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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;


public class E {
	private static int n;
	private static int[] a;
	private static int[] b;
	private static String s;
	private static HashMap<Integer, ArrayList<Integer>> g;
	private static long pp, qq, rr;

	public static void main(String[] args) {
		n = ini();
		a = ina(n);
		b = ina(n);
		
		int[] d = new int[n];
		for(int i=0; i<n; i++) {
			d[i] = a[i];
		}
		
		int[] e = new int[n];
		for(int i=0; i<n; i++) {
			e[i] = b[i];
		}

		new MergeSort().sort(d, 0, n-1);
		new MergeSort().sort(e, 0, n-1);
		
		int[] c = new int[n];
		
		for(int i=0; i<n; i++) {
			c[i] = e[n-Arrays.binarySearch(d, a[i])-1];
		}
		
		long ans = 0;
		for(int i=0; i<n; i++) {
//			println(a[i]+" "+c[i]);
			ans += (n-i)*1L*(i+1)*a[i]*c[i];
		}

		println(ans%998244353);
		out.flush();
		out.close();

	}
	
	static class MergeSort 
	{ 
	    // Merges two subarrays of arr[]. 
	    // First subarray is arr[l..m] 
	    // Second subarray is arr[m+1..r] 
	    void merge(int arr[], int l, int m, int r) 
	    { 
	        // Find sizes of two subarrays to be merged 
	        int n1 = m - l + 1; 
	        int n2 = r - m; 
	  
	        /* Create temp arrays */
	        int L[] = new int [n1]; 
	        int R[] = new int [n2]; 
	  
	        /*Copy data to temp arrays*/
	        for (int i=0; i<n1; ++i) 
	            L[i] = arr[l + i]; 
	        for (int j=0; j<n2; ++j) 
	            R[j] = arr[m + 1+ j]; 
	  
	  
	        /* Merge the temp arrays */
	  
	        // Initial indexes of first and second subarrays 
	        int i = 0, j = 0; 
	  
	        // Initial index of merged subarry array 
	        int k = l; 
	        while (i < n1 && j < n2) 
	        { 
	            if (L[i] <= R[j]) 
	            { 
	                arr[k] = L[i]; 
	                i++; 
	            } 
	            else
	            { 
	                arr[k] = R[j]; 
	                j++; 
	            } 
	            k++; 
	        } 
	  
	        /* Copy remaining elements of L[] if any */
	        while (i < n1) 
	        { 
	            arr[k] = L[i]; 
	            i++; 
	            k++; 
	        } 
	  
	        /* Copy remaining elements of R[] if any */
	        while (j < n2) 
	        { 
	            arr[k] = R[j]; 
	            j++; 
	            k++; 
	        } 
	    } 
	  
	    // Main function that sorts arr[l..r] using 
	    // merge() 
	    void sort(int arr[], int l, int r) 
	    { 
	        if (l < r) 
	        { 
	            // Find the middle point 
	            int m = (l+r)/2; 
	  
	            // Sort first and second halves 
	            sort(arr, l, m); 
	            sort(arr , m+1, r); 
	  
	            // Merge the sorted halves 
	            merge(arr, l, m, r); 
	        } 
	    } 
	  
	   
	}

	//NONPROBLEM CODE

	private static InputReader in = new InputReader(System.in);
	private static PrintWriter out = new PrintWriter(System.out);

	private static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;

		public InputReader(InputStream st) {
			this.stream = st;
		}

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

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

		public String readString() {
			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 String nextLine() {
			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 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;
		}

	}

	//INPUT SHORTCUTS

	private static int[] ina(int n) {
		int[] temp = new int[n];
		for (int i = 0; i < n; i++) {
			temp[i] = in.nextInt();
		}
		return temp;
	}

	private static int ini() {
		return in.nextInt();
	}

	private static String ins() {
		return in.readString();
	}

	//OTHER SHORTCUTS
	public static void sort(int[] a) {
		Arrays.sort(a);
	}

	//PRINT SHORTCUTS

	private static void println(Object... o) {
		for (Object x : o) {
			out.write(x + " ");
		}
		out.write("\n");
	}

	private static void print(Object... o) {
		for (Object x : o) {
			out.write(x + "");
		}
	}

	private static void printAll(Object... o) {
		for (Object x : o) {
			out.write(x + " ");
		}
	}

	private static void debug(Object... o) {
		for (Object x : o) {
			out.write(x + " ");
		}
		out.write("\n");
		out.flush();
	}

	private static HashMap<Integer, ArrayList<Integer>> intree(int n) {

		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();
		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < n - 1; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
			g.get(v).add(u);
		}

		return g;
	}
}
