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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cunbidun
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ETwoArraysAndSumOfFunctions solver = new ETwoArraysAndSumOfFunctions();
        solver.solve(1, in, out);
        out.close();
    }

    static class ETwoArraysAndSumOfFunctions {
        private static final int MOD = 998244353;
        private InputReader in;
        private PrintWriter out;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.in = in;
            this.out = out;
            int n = in.nextInt();
            long[] a = in.nextLongArray(n, 1);
            long[] b = in.nextLongArray(n, 1);
            MergeSort.sort(b, 1, n, Comparator.reverseOrder());
            for (int i = 1; i <= n; i++) {
                a[i] = a[i] * i * (n - i + 1);
            }
            MergeSort.sort(a, 1, n);
            int ans = 0;
            for (int i = 1; i <= n; i++) {
                int tmp = (int) (((a[i] % MOD) * b[i]) % MOD);
                ans = Op.addMod(ans, tmp, MOD);
            }
            out.println(ans);
        }

    }

    static class Op {
        public static int addMod(int x, int y, int MOD) {
            return ((x + y) >= MOD ? x + y - MOD : x + y);
        }

    }

    static class MergeSort {
        private static final int CUTOFF = 7;

        private MergeSort() {
        }

        private static void merge(Comparable[] src, Comparable[] dst, int lo, int mid, int hi) {
            int i = lo, j = mid + 1;
            for (int k = lo; k <= hi; k++) {
                if (i > mid) dst[k] = src[j++];
                else if (j > hi) dst[k] = src[i++];
                else if (less(src[j], src[i])) dst[k] = src[j++];   //
                else dst[k] = src[i++];
            }
        }

        private static void sort(Comparable[] src, Comparable[] dst, int lo, int hi) {
            if (hi <= lo + CUTOFF) {
                insertionSort(dst, lo, hi);
                return;
            }
            int mid = lo + (hi - lo) / 2;
            sort(dst, src, lo, mid);
            sort(dst, src, mid + 1, hi);
            if (!less(src[mid + 1], src[mid])) {
                System.arraycopy(src, lo, dst, lo, hi - lo + 1);
                return;
            }

            merge(src, dst, lo, mid, hi);
        }

        private static void insertionSort(Comparable[] a, int lo, int hi) {
            for (int i = lo; i <= hi; i++)
                for (int j = i; j > lo && less(a[j], a[j - 1]); j--)
                    swap(a, j, j - 1);
        }

        private static void swap(Object[] a, int i, int j) {
            Object swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }

        private static boolean less(Comparable a, Comparable b) {
            return a.compareTo(b) < 0;
        }

        private static boolean less(Object a, Object b, Comparator comparator) {
            return comparator.compare(a, b) < 0;
        }

        private static void merge(Object[] src, Object[] dst, int lo, int mid, int hi, Comparator comparator) {
            int i = lo, j = mid + 1;
            for (int k = lo; k <= hi; k++) {
                if (i > mid) dst[k] = src[j++];
                else if (j > hi) dst[k] = src[i++];
                else if (less(src[j], src[i], comparator)) dst[k] = src[j++];
                else dst[k] = src[i++];
            }
        }

        private static void sort(Object[] src, Object[] dst, int lo, int hi, Comparator comparator) {
            if (hi <= lo + CUTOFF) {
                insertionSort(dst, lo, hi, comparator);
                return;
            }
            int mid = lo + (hi - lo) / 2;
            sort(dst, src, lo, mid, comparator);
            sort(dst, src, mid + 1, hi, comparator);
            if (!less(src[mid + 1], src[mid], comparator)) {
                System.arraycopy(src, lo, dst, lo, hi - lo + 1);
                return;
            }

            merge(src, dst, lo, mid, hi, comparator);
        }

        private static void insertionSort(Object[] a, int lo, int hi, Comparator comparator) {
            for (int i = lo; i <= hi; i++)
                for (int j = i; j > lo && less(a[j], a[j - 1], comparator); j--)
                    swap(a, j, j - 1);
        }

        public static void sort(Comparable[] a, int lo, int hi) {
            Comparable[] aux = a.clone();
            sort(aux, a, lo, hi);
        }

        public static long[] sort(long[] input, int lo, int hi) {
            Long[] a = new Long[input.length];
            for (int ctr = 0; ctr < input.length; ctr++) a[ctr] = input[ctr];
            sort(a, lo, hi);
            for (int ctr = 0; ctr < a.length; ctr++) input[ctr] = a[ctr];
            return input;
        }

        public static void sort(Object[] a, int lo, int hi, Comparator comparator) {
            Object[] aux = a.clone();
            sort(aux, a, lo, hi, comparator);
        }

        public static long[] sort(long[] input, int lo, int hi, Comparator comparator) {
            Long[] a = new Long[input.length];
            for (int ctr = 0; ctr < input.length; ctr++) a[ctr] = input[ctr];
            sort(a, lo, hi, comparator);
            for (int ctr = 0; ctr < a.length; ctr++) input[ctr] = a[ctr];
            return input;
        }

    }

    static class InputReader extends InputStream {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 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 {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                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 {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long[] nextLongArray(int length, int stIndex) {
            long[] arr = new long[length + stIndex];
            for (int i = stIndex; i < stIndex + length; i++)
                arr[i] = nextLong();
            return arr;
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}

