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.
import java.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        long a[]=sc.readArrayLong(n);
        long b[]=sc.readArrayLong(n);
        long ans=0;
        for (int i=0;i<n;i++){
            ans+=(a[i]*b[i]);
        }
        long max=ans;
        for (int i=0;i<n;i++){
            long check=ans;
            int x=i,y=i;
            while (x>=0&&y<n){
                long p1=a[x]*b[x];
                long p2=a[y]*b[y];
                long p3=a[x]*b[y];
                long p4=a[y]*b[x];
                check-=(p1+p2);
                check+=(p3+p4);
                max=Math.max(max,check);
                x--;
                y++;
            }
                x = i;
                y = i + 1;
                check = ans;
            if (y<n) {
                while (x>=0&&y<n){
                    long p1=a[x]*b[x];
                    long p2=a[y]*b[y];
                    long p3=a[x]*b[y];
                    long p4=a[y]*b[x];
                    check-=(p1+p2);
                    check+=(p3+p4);
                    max=Math.max(max,check);
                    x--;
                    y++;
                }
            }
        }
        System.out.println(max);
    }

//        out.flush();



    //------------------------------------if-------------------------------------------------------------------------------------------------------------------------------------------------
    //sieve
    static void primeSieve(int a[]){
        //mark all odd number as prime
        for (int i=3;i<a.length;i+=2){
            a[i]=1;
        }
        for (long i=3;i<a.length;i+=2){
            //if the number is marked then it is prime
            if (a[(int) i]==1){
                //mark all muliple of the number as not prime
                for (long j=i*i;j<a.length;j+=i){
                    a[(int)j]=0;
                }
            }
        }
        a[2]=1;
        a[1]=a[0]=0;
    }
    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    static String sortString(String s) {
        char temp[] = s.toCharArray();
        Arrays.sort(temp);
        return new String(temp);
    }
    static class Pair implements Comparable<Pair> {
        int a;
        long b;

        public Pair(int a, long b) {
            this.a = a;
            this.b = b;
        }
        //        to sort first part
//        public int compareTo(Pair other) {
//            if (this.a == other.a) return other.b > this.b ? -1 : 1;
//            else if (this.a > other.a) return 1;
//            else return -1;
//        }
//        public int compareTo(Pair other) {
//            if (this.b == other.b) return 0;
//            if (this.b < other.b) return 1;
//            else return -1;
//        }
        //sort on the basis of first part only
        public int compareTo(Pair other) {
            if (this.a == other.a) return 0;
            else if (this.a > other.a) return 1;
            else return -1;
        }

    }
    static int[] frequency(String s){
        int fre[]= new int[26];
        for (int i=0;i<s.length();i++){
            fre[s.charAt(i)-'a']++;
        }
        return fre;
    }
    static long LOWERBOUND(long a[],long k){
        int s=0,e=a.length-1;
        long ans=-1;
        while (s<=e){
            int mid=(s+e)/2;
            if (a[mid]<=k){
                ans=mid;
                s=mid+1;
            }
            else {
                e=mid-1;
            }
        }
        return ans;
    }
    static int mod =(int)(1e9+7);
    static long mod(long x) {
        return ((x % mod + mod) % mod);
    }
    static long add(long x, long y) {
        return mod(mod(x) + mod(y));
    }
    static long mul(long x, long y) {
        return mod(mod(x) * mod(y));
    }
    //Fast Power(logN)
    static int fastPower(long a,long n){
        int ans=1;
        while (n>0){
            long lastBit=n&1;
            if (lastBit==1){
                ans=(int)mul(ans,a);
            }

            a=(int)mul(a,a);
            n>>=1;
        }
        return ans;
    }
    static int[] find(int n, int start, int diff) {
        int a[] = new int[n];
        a[0] = start;
        for (int i = 1; i < n; i++) a[i] = a[i - 1] + diff;
        return a;
    }
    static void swap(int a, int b) {
        int c = a;
        a = b;
        b = c;
    }
    static void printArray(int a[]) {
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
    }
    static boolean sorted(int a[]) {
        int n = a.length;
        boolean flag = true;
        for (int i = 0; i < n - 1; i++) {
            if (a[i] > a[i + 1]) flag = false;
        }
        if (flag) return true;
        else return false;
    }
    public static int findlog(long n) {
        if (n == 0)
            return 0;

        if (n == 1)
            return 0;
        if (n == 2)
            return 1;
        double num = Math.log(n);
        double den = Math.log(2);
        if (den == 0)
            return 0;
        return (int) (num / den);
    }
    public static long gcd(long a, long b) {
        if (b % a == 0)
            return a;
        return gcd(b % a, a);
    }
    public static int gcdInt(int a, int b) {

        if (b % a == 0)
            return a;

        return gcdInt(b % a, a);

    }
    static void sortReverse(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        //        Collections.sort.(l);
        Collections.sort(l, Collections.reverseOrder());
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readArrayLong(long n) {
            long[] a = new long[(int) n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}