You are given two arrays a and b, both of length n.

Let's define a function f(l, r) = ∑_{l ≤ i ≤ r} a_i ⋅ b_i.

Your task is to reorder the elements (choose an arbitrary order of elements) of the array b to minimize the value of ∑_{1 ≤ l ≤ r ≤ n} f(l, r). Since the answer can be very large, you have to print it modulo 998244353. Note that you should minimize the answer but not its remainder.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a and b.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6), where a_i is the i-th element of a.

The third line of the input contains n integers b_1, b_2, ..., b_n (1 ≤ b_j ≤ 10^6), where b_j is the j-th element of b.

Output

Print one integer — the minimum possible value of ∑_{1 ≤ l ≤ r ≤ n} f(l, r) after rearranging elements of b, taken modulo 998244353. Note that you should minimize the answer but not its remainder.

Examples

Input


5
1 8 7 2 4
9 7 2 9 3


Output


646


Input


1
1000000
1000000


Output


757402647


Input


2
1 3
4 2


Output


20






import java.io.*;
import java.util.*;
import java.math.BigInteger; 
import java.lang.*;





public class Main {
    
    
    
    
   static class sort implements Comparator<int[]>
   {
        public int compare(int[] a,int[] b)
        {
            
            return -b[0]+a[0];
        }
   }
   static class sort1 implements Comparator<long[]>
   {
        public int compare(long[] a,long[] b)
        {
            
          long c = -(a[0]-a[1]) + (b[0]-b[1]);

          if(c==0l) return 0;
          if(c>0l) return 1;
          return -1;
        }
   }
   static class sort5 implements Comparator<long[]>
   {
        public int compare(long[] a,long[] b)
        {
            
           double d1,d2;
           d1 = (a[0]+0.00)/(a[1]+0.00);
           d2 = (b[0]+0.00)/(b[1]+0.00);
           //int v = Double.comapre(d2,d1);
           double eph = 0.000000000000001;
           double d = (d2-d1);
          // pr(d1+" "+d2);
           if(d>eph) return 1;
           else if(d<eph) return -1;
           if(a[1]>b[1]) return 1;
           else if(b[1]>a[1]) return -1;
           return 0;
        }
   }
   static class sort11 implements Comparator<double[]>
   {
        public int compare(double[] a,double[] b)
        {
            //if(a[0] == b[0]) return a[1]-b[1];
           if(a[1] < b[1]) return -1;
           else if(a[1] > b[1]) return 1;
           return 0;
        }
   }
   public static String[] F(BufferedReader bf) throws Exception
    {
        return (bf.readLine().split(" "));
    }
    
   public static void pr(PrintWriter out,Object o)
   {
      
    out.println(o.toString());//out.flush();
    
   }
   public static void prW(PrintWriter out,Object o)
   {
      
    out.print(o.toString());//out.flush();
    
   }
   public static int intIn(String st)
   {
      return Integer.parseInt(st);
   }
   
   
    
    public static void pr(Object o)
    {
        System.out.println(o.toString());
    }
    public static void prW(Object o)
    {
        System.out.print(o.toString());
    }
    
   
    public static int inInt(String s)
    {
        return Integer.parseInt(s);
    }
    public static long in(String s)
    {
        return Long.parseLong(s);
    }
 
 
    static int[] toIntArray(String[] m) 
    { 
        int[] p=new int[m.length];
        for(int o=0;o<m.length;o++)
        {
            p[o]= inInt(m[o]);
        }
        return p;
    }
    static double[] toDArray(String[] m) 
    { 
        double[] p=new double[m.length];
        for(int o=0;o<m.length;o++)
        {
            p[o]= Double.parseDouble(m[o]);
        }
        return p;
    }
    static long[] toLArray(String[] m) 
    { 
       long[] p=new long[m.length];
        for(int o=0;o<m.length;o++)
        {
            p[o]= in(m[o]);
        }
        return p;
    }
   
     static long gcd(long a, long b)
        {
          if (b == 0)
            return a;
          return gcd(b, a % b); 
        }
     
        static long pow(long x, long y, long p)
      {
        if(y == 0) return 1l;
        long res = 1; // Initialize result
     
        x = x % p; // Update x if it is more than or
        // equal to p
     
        if (x == 0)
          return 0l; // In case x is divisible by p;
     
        while (y > 0)
        {
     
          // If y is odd, multiply x with result
          if ((y & 1) != 0)
            res = (res * x) % p;
     
          // y must be even now
          y = y >> 1; // y = y/2
          x = (x * x) % p;
        }
        return res;
      }
    
   
    static int nCr(int n, int r, int p)
    {
        if (r > n - r)
            r = n - r;
 
        // The array C is going to store last
        // row of pascal triangle at the end.
        // And last entry of last row is nCr
        int C[] = new int[r + 1];
 
        C[0] = 1; // Top row of Pascal Triangle
 
        // One by constructs remaining rows of Pascal
        // Triangle from top to bottom
        for (int i = 1; i <= n; i++) {
 
            // Fill entries of current row using previous
            // row values
            for (int j = Math.min(i, r); j > 0; j--)
 
                // nCj = (n-1)Cj + (n-1)C(j-1);
                C[j] = (C[j] + C[j - 1]) % p;
        }
        return C[r];
    }
    // F(o,-1,tm,vis,par,o,mat);
   public static int log(int x)
   {
       boolean bol = true;

       if(((x-1)&x) == 0) bol=false;

       int c=0;
       while(x > 0)
       {
        x=(x/2);
        c++;
       }

       if(!bol) c--;
       return c;

   }

   
   static class sor implements Comparator<long[]>
   {
      public int compare(long[] a,long[] b)
      {
         if(a[0] == b[0])
         {
            if(a[1] < b[1]) return -1;
            return 1;
         }
         if(a[0] > b[0]) return 1;
         return -1;
      }
   }


    static long ncr(int n, int r)
    {
 
        // p holds the value of n*(n-1)*(n-2)...,
        // k holds the value of r*(r-1)...
        long p = 1, k = 1;
        if(n<r) return 0l;
 
        // C(n, r) == C(n, n-r),
        // choosing the smaller value
        if (n - r < r) {
            r = n - r;
        }
 
        if (r != 0) {
            while (r > 0) {
                p *= n;
                k *= r;
 
                // gcd of p, k
                long m = __gcd(p, k);
 
                // dividing by gcd, to simplify
                // product division by their gcd
                // saves from the overflow
                p /= m;
                k /= m;
 
                n--;
                r--;
            }
 
            // k should be simplified to 1
            // as C(n, r) is a natural number
            // (denominator should be 1 ) .
        }
        else {
            p = 1;
        }
 
        // if our approach is correct p = ans and k =1
        return p;
    }
 
    static long __gcd(long n1, long n2)
    {

        if(n1==0l) return n2;
        if(n2==0l) return n1;
        if(n1==1l || n2==1l) return 1l;
       // long gcd = 1;
        if(n1 == n2)  return n1;
        if(n1>n2) return __gcd(n1%n2,n2);
        return __gcd(n1,n2%n1);
        
    }
  
    public static void main (String[] args) throws Exception {
        
        BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);;;
        
        //int[] map=new int[1000001];
      
       int yy=1;//inInt(bf.readLine());
       


        
        for(int w=0;w<yy;w++)
        {
            // String str = bf.readLine();
          out.flush();
         
            String[] xlp = bf.readLine().split(" ");;;;;;
            //String st = bf.readLine();
        int n;//boolean bol=false;
           int m;//long a,b,c;
           int ioo;
          // int  k;//pr(out,"vbc");
         n=inInt(xlp[0]);//m=inInt(xlp[1]);//int ta=inInt(xlp[2]);int tb=inInt(xlp[3]);k=inInt(xlp[4]);
       //  k=inInt(xlp[2]);

         long[] a= toLArray(F(bf));
         long[] b = toLArray(F(bf));

        PriorityQueue<Long> pq=new PriorityQueue<>();
        for(long lx : b) pq.add((-1l*lx));

        int i,j;i=j=0;j=n-1;
        
        long sum=0l;
        long mod = 998244353l;
        long s1,s2;
        s1=1l;s2=n+0l;
        for( i=0;i<n;i++)
        {
            long mul = ((s1)*(s2));
            a[i] = (a[i]*mul);s1++;s2--;
        }
        Arrays.sort(a);
        j=n-1;i=0;
        while(i<n)
        {
            long val = (pq.remove()*-1l);
            sum = ((sum%mod) + ((a[i]%mod)*(val%mod))%mod)%mod;
            i++;j--;
        }
        

        pr(out,(sum%mod));



          
          




      

         
         
         



         
         
   }
    out.close();
   bf.close();
}}


/*
5 10 20 10 3
7 9 18 19 20
3 6 7 8 9 10 14 15 16 17


Kickstart
 String rp;
            rp = "Case #"+(w+1)+": "+(n-ans)+" ";
static int[][] dir={{0,1},{1,0},{-1,0},{0,-1}};

static class SegmentTreeRMQ 
    { 
    int st[]; 
    int minVal(int x, int y) { 
        return (x > y) ? x : y; 
    } 
  
    
    int getMid(int s, int e) { 
        return s + (e - s) / 2; 
    } 
  
    
    int RMQUtil(int ss, int se, int qs, int qe, int index) 
    { 
        
        if (qs <= ss && qe >= se) 
            return st[index]; 
  
        // If segment of this node is outside the given range 
        if (se < qs || ss > qe) 
            return Integer.MIN_VALUE; 
  
        // If a part of this segment overlaps with the given range 
        int mid = getMid(ss, se); 
        return minVal(RMQUtil(ss, mid, qs, qe, 2 * index + 1), 
                RMQUtil(mid + 1, se, qs, qe, 2 * index + 2)); 
    } 
  
    // Return minimum of elements in range from index qs (query 
    // start) to qe (query end).  It mainly uses RMQUtil() 
    int RMQ(int n, int qs, int qe) 
    { 
        // Check for erroneous input values 
        
  
        return RMQUtil(0, n - 1, qs, qe, 0); 
    } 
  
    // A recursive function that constructs Segment Tree for 
    // array[ss..se]. si is index of current node in segment tree st 
    int constructSTUtil(int arr[], int ss, int se, int si) 
    { 
        // If there is one element in array, store it in current 
        //  node of segment tree and return 
        if (ss == se) { 
            st[si] = arr[ss]; 
            return arr[ss]; 
        } 
  
        // If there are more than one elements, then recur for left and 
        // right subtrees and store the minimum of two values in this node 
        int mid = getMid(ss, se); 
        st[si] = minVal(constructSTUtil(arr, ss, mid, si * 2 + 1), 
                constructSTUtil(arr, mid + 1, se, si * 2 + 2)); 
        return st[si]; 
    } 
  
    
    void con(int arr[]) 
    { 
        // Allocate memory for segment tree 
  
        //Height of segment tree 
        int n = (arr.length);
        int x = (int) (Math.ceil(Math.log(n) / Math.log(2))); 
  
        //Maximum size of segment tree 
        int max_size = 2 * (int) Math.pow(2, x) - 1; 
        st = new int[max_size]; // allocate memory 
  
        // Fill the allocated memory st 
        constructSTUtil(arr, 0, n - 1, 0); 
    }
    }
     static class DSU {
    
    int[] p;int[] sz;int op;int c;;
    int[] last;
    public void G(int n)
    {
        last=new int[n];
        p=new int[n];
        sz=new int[n];c=n;
        op=n;
        for(int h=0;h<n;h++)
        {
            sz[h]=1;p[h]=h;
            last[h]=h;
        }
    }
    public int find(int x)
    {
        int y=x;
        while(x!=p[x]) x=p[x];
        while(y!=p[y])
        {
            int tem=p[y];
            p[y]=x;y=tem;
        }
        return p[y];
    }
    public void union(int a,int b)
    {
        int x,y;
        x=find(a);y=find(b);
        if(x==y) return;
        if(sz[x]>sz[y])
        {
            p[y] = x;
            sz[x]+=sz[y];
            last[x]=Math.max(last[x],last[y]);
        }
        else
        {
            p[x]=y;sz[y]+=sz[x];
            last[y]=Math.max(last[y],last[x]);
        }
        c--;
        
    }}

    static long pow(long x, long y, long p)
      {
        long res = 1; // Initialize result
     
        x = x % p; // Update x if it is more than or
        // equal to p
     
        if (x == 0)
          return 0l; // In case x is divisible by p;
     
        while (y > 0)
        {
     
          // If y is odd, multiply x with result
          if ((y & 1) != 0)
            res = (res * x) % p;
     
          // y must be even now
          y = y >> 1; // y = y/2
          x = (x * x) % p;
        }
        return res;
      }
      static long gcd(long a, long b)
        {
          if (b == 0)
            return a;
          return gcd(b, a % b); 
        }
        static int gcd(int a, int b,int o)
        {
          if (b == 0)
            return a;
          return gcd(b, a % b,o); 
        }

Geometric median

public static double F(double[] x,double[] w)
    {
        double d1,d2;
        double S=0.00;
        for(double dp : w) S += dp;
        int k = 0;
        double sum = S - w[0]; // sum is the total weight of all `x[i] > x[k]`

        while(sum > S/2)
        {
            ++k;
            sum -= w[k];
        }
        d1=x[k];
        return d1;
        k = w.length-1;
       sum = S - w[k]; // sum is the total weight of all `x[i] > x[k]`

        while(sum > S/2)
        {
            --k;
            sum -= w[k];
        }
        d2=x[k];
        return new double[]{d1,d2};
    }
*/



























