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D. Maximum Sum of Products

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given two integer arrays $$$a$$$ and $$$b$$$ of length $$$n$$$.

You can reverse at most one subarray (continuous subsegment) of the array $$$a$$$.

Your task is to reverse such a subarray that the sum $$$\sum\limits_{i=1}^n a_i \cdot b_i$$$ is maximized.

Input

The first line contains one integer $$$n$$$ ($$$1 \le n \le 5000$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^7$$$).

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 10^7$$$).

Output

Print single integer — maximum possible sum after reversing at most one subarray (continuous subsegment) of $$$a$$$.

Examples

Input

5 2 3 2 1 3 1 3 2 4 2

Output

29

Input

2 13 37 2 4

Output

174

Input

6 1 8 7 6 3 6 5 9 6 8 8 6

Output

235

Note

In the first example, you can reverse the subarray $$$[4, 5]$$$. Then $$$a = [2, 3, 2, 3, 1]$$$ and $$$2 \cdot 1 + 3 \cdot 3 + 2 \cdot 2 + 3 \cdot 4 + 1 \cdot 2 = 29$$$.

In the second example, you don't need to use the reverse operation. $$$13 \cdot 2 + 37 \cdot 4 = 174$$$.

In the third example, you can reverse the subarray $$$[3, 5]$$$. Then $$$a = [1, 8, 3, 6, 7, 6]$$$ and $$$1 \cdot 5 + 8 \cdot 9 + 3 \cdot 6 + 6 \cdot 8 + 7 \cdot 8 + 6 \cdot 6 = 235$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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