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.*;
import java.lang.*;

public class B{
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static long MOD = (long) (1e9 + 7);
    //    static long MOD = 998244353;
    static long MOD2 = MOD * MOD;
    static FastReader sc = new FastReader();
    static int pInf = Integer.MAX_VALUE;
    static int nInf = Integer.MIN_VALUE;
    static long ded = (long)(1e17)+9;
    public static void main(String[] args) throws Exception {
        int test = 1;
//        test = sc.nextInt();
        for (int i = 1; i <= test; i++){
//            out.print("Case #"+i+": ");
            solve();
        }
        out.flush();
        out.close();
    }
    static int n;
    static void solve(){
        n = sc.nextInt();
        long[] a = new long[n];
        long[] b = new long[n];
        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }
        long ans = 0L;
        long[] pre = new long[n+1];
        for(int i = 0; i < n; i++){
            b[i] = sc.nextInt();
            ans += (a[i]*b[i]);
            pre[i+1] = pre[i]+(a[i]*b[i]);
        }
        for(int i= 0; i < n; i++){
            //if rotation is around i;
            int l = i-1;
            int r = i+1;
            long temp = (a[i]*b[i]);
            while(e(l)&&e(r)){
                temp += (a[l]*b[r]);
                temp += (a[r]*b[l]);
                long temp2 = temp;
                l--;
                r++;
                if(e(l)){
                    temp2 += (pre[l+1]);
                }
                if(e(r)){
                    temp2 += (pre[n]-pre[r]);
                }
                ans = Math.max(ans,temp2);
            }
        }
        for(int i= 0; i < n; i++){
            int l = i;
            int r = i+1;
            long temp = 0L;
            while(e(l)&&e(r)){
                temp += (a[l]*b[r]);
                temp += (a[r]*b[l]);
                long temp2 = temp;
                l--;
                r++;
                if(e(l)){
                    temp2 += (pre[l+1]);
                }
                if(e(r)){
                    temp2 += (pre[n]-pre[r]);
                }
                ans = Math.max(ans,temp2);
            }
        }
        out.println(ans);
    }
    static boolean e(int i){
        return i>=0&&i<n;
    }
    static class Pair implements Comparable<Pair> {
        int x;
        int y;
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        @Override
        public int compareTo(Pair o){
            if(this.x==o.x){
                return -1*(o.y-this.y);
            }
            return this.x-o.x;
        }

        @Override
        public String toString() {
            return "Pair{" + "x=" + x + ", y=" + y + '}';
        }

        public boolean equals(Pair o){
            return this.x==o.x&&this.y==o.y;
        }
    }
    public static long mul(long a, long b) {
        return ((a % MOD) * (b % MOD)) % MOD;
    }
    public static long add(long a, long b) {
        return ((a % MOD) + (b % MOD)) % MOD;
    }
    public static long c2(long n) {
        if ((n & 1) == 0) {
            return mul(n / 2, n - 1);
        } else {
            return mul(n, (n - 1) / 2);
        }
    }
    //Shuffle Sort
    static final Random random = new Random();
    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n); int temp= a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }
    //Brian Kernighans Algorithm
    static long countSetBits(long n) {
        if (n == 0) return 0;
        return 1 + countSetBits(n & (n - 1));
    }
    //Euclidean Algorithm
    static long gcd(long A, long B) {
        if (B == 0) return A;
        return gcd(B, A % B);
    }
    //Modular Exponentiation
    static long fastExpo(long x, long n) {
        if (n == 0) return 1;
        if ((n & 1) == 0) return fastExpo((x * x) % MOD, n / 2) % MOD;
        return ((x % MOD) * fastExpo((x * x) % MOD, (n - 1) / 2)) % MOD;
    }
    //AKS Algorithm
    static boolean isPrime(long n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        for (int i = 5; i <= Math.sqrt(n); i += 6)
            if (n % i == 0 || n % (i + 2) == 0) return false;
        return true;
    }
    public static long modinv(long x) {
        return modpow(x, MOD - 2);
    }
    public static long modpow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        long x = modpow(a, b / 2);
        x = (x * x) % MOD;
        if (b % 2 == 1) {
            return (x * a) % MOD;
        }
        return x;
    }


    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}