class Solution:

# Time: O(n)

# Space: O(1)

def max_rotate_function(self, nums: list[int]) -> int:

total = sum(nums)

cur = sum(i * v for i, v in enumerate(nums))

best = cur

for k in range(1, len(nums)):

# rotating clockwise by k moves the last element of arr_(k-1) to index 0

# and adds total to every other index: F(k) = F(k-1) + total - n * nums[n - k]

cur += total - len(nums) * nums[-k]

best = max(best, cur)

return best