Make My Array EqualYou are given an array 𝐴A of length 𝑁N.Determine if it is possible to make all the elements of 𝐴A equal by performing the following operation any number of times (possibly, zero):Choose two distinct indices 𝑖i and 𝑗j (1≤𝑖,𝑗≤𝑁1≤i,j≤N, 𝑖≠𝑗i=j); andUpdate the value at index 𝑖i by setting 𝐴𝑖A i​ to 𝐴𝑖+𝐴𝑗A i​ +A j​ .For example, if 𝐴=[1,5,3,5,6]A=[1,5,3,5,6],Choosing 𝑖=5i=5 and 𝑗=3j=3 would result in the array [1,5,3,5,9][1,5,3,5,9], since we replace 𝐴5A 5​ with 𝐴5+𝐴3=9A 5​ +A 3​ =9.Choosing 𝑖=2i=2 and 𝑗=4j=4 would instead result in the array [1,10,3,5,6][1,10,3,5,6].Output "YES" if it is possible to make all elements of the array equal after performing several (possibly, zero) of these operations, otherwise output "NO" (without quotes).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 length of array.The second line of each test case contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ , denoting the initial array.Output FormatFor each test case, print Yes if it is possible to make all elements of array equal using any number of operations, otherwise print No.You may print each character of the output in either uppercase or lowercase (for example, the strings YES, yEs, yes, and yeS will all be treated as identical).Constraints1≤𝑇≤1051≤T≤10 5 1≤𝑁≤2⋅1051≤N≤2⋅10 5 0≤𝐴𝑖≤1090≤A i​ ≤10 9 The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput331 1 121 231 0 0YESNOYES

You are given an array 𝐴A of size 𝑁N.You can rearrange the elements of 𝐴A as you want. After that, construct an array 𝐵B of size 𝑁N as:𝐵1=𝐴1B 1​ =A 1​ ;𝐵𝑖=𝐵𝑖−1B i​ =B i−1​ && 𝐴𝑖A i​ for all 2≤𝑖≤𝑁2≤i≤N, where && denotes the bitwise AND operator.Find the lexicographically largest possible array 𝐵B.For two arrays 𝑋X and 𝑌Y, both of size 𝑁N, the array 𝑋X is said to be lexicographically larger than array 𝑌Y, if, in the first position where 𝑋X and 𝑌Y differ, 𝑋𝑖>𝑌𝑖X i​ >Y i​ .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 contains 𝑁N, the size of the array 𝐴A.The second line of each test case contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ .Output FormatFor each test case, output on a new line, 𝑁N space separated integers denoting the lexicographically largest array 𝐵B that can be formed by any rearrangement of 𝐴A.Constraints1≤𝑇≤2⋅1041≤T≤2⋅10 4 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases does not exceed 2⋅1052⋅10 5 .

You are given an array 𝐴A of size 𝑁N.You can rearrange the elements of 𝐴A as you want. After that, construct an array 𝐵B of size 𝑁N as:𝐵1=𝐴1B 1​ =A 1​ ;𝐵𝑖=𝐵𝑖−1⊕𝐴𝑖B i​ =B i−1​ ⊕A i​ for all 2≤𝑖≤𝑁2≤i≤N, where ⊕⊕ denotes the bitwise XOR operator.Find a rearrangement of 𝐴A such that 𝐵𝑖≠0B i​ =0 for all 1≤𝑖≤𝑁1≤i≤N.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 contains 𝑁N, the size of the array 𝐴A.The second line of each test case contains 𝑁N space-separated integers : 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ .Output FormatFor each test case, output on a new line, 𝑁N space-separated integers denoting the rearrangement of 𝐴A satisfying the conditions.In case no such rearrangement exists, print −1−1 instead.Constraints1≤𝑇≤2⋅1041≤T≤2⋅10 4 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases does not exceed 2⋅1052⋅10 5 .Sample 1:InputOutput431 2 351 2 3 4 531 2 211-11 2 4 3 51 2 21Explanation:Test case 11 : It can be shown that it's impossible to rearrange 𝐴A in a valid way.Test case 22 : A possible rearrangement of array 𝐴A is [1,2,4,3,5][1,2,4,3,5] and the corresponding array 𝐵B is [1,3,7,4,1][1,3,7,4,1]. Here 𝐵𝑖≠0B i​ =0 for all 1≤𝑖≤𝑁1≤i≤N.

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.

The two versions of the problem are different. You may want to read both versions. You can make hacks only if both versions are solved.You are given an array a𝑎 of length n𝑛. Start with c=0𝑐=0. Then, for each i𝑖 from 11 to n𝑛 (in increasing order) do exactly one of the following:Option 11: set c𝑐 to c+ai𝑐+𝑎𝑖.Option 22: set c𝑐 to |c+ai||𝑐+𝑎𝑖|, where |x||𝑥| is the absolute value of x𝑥.Let the maximum final value of c𝑐 after the procedure described above be equal to k𝑘. Find k𝑘.InputThe first line contains a single integer t𝑡 (1≤t≤1041≤𝑡≤104) — the number of test cases.The first line of each test case contains a single integer n𝑛 (2≤n≤2⋅1052≤𝑛≤2⋅105).The second line of each case contains n𝑛 integers a1𝑎1, a2𝑎2, a3𝑎3, ……, an𝑎𝑛 (−109≤ai≤109−109≤𝑎𝑖≤109).The sum of n𝑛 over all test cases does not exceed 3⋅1053⋅105.OutputFor each test case, output a single integer — the value of k𝑘.ExampleinputCopy5410 -9 -3 481 4 3 4 1 4 3 43-1 -2 -34-1000000000 1000000000 1000000000 100000000041 9 8 4outputCopy6246400000000022NoteIn the first test case, if we set c𝑐 to its absolute value every time we add to it, we end up with 66. It can be shown that this is the maximum result.In the second test case, taking the absolute value will never change anything, so we can just sum the array without doing anything to get 2424.In the third test case, it is optimal to wait until the end to set c𝑐 to its absolute value, resulting in an answer of 66.

Redundant ArrayChef has an array 𝐴A containing 𝑁N positive integers.He can perform the following operation on the array as many times as he likes:Choose integers 𝐿L and 𝑅R such that 1≤𝐿≤𝑅≤𝑁1≤L≤R≤N;Choose a positive integer 𝑥x;For every index 𝑖i from 𝐿L to 𝑅R (inclusive of both), set 𝐴𝑖=𝑥A i​ =x.The cost of such an operation is (𝑅−𝐿+1)⋅𝑥(R−L+1)⋅x.Find the minimum cost required to make all the elements of 𝐴A equal.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists two lines of input.The first line of each test case contains a single integer 𝑁N — the size of the array.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ .Output FormatFor each test case, output on a new line the minimum cost needed to make all the elements of 𝐴A equal.Constraints1≤𝑇≤2×1051≤T≤2×10 5 1≤𝑁≤2×1051≤N≤2×10 5 1≤𝐴𝑖≤𝑁1≤A i​ ≤NThe sum of 𝑁N over all test cases does not exceed 2×1052×10 5 Sample 1:InputOutput352 4 3 2 233 3 371 3 7 5 1 4 3405