consider the following process:Let 𝑆=0S=0 initially.For each 𝑖i from 11 to 𝑁N in order, update 𝑆S to either (𝑆+𝐴𝑖)(S+A i​ ) or (𝑆×𝐴𝑖)(S×A i​ ).That is, either add 𝐴𝑖A i​ to 𝑆S or multiply 𝑆S by 𝐴𝑖A i​ .Before performing the process, you're allowed to freely rearrange the elements of 𝐴A as you like.If you choose the rearrangement of 𝐴A and the sequence of operations optimally, what's the maximum possible value of 𝑆S that you can obtain?This maximum value can be very large, so print it modulo 109+710 9 +7.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains a single integer 𝑁N — the number of elements in the array.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ - the elements of the array.Output FormatFor each test case, output on a new line the maximum possible value of 𝑆S, modulo 109+710 9 +7.Constraints1≤𝑇≤1031≤T≤10 3 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput244 2 5 231 2 1804Explanation:Test case 11: Choose the rearrangement 𝐴=[2,2,5,4]A=[2,2,5,4]. Then,Add 𝐴1=2A 1​ =2 to 𝑆S. Now, 𝑆=2S=2.Add 𝐴2=2A 2​ =2 to 𝑆S. Now, 𝑆=4S=4.Multiply 𝑆S by 𝐴3=5A 3​ =5. Now, 𝑆=20S=20.Multiply 𝑆S by 𝐴4=4A 4​ =4. Now, 𝑆=80S=80.This is the maximum value that can be obtained.Test case 22: Choose any rearrangement and sum up all the numbers to get 1+1+2=41+1+2=4.This is the maximum value that can be obtained.

Initially, we had one array, which was a permutation of size n𝑛 (an array of size n𝑛 where each integer from 11 to n𝑛 appears exactly once).We performed q𝑞 operations. During the i𝑖-th operation, we did the following:choose any array we have with at least 22 elements;split it into two non-empty arrays (prefix and suffix);write two integers li𝑙𝑖 and ri𝑟𝑖, where li𝑙𝑖 is the maximum element in the left part which we get after the split, and ri𝑟𝑖 is the maximum element in the right part;remove the array we've chosen from the pool of arrays we can use, and add the two resulting parts into the pool.For example, suppose the initial array was [6,3,4,1,2,5][6,3,4,1,2,5], and we performed the following operations:choose the array [6,3,4,1,2,5][6,3,4,1,2,5] and split it into [6,3][6,3] and [4,1,2,5][4,1,2,5]. Then we write l1=6𝑙1=6 and r1=5𝑟1=5, and the arrays we have are [6,3][6,3] and [4,1,2,5][4,1,2,5];choose the array [4,1,2,5][4,1,2,5] and split it into [4,1,2][4,1,2] and [5][5]. Then we write l2=4𝑙2=4 and r2=5𝑟2=5, and the arrays we have are [6,3][6,3], [4,1,2][4,1,2] and [5][5];choose the array [4,1,2][4,1,2] and split it into [4][4] and [1,2][1,2]. Then we write l3=4𝑙3=4 and r3=2𝑟3=2, and the arrays we have are [6,3][6,3], [4][4], [1,2][1,2] and [5][5].You are given two integers n𝑛 and q𝑞, and two sequences [l1,l2,…,lq][𝑙1,𝑙2,…,𝑙𝑞] and [r1,r2,…,rq][𝑟1,𝑟2,…,𝑟𝑞]. A permutation of size n𝑛 is called valid if we can perform q𝑞 operations and produce the given sequences [l1,l2,…,lq][𝑙1,𝑙2,…,𝑙𝑞] and [r1,r2,…,rq][𝑟1,𝑟2,…,𝑟𝑞].Calculate the number of valid permutations.InputThe first line contains two integers n𝑛 and q𝑞 (1≤q<n≤3⋅1051≤𝑞<𝑛≤3⋅105).The second line contains q𝑞 integers l1,l2,…,lq𝑙1,𝑙2,…,𝑙𝑞 (1≤li≤n1≤𝑙𝑖≤𝑛).The third line contains q𝑞 integers r1,r2,…,rq𝑟1,𝑟2,…,𝑟𝑞 (1≤ri≤n1≤𝑟𝑖≤𝑛).Additional constraint on the input: there exists at least one permutation which can produce the given sequences [l1,l2,…,lq][𝑙1,𝑙2,…,𝑙𝑞] and [r1,r2,…,rq][𝑟1,𝑟2,…,𝑟𝑞].OutputPrint one integer — the number of valid permutations, taken modulo 998244353998244353.ExamplesinputCopy6 36 4 45 5 2outputCopy30inputCopy10 1109outputCopy1814400inputCopy4 124outputCopy8

You are given two integers n and x. You have to construct an array of positive integers nums of size n where for every 0 <= i < n - 1, nums[i + 1] is greater than nums[i], and the result of the bitwise AND operation between all elements of nums is x.Return the minimum possible value of nums[n - 1]. Example 1:Input: n = 3, x = 4Output: 6Explanation:nums can be [4,5,6] and its last element is 6.Example 2:Input: n = 2, x = 7Output: 15Explanation:nums can be [7,15] and its last element is 15. Constraints:1 <= n, x <= 108