13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T719,

You 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 $$$a$$$.

Note

In the first example, you can reverse the subarray $

Maximum Sum of Products

Examples