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.util.Queue;
import java.util.LinkedList;
import java.util.Stack;

public class Main
{
    @SuppressWarnings("unchecked")
   
      public static void main(String args[])throws IOException
    {
        Reader ob=new Reader();
        Writer out=new Writer(System.out);
        Random oo=new Random();
        int n=ob.nI();
        long a[]=ob.NLA(n);
        long b[]=ob.NLA(n),k=1;
        for(int i=0;i<n;i++)
        a[i]*=(k*(n-k++ +1));
        RA(a);
        Arrays.sort(a);
        long m=998244353;
        long sum=0;
        RA(b);
        Arrays.sort(b);
        for(int i=0;i<n;i++)
        sum+=(((a[i]%m)*b[n-1-i])%m);
        out.pln(sum%m);
        out.flush();
}
 public static int[] RA(int [] array){
		Random rgen = new Random();  // Random number generator			
 
		for (int i=0; i<array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
 
		return array;
	}
	
 public static long[] RA(long [] array){
		Random rgen = new Random();  // Random number generator			
 
		for (int i=0; i<array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
 
		return array;
	}
static long inverse(long x, long p)
    {
        return pow(x, p - 2, p);
    }
static boolean isPrime(long n)
{
    long h=(long)Math.sqrt(n);
    for(long i=2;i<=h;i++)
    if(n%i==0)
    return false;
    return true&&n!=1;
}
    static long gcd(long a,long b)
    {
        if(a<b)
        return gcd(b,a);
        else if(b==0)
        return a;
        else
        return gcd(b,a%b);
    }
    static long pow(long a,long b,long mod){
		if(b == 0)	return 1;
		long t = pow(a,b>>1,mod);
		t = (t * t) % mod;
		if((b & 1) == 1)	t = (t * a);
		if(t >= mod)	t %= mod;
		return t;
}
    static long pow(long a,long b){
		if(b == 0)	return 1;
		long t = pow(a,b>>1);
		t = (t * t);
		if((b & 1) == 1)	t = (t * a);
		return t;
}
    static void seive(int n,int prime[])//1 for prime -1 for not prime
    {
        for(int i=2;i<=n;i++)
            if(prime[i]==0)
            {
                prime[i]=1;
                for(int j=2;j*i<=n;j++)
                prime[j*i]=-1;
            }
    }
    static int max(int ...a)
    {
        int m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.max(m,a[i]);
        return m;
        
    }
    static long max(long ...a)
    {
        long m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.max(m,a[i]);
        return m;
    }
    static int min(int ...a)
    {
        int m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.min(m,a[i]);
        return m;
    }
    static long min(long ...a)
    {
        long m=a[0];
        for(int i=0;i<a.length;i++)
        m=Math.min(m,a[i]);
        return m;
    }
    static class Pair<T1,T2>
    {
        T1 x;T2 y;
        Pair(T1 xx,T2 yy)
        {
            x=xx;
            y=yy;
        }
    }
    
	static class Writer {
		private final PrintWriter p;
		Writer(OutputStream o) {
			p = new PrintWriter(new BufferedWriter(new OutputStreamWriter(o)));
		}
		void p(Object... o1) {
			for (Object o11 : o1) {
				p.print(o11 + "" );
			}
		}
		void p(String s) {
			p.print(s);
		}
		void pln(Object... o1) {
			p(o1);
			p.println();
		}
		void flush() {
			p.flush();
		}
		void close() {
			p.close();
		}
	}
    static class Reader {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;
		int flag=0;
		FileReader file;
		Reader()
		{
		  }
		  Reader(String x)throws IOException
		  {
		      flag=1;
		      file=new FileReader(x);
		  }
		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nl() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
		public String n() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		public long nL() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nI() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int[] NIA(int n) //nextINtArray
		{
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nI();
			}
			return arr;
		}
		public int[] NIA1(int n) //nextINtArray
		{
			int[] arr = new int[n+1];
			for (int i = 1; i <=n; i++) {
				arr[i] = nI();
			}
			return arr;
		}
		
		public long[] NLA(int n) //nextLongArray
		{
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nL();
			}
			return arr;
}
		public long[] NLA1(int n) //nextLongArray
		{
			long[] arr = new long[n+1];
			for (int i = 1; i <=n; i++) {
				arr[i] = nL();
			}
			return arr;
}
		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
static class DSU
{
    int a[],size[],c=1;
    HashMap<String,Integer> hm=new HashMap<String,Integer>();
    DSU(int n)
    {
        a=new int[n+1];
        size=new int[n+1];
        for(int i=1;i<=n;i++)
    {
        a[i]=i;
        size[i]=1;
    }
    }
    void add(String x,int i)
    {
        hm.put(x,i);
    }
    int find(int n)
    {
        while(a[n]!=n)
        {
            a[n]=a[a[n]];
        n=a[n];
    }
        return n;
    }
    void union(int a1,int b)
    {
        int x=find(a1);
        int y=find(b);
        if(size[x]>size[y])
    {
        a[y]=x;
        size[x]+=size[y];
    }
    else
    {
       a[x]=y;
       size[y]+=size[x];
    }
}
        //System.out.println(Arrays.toString(a));
     int query(String x,String y)
     {
         int p=-1,q=-1;
         if(hm.containsKey(x))
         p=hm.get(x);
         else
         {
             p=c;
         hm.put(x,c++);
         
        }
         if(hm.containsKey(y))
         q=hm.get(y);
         else
         {
             q=c;
         hm.put(y,c++);
        }
        int m=find(p),n=find(q);
        if(m!=n)
        {
        union(m,n);
            return 2;
        }
        else
        return 1;
}
}
class Segment
{
    int sum[];
    void build(int a[],int v,int l,int r)
    {
        if(l==r)
        sum[v]=a[l];
        else
        {
            int m=(l+r)/2;
            build(a,v*2,l,m);
            build(a,2*v+1,m+1,r);
            sum[v]=sum[v*2]+sum[2*v+1];
        }
    }
    void update(int a[],int l,int r,int x,int v,int y)
    {
        if(l==r&&r==y)
            sum[v]+=x;
        else if(l>y||y>r)
        return;
        else
        {
            int m=(l+r)/2;
            update(a,l,m,x,2*v,y);
            update(a,m+1,r,x,2*v+1,y);
            sum[v]=sum[2*v]+sum[2*v+1];
        }
    }
    int query(int v,int l,int r,int x,int y)
    {
        if(x>r||y<l)
        return 0;
        else if(x<=l&&r<=y)
        return sum[v];
        else
        {
            int m=(l+r)/2;
        return query(2*v,l,m,x,y)+query(2*v+1,m+1,r,x,y);  
    }
}
}

static class Trie
  {
      Trie child[]=new Trie[26];
      int count=0;
    }
   /* void insert(String a)
    {
        Trie tmp=root;
        for(int i=0;i<a.length();i++)
        {
            int v=a.charAt(i)-'a';
            if(tmp.child[v]==null)
            {
                tmp.child[v]=new Trie();
                
            }
                tmp=tmp.child[v];
            }
            if(tmp.count==0)
            r++;
            tmp.count=1;
        }*/
    }
    