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 ∑_{i=1}^n a_i ⋅ b_i is maximized.

Input

The first line contains one integer n (1 ≤ n ≤ 5000).

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^7).

The third line contains n integers b_1, b_2, ..., b_n (1 ≤ b_i ≤ 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 ⋅ 1 + 3 ⋅ 3 + 2 ⋅ 2 + 3 ⋅ 4 + 1 ⋅ 2 = 29.

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

In the third example, you can reverse the subarray [3, 5]. Then a = [1, 8, 3, 6, 7, 6] and 1 ⋅ 5 + 8 ⋅ 9 + 3 ⋅ 6 + 6 ⋅ 8 + 7 ⋅ 8 + 6 ⋅ 6 = 235.
#region Header
#!/usr/bin/env python3
# from typing import *

import sys
import io
import math
import collections
import decimal
import itertools
import bisect
import heapq


def input():
    return sys.stdin.readline()[:-1]


# sys.setrecursionlimit(1000000)
#endregion

# _INPUT = """# paste here...
# """
# sys.stdin = io.StringIO(_INPUT)


def main():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    max_diff = 0
    for i in range(N):
        j1 = i-1
        j2 = i+1
        diff = 0
        while 0 <= j1 and j2 <= N-1:
            diff += -(A[j2]-A[j1])*(B[j2]-B[j1])
            max_diff = max(max_diff, diff)
            j1 -= 1
            j2 += 1

    for i in range(N-1):
        j1 = i
        j2 = i+1
        diff = 0
        while 0 <= j1 and j2 <= N-1:
            diff += -(A[j2]-A[j1])*(B[j2]-B[j1])
            max_diff = max(max_diff, diff)
            j1 -= 1
            j2 += 1

    original_prod = sum(A[i] * B[i] for i in range(N))
    if max_diff > 0:
        ans = original_prod + max_diff
        print(ans)
    else:
        print(original_prod)

if __name__ == '__main__':
    main()
