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Given an array of integers `A`

and let *n* to be its length.

Assume `B`

to be an array obtained by rotating the array _{k}`A`

*k* positions clock-wise, we define a "rotation function" `F`

on `A`

as follow:

`F(k) = 0 * B`

._{k}[0] + 1 * B_{k}[1] + ... + (n-1) * B_{k}[n-1]

Calculate the maximum value of `F(0), F(1), ..., F(n-1)`

.

**Note:**

*n* is guaranteed to be less than 10^{5}.

**Example:**

A = [4, 3, 2, 6] F(0) = (0 * 4) + (1 * 3) + (2 * 2) + (3 * 6) = 0 + 3 + 4 + 18 = 25 F(1) = (0 * 6) + (1 * 4) + (2 * 3) + (3 * 2) = 0 + 4 + 6 + 6 = 16 F(2) = (0 * 2) + (1 * 6) + (2 * 4) + (3 * 3) = 0 + 6 + 8 + 9 = 23 F(3) = (0 * 3) + (1 * 2) + (2 * 6) + (3 * 4) = 0 + 2 + 12 + 12 = 26 So the maximum value of F(0), F(1), F(2), F(3) is F(3) = 26.

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