Vasya's house is situated in a forest, and there is a mushroom glade near it. The glade consists of two rows, each of which can be divided into n consecutive cells. For each cell Vasya knows how fast the mushrooms grow in this cell (more formally, how many grams of mushrooms grow in this cell each minute). Vasya spends exactly one minute to move to some adjacent cell. Vasya cannot leave the glade. Two cells are considered adjacent if they share a common side. When Vasya enters some cell, he instantly collects all the mushrooms growing there.

Vasya begins his journey in the left upper cell. Every minute Vasya must move to some adjacent cell, he cannot wait for the mushrooms to grow. He wants to visit all the cells exactly once and maximize the total weight of the collected mushrooms. Initially, all mushrooms have a weight of 0. Note that Vasya doesn't need to return to the starting cell.

Help Vasya! Calculate the maximum total weight of mushrooms he can collect.

Input

The first line contains the number n (1 ≤ n ≤ 3·105) — the length of the glade.

The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 106) — the growth rate of mushrooms in the first row of the glade.

The third line contains n numbers b1, b2, ..., bn (1 ≤ bi ≤ 106) is the growth rate of mushrooms in the second row of the glade.

Output

Output one number — the maximum total weight of mushrooms that Vasya can collect by choosing the optimal route. Pay attention that Vasya must visit every cell of the glade exactly once.

Examples

Input

3
1 2 3
6 5 4


Output

70


Input

3
1 1000 10000
10 100 100000


Output

543210

Note

In the first test case, the optimal route is as follows: 

<image> Thus, the collected weight of mushrooms will be 0·1 + 1·2 + 2·3 + 3·4 + 4·5 + 5·6 = 70.

In the second test case, the optimal route is as follows: 

<image> Thus, the collected weight of mushrooms will be 0·1 + 1·10 + 2·100 + 3·1000 + 4·10000 + 5·100000 = 543210.
import java.util.*;
import java.io.*;
import java.io.FileWriter; 

// Solution

public class Main 
{    
  public static void main (String[] argv) 
  {
	  new Main();
  } 
     
  
  boolean test = true;  
  final int[][] dirs = {{0,1}, {0,-1}, {-1,0}, {1,0}, {1,1},{1,-1},{-1,1},{-1,-1}};
  final int MOD = 998244353;//1000000007;  
  int n_bit = 1000000;
  int[] bit;
  
  public Main()   {
	FastReader in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
	
     
    //FastReader in = new FastReader(new BufferedReader(new FileReader("Main.in")));   
    
    //int nt = in.nextInt();    
    int nt = 1;
    //StringBuilder sb = new StringBuilder();
    
    
    for (int it = 0; it < nt; it++) 
    {
       int n = in.nextInt();
       
       int[] a = new int[n];
       int[] b = new int[n];
       long[] dpU = new long[n];
       long[] dpD = new long[n];
       long[] fU = new long[n];
       long[] fD= new long[n];
       
       long[] sumU = new long[n];
       long[] sumD = new long[n];
       
       for (int i = 0; i < n; i++)
       {
           a[i] = in.nextInt();
       }
       
       for (int i = 0; i < n; i++)
       {
           b[i] = in.nextInt();
       }
       
       sumU[n-1] = a[n-1];
       sumD[n-1] = b[n-1];
       for (int i = n-2; i >= 0; i--)
       {
           sumU[i] = sumU[i+1] + a[i];
           sumD[i] = sumD[i+1] + b[i];           
       }
       fU[n-1] = b[n-1];
       fD[n-1] = a[n-1];
       
       for (int i = n-2; i >= 0; i--)
       {
           long mul = 2L * n - 2 * i - 1;
           fU[i] = fU[i+1] + (i+2 < n ? sumU[i+2] : 0) + sumD[i+1] + a[i+1] + b[i] * mul;
           fD[i] = fD[i+1] + (i+2 < n ? sumD[i+2] : 0) + sumU[i+1] + b[i+1] + a[i] * mul;        
       }
       
       dpU[n-1] = b[n-1];
       dpD[n-1] = a[n-1];
       for (int i = n - 2; i >= 0; i--)
       {
           long val =  (sumU[i+1] + sumD[i+1]) * 2;
           dpU[i] = Math.max(fU[i], b[i] + val + dpD[i+1]); 
           dpD[i] = Math.max(fD[i], a[i] + val + dpU[i+1]); 
       }
       //StringBuilder sb = new StringBuilder();
       //for (int v : ans)sb.append(nums[v-1] + "\n");
       
       System.out.println(dpU[0]);
       //System.out.print(sb);
    }
    //System.out.print(sb);
  }
  
  private boolean nextToSome(int[][] b, int SOME,  int i, int j, int n, int m)
  {
      if (i == 0 || i == n - 1 || j == 0 || j == m - 1) return true;
      
      for (int[] dir : dirs)
      {
          int x = i + dir[0], y = j + dir[1];
          if (b[x][y] == SOME)
              return true;
      }
      return false;
  }
  
  private int query(int p)
  {
      int sum = 0;
      for (; p > 0; p -= (p & (-p)))
      {
          sum += bit[p];
      }
      return sum;
  }
  
  private void add(int p, int val)
  {
      //System.out.println("add to BIT " + p);
      for (; p <= n_bit; p += (p & (-p)))
      {
          bit[p] += val;
      }
  }
  
  
  
  private List<Integer> getMinFactor(int sum)
  {
      List<Integer>  factors = new ArrayList<>();
      
               for (int sz = 2; sz <= sum / sz; sz++){
                   if (sum % sz == 0) {
                       factors.add(sz);
                       factors.add(sum / sz);
                   }
               }
               if (factors.size() == 0)
                   factors.add(sum);
          
      return factors;
  }
  
  /* Tree class */
  class Tree {
      int V = 0;
      int root = 0;
      List<Integer>[] nbs;
      int[][] timeRange;
      int[] subTreeSize;
      int t;
      boolean dump = false;
      
      public Tree(int V, int root)
      {
          if (dump) 
              System.out.println("build tree with size = " + V + ", root = " + root); 
          
          this.V = V;          
          this.root = root;
          nbs = new List[V];
          subTreeSize = new int[V];
          for (int i = 0; i < V; i++)
              nbs[i] = new ArrayList<>();
          
              
      }
      
      public void doneInput()
      {
          dfsEuler();
      }
      
      public void addEdge(int p, int q)
      {
          nbs[p].add(q);
          nbs[q].add(p);
      }
      
      private void dfsEuler()
      {
          timeRange = new int[V][2];          
          t = 1;
          dfs(root);           
      }
      
      private void dfs(int node)
      {
          if (dump)
              System.out.println("dfs on node " + node + ", at time " + t);
          timeRange[node][0] = t;
          
          for (int next : nbs[node]) {
              if (timeRange[next][0] == 0)
              {
                  ++t;
                  dfs(next);                  
              }
          }
          timeRange[node][1] = t;
          subTreeSize[node] = t - timeRange[node][0] + 1;
      }
      
      public List<Integer> getNeighbors(int p) {
          return nbs[p];
      }
      
      public int[] getSubTreeSize(){
          return subTreeSize;
      }
      
      public int[][] getTimeRange()
      {
          if (dump){
              for (int i = 0; i < V; i++){
                  System.out.println(i + ": " + timeRange[i][0] + " - " + timeRange[i][1]);
              }
          }
          return timeRange;
      }
      
  }
  
  /* segment tree */
  class SegTree {
      long[] tree;
      long[] lazy;
      int n;
      boolean dump = false;
      
      public SegTree(int n)
      {
          if (dump)
              System.out.println("create segTree with size " + n);
          this.n = n;
          tree = new long[n*4];
          lazy = new long[n*4];
      }
      
      public SegTree(int n, int[] a) {
          this(n);
          buildTree(1, 0, n-1, a);
      }
      
      private void buildTree(int node, int lo, int hi, int[] a)
      {
          if (lo == hi) {
              tree[node] = a[lo];
              return;
          }
          
          int m = (lo + hi) / 2;
          buildTree(node * 2, lo, m, a);
          buildTree(node * 2 + 1, m + 1, hi, a);
          pushUp(node, lo, hi);
      }
      
      
      private void pushUp(int node, int lo, int hi)
      {
          if (lo >= hi) return;
          
          // add combine fcn
      }
      
      private void pushDown(int node, int lo, int hi)
      {
          if (lo > hi || lazy[node] == 0) return;
          
          tree[node] += lazy[node];
          tree[node] %= MOD;
          
          if (lo < hi) {              
              lazy[node * 2] += lazy[node];
              lazy[node * 2 + 1] += lazy[node];
              lazy[node * 2] %= MOD;
              lazy[node * 2 + 1] %= MOD;
          }
          
          lazy[node] = 0;
      }
      
      public void rangeUpdate(int fr, int to, long val)
      {
          if (dump)
              System.out.println("rangeUpdate : " + fr + " - " + to + " delta = " + val);
          rangeUpdate(1, 0, n-1, fr, to, val);
      }
      
      public long pointQuery(int p)
      {
          return pointQuery(1, 0, n-1, p);
      }
      
      
      private void rangeUpdate(int node, int lo, int hi, int fr, int to, long val)
      {
          if (dump)
              System.out.println("rangeUpdate : " + node + "[" + lo + " - " + hi + "]" + fr + " - " + to + " delta = " + val);
          
          pushDown(node, lo, hi);
          
          if (lo == fr && hi == to) {
              lazy[node] = val;              
              return;
          }
          
          int m = (lo + hi) / 2;
          if (to <=  m) 
              rangeUpdate(node * 2 , lo, m, fr, to, val);
          else if (fr > m)
              rangeUpdate(node * 2 + 1, m + 1, hi, fr, to, val);
          else {
              rangeUpdate(node * 2, lo, m, fr, m, val);
              rangeUpdate(node * 2 + 1, m + 1, hi, m + 1, to, val);
          }
          
          pushUp(node, lo, hi);          
      }
  
      /* pre-condition: lo <= p <= hi */
      private long pointQuery(int node, int lo, int hi, int p)
      {
          pushDown(node, lo, hi);
          
          if (lo == hi)
          {
              return tree[node];
          }
          
          int m = (lo + hi) / 2;
          if (p <= m) 
              return pointQuery(node * 2, lo, m, p);
          else
              return pointQuery(node * 2 + 1, m + 1, hi, p);
      }      
  
  }
  
  
  private long inv(long v)
  {
      return pow(v, MOD-2);
  }
  
  private long pow(long v, int p)
  {
      long ans = 1;
      while (p > 0)
      {
          if (p % 2 == 1)
              ans = ans * v % MOD;
          v = v * v % MOD;
          p = p / 2;
      }
      return ans;
  }
  
  private double dist(double x, double y, double xx, double yy)
  {
      return Math.sqrt((xx - x) * (xx - x) + (yy - y) * (yy - y));
  }
  

  
 
  private int mod_add(int a, int b) {
      int v = a + b;
      if (v >= MOD) v -= MOD;
      return v;
  }
  
  
  private long overlap(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {
      if (x1 > x3) return overlap(x3, y3, x4, y4, x1, y1, x2, y2);
      
      if (x3 > x2 || y4 < y1 || y3 > y2) return 0L;
      
      //(x3, ?, x2, ?)
      int yL = Math.max(y1, y3);
      int yH = Math.min(y2, y4); 
      int xH = Math.min(x2, x4);
      
      return f(x3, yL, xH, yH);
  }
  //return #black cells in rectangle
  private long f(int x1, int y1, int x2, int y2) {
      long dx = 1L + x2 - x1;
      long dy = 1L + y2 - y1;
      if (dx % 2 == 0 || dy % 2 == 0 || (x1 + y1) % 2 == 0) 
          return 1L * dx * dy / 2;
      return 1L * dx * dy / 2 + 1;
  }
  
  private int distM(int x, int y, int xx, int yy) {
      return abs(x - xx) + abs(y - yy);
  }
  
  private boolean less(int x, int y, int xx, int yy) {
      return x < xx || y > yy;
  }
  
  private int mul(int x, int y) {
      return (int)(1L * x * y % MOD);
  }
  
  
 
  
  private int nBit1(int v) {
      int v0 = v;
      int c = 0;
      while (v != 0) {
          ++c;
          v = v & (v - 1);
      }
      return c;
  }
  
  private long abs(long v) {
      return v > 0 ? v : -v;
  }
  
  private int abs(int v) {
      return v > 0 ? v : -v;
  }
  
  private int common(int v) {
      int c = 0;
      while (v != 1) {
          v = (v >>> 1);
          ++c;
      }
      
      return c;
  }
  
  private void reverse(char[] a, int i, int j) {
      while (i < j) {
          swap(a, i++, j--);
      }
  }
  
  private void swap(char[] a, int i, int j) {
      char t = a[i];
      a[i] = a[j];
      a[j] = t;
  }
  
  private int gcd(int x, int y) {
      if (y == 0) return x;
      return gcd(y, x % y);
  }
  private long gcd(long x, long y) {
      if (y == 0) return x;
      return gcd(y, x % y);
  }
  private int max(int a, int b) {
      return a >  b ? a : b;
  }
  
  private long max(long a, long b) {
      return a >  b ? a : b;
  }
  
  private int min(int a, int b) {
      return a >  b ? b : a;
  }
  
  private long min(long a, long b) {
      return a >  b ? b : a;
  }
  
  static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader(BufferedReader in)
        {            
            br = in;
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    String line = br.readLine();
                    if (line == null || line.length() == 0) return "";
                    st = new StringTokenizer(line);
                }
                catch (IOException  e)
                {
                    return "";
                    //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)
            {
                return null;
                //e.printStackTrace();
            }
            return str;
        }
    }
}