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.
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from __future__ import print_function # for PyPy2
# from itertools import permutations
# from functools import cmp_to_key	# for adding custom comparator
# from fractions import Fraction
# from collections import *
from sys import stdin
# from bisect import *
# from heapq import *
# from math import *
 
g   = lambda : stdin.readline().strip()
gl  = lambda : g().split()
gil = lambda : [int(var) for var in gl()]
gfl = lambda : [float(var) for var in gl()]
gcl = lambda : list(g())
gbs = lambda : [int(var) for var in g()]
mod = int(1e9)+7
inf = float("inf")


n, = gil()
a, b = gil(), gil()

ans = 0
base = 0

# cal ans for odd len
for ci in range(n):
	lo, ro, le, re, anso, anse = ci-1, ci+1, ci, ci+1, 0, 0
	base += a[ci]*b[ci]

	while (le >= 0 and re < n) or (lo >= 0 and ro < n):
		if (le >= 0 and re < n):anse += (a[le]-a[re])*b[re] + (a[re]- a[le])*b[le]  ;ans = max(anse, ans)
		if (lo >= 0 and ro < n):anso += (a[lo]- a[ro])*b[ro] + (a[ro]- a[lo])*b[lo] ;ans = max(anso, ans)
		le -= 1;re += 1;lo -= 1;ro += 1

print(ans+base)