Given an array(0-based indexing), you have to find the max sum of i*A[i] where A[i] is the element at index i in the array. The only operation allowed is to rotate(clock-wise or counter clock-wise) the array any number of times.

Example 1:

Input:
N = 4
A[] = {8,3,1,2}
Output: 29
Explanation: Above the configuration
possible by rotating elements are
3 1 2 8 here sum is 3*0+1*1+2*2+8*3 = 29
1 2 8 3 here sum is 1*0+2*1+8*2+3*3 = 27
2 8 3 1 here sum is 2*0+8*1+3*2+1*3 = 17
8 3 1 2 here sum is 8*0+3*1+1*2+2*3 = 11
Here the max sum is 29

Your Task:
Your task is to complete the function max_sum which takes two arguments which is the array A [ ] and its size and returns an integer value denoting the required max sum.

Expected Time Complexity: O(N).
Expected Auxiliary Space: O(1).

Constraints:
1<=N<=10⁴
1<=A[]<1000