The student council is preparing for the relay race at the sports festival.

The council consists of n members. They will run one after the other in the race, the speed of member i is s_i. The discrepancy d_i of the i-th stage is the difference between the maximum and the minimum running speed among the first i members who ran. Formally, if a_i denotes the speed of the i-th member who participated in the race, then d_i = max(a_1, a_2, ..., a_i) - min(a_1, a_2, ..., a_i).

You want to minimize the sum of the discrepancies d_1 + d_2 + ... + d_n. To do this, you are allowed to change the order in which the members run. What is the minimum possible sum that can be achieved?

Input

The first line contains a single integer n (1 ≤ n ≤ 2000) — the number of members of the student council.

The second line contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 10^9) – the running speeds of the members.

Output

Print a single integer — the minimum possible value of d_1 + d_2 + ... + d_n after choosing the order of the members.

Examples

Input


3
3 1 2


Output


3


Input


1
5


Output


0


Input


6
1 6 3 3 6 3


Output


11


Input


6
104 943872923 6589 889921234 1000000000 69


Output


2833800505

Note

In the first test case, we may choose to make the third member run first, followed by the first member, and finally the second. Thus a_1 = 2, a_2 = 3, and a_3 = 1. We have:

  * d_1 = max(2) - min(2) = 2 - 2 = 0. 
  * d_2 = max(2, 3) - min(2, 3) = 3 - 2 = 1. 
  * d_3 = max(2, 3, 1) - min(2, 3, 1) = 3 - 1 = 2. 



The resulting sum is d_1 + d_2 + d_3 = 0 + 1 + 2 = 3. It can be shown that it is impossible to achieve a smaller value.

In the second test case, the only possible rearrangement gives d_1 = 0, so the minimum possible result is 0.
import java.io.*;
import java.util.*;
import java.util.ArrayList;
import java.util.Arrays.*;
import java.util.Map.Entry;

import static java.util.Collections.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Solution {
    static final int SCAN_LINE_LENGTH = 1_000_002;
    private static final boolean thread = false;
    @SuppressWarnings("all")
    static final boolean HAS_TEST_CASES = (1 == 0) ? true : false;

    static int n, a[], e[][], vis[], m, b[];
    @SuppressWarnings("all")
    private static ArrayList<Integer> adj[], v = new ArrayList<>();
    static long gcd = 1;
    static HashMap<Integer, Integer> pos;

    @SuppressWarnings("unchecked")
    static void solve() throws Exception {
        n = ni();
        a = na(n);
        long ans = Long.MAX_VALUE;
        sort(a);
        long dp[][] = new long[n + 1][n + 1];
        for (int i = 0; i < dp.length; i++) {
            fill(dp[i], -1);
        }
        for (int i = 0; i < a.length; i++) {
            ans = min(ans, find(a, i, i, dp));
        }
        pn(ans);
    }

    private static long find(int[] a, int sr, int des, long[][] dp) {
        if (dp[sr][des] != -1)
            return dp[sr][des];
        int i = sr - 1;
        int j = des + 1;
        long ans = Long.MAX_VALUE;
        if (i > -1)
            ans = min(ans, find(a, i, des, dp) + (a[des] - a[i]));
        if (j < n)
            ans = min(ans, find(a, sr, j, dp) + (a[j] - a[sr]));
        return dp[sr][des] = (ans == Long.MAX_VALUE ? 0l : ans);
    }

    public static void main(final String[] args) throws Exception {
        if (!thread) {
            final int testcases = HAS_TEST_CASES ? ni() : 1;
            for (int i = 1; i <= testcases; i++) {
                // pni(i + " t");
                // out.print("Case #" + (i) + ": ");
                try {
                    solve();
                } catch (final Exception e) {
                    // pni("idk Exception");
                    // e.printStackTrace(System.err);
                    // System.exit(0);
                    throw e;
                }
            }
            out.flush();
        }
        r.close();
        out.close();
    }

    @SuppressWarnings("all")
    private static final int MOD = (int) (1e9 + 7), MOD_FFT = 998244353;
    private static final Reader r = new Reader();
    private static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    public static long[] enumPows(int a, int n, int mod) {
        a %= mod;
        long[] pows = new long[n + 1];
        pows[0] = 1;
        for (int i = 1; i <= n; i++)
            pows[i] = pows[i - 1] * a % mod;
        return pows;
    }

    @SuppressWarnings("all")
    private static boolean eq(long a, long b) {
        return Long.compare(a, b) == 0;
    }

    @SuppressWarnings("all")
    private static ArrayList<Integer> seive(int n) {
        ArrayList<Integer> p = new ArrayList<>();
        int[] f = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            if (f[i] == 1)
                continue;
            for (int j = i * i; j <= n && j < f.length; j += i) {
                f[j] = 1;
            }
        }
        for (int i = 2; i < f.length; i++) {
            if (f[i] == 0)
                p.add(i);
        }
        return p;
    }

    @SuppressWarnings("all")
    private static void s(int[] a) {
        Integer[] t = new Integer[a.length];
        for (int i = 0; i < t.length; i++) {
            t[i] = a[i];
        }
        sort(t);
        for (int i = 0; i < t.length; i++) {
            a[i] = t[i];
        }
    }

    int pow(int a, int b, int m) {
        int ans = 1;
        while (b != 0) {
            if ((b & 1) != 0)
                ans = (ans * a) % m;
            b /= 2;
            a = (a * a) % m;
        }
        return ans;
    }

    int modinv(int k) {
        return pow(k, MOD - 2, MOD);
    }

    @SuppressWarnings("all")
    private static void swap(final int i, final int j) {
        final int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    @SuppressWarnings("all")
    private static boolean isMulOverflow(final long A, final long B) {
        if (A == 0 || B == 0)
            return false;
        final long result = A * B;
        if (A == result / B)
            return true;
        return false;
    }

    @SuppressWarnings("all")
    private static int gcd(final int a, final int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    @SuppressWarnings("all")
    private static long gcd(final long a, final long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    @SuppressWarnings("all")
    private static class Pair<T, E> implements Comparable<Pair<T, E>> {
        T fir;
        E snd;

        Pair() {
        }

        Pair(final T x, final E y) {
            this.fir = x;
            this.snd = y;
        }

        // @Override
        // @SuppressWarnings("unchecked")
        // public int compareTo(final Pair<T, E> o) {
        // final int c = ((Comparable<T>) fir).compareTo(o.fir);
        // return c != 0 ? c : ((Comparable<E>) snd).compareTo(o.snd);
        // }
        @Override
        @SuppressWarnings("unchecked")
        public int compareTo(final Pair<T, E> o) {
            final int c = ((Comparable<T>) fir).compareTo(o.fir);
            return c;
        }

    }

    @SuppressWarnings("all")
    private static class pi implements Comparable<pi> {
        int fir, snd;

        pi() {
        }

        pi(final int a, final int b) {
            fir = a;
            snd = b;
        }

        public int compareTo(final pi o) {
            return fir == o.fir ? snd - o.snd : fir - o.fir;
        }

        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result + fir;
            result = prime * result + snd;
            return result;
        }

        @Override
        public boolean equals(Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            pi other = (pi) obj;
            if (fir != other.fir)
                return false;
            if (snd != other.snd)
                return false;
            return true;
        }

    }

    @SuppressWarnings("all")
    private static <T> void checkV(final Vector<T> adj[], final int i) {
        adj[i] = adj[i] == null ? new Vector<>() : adj[i];
    }

    private static <T> void checkV(final ArrayList<T> adj[], final int i) {
        adj[i] = adj[i] == null ? new ArrayList<>() : adj[i];
    }

    @SuppressWarnings("all")
    private static int[] na(final int n) throws Exception {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }

    @SuppressWarnings("all")
    private static int[] na1(final int n) throws Exception {
        final int[] a = new int[n + 1];
        for (int i = 1; i < a.length; i++) {
            a[i] = ni();
        }
        return a;
    }

    @SuppressWarnings("all")
    private static String n() throws IOException {
        return r.readToken();
    }

    @SuppressWarnings("all")
    private static char[] ns() throws IOException {
        return r.readToken().toCharArray();
    }

    @SuppressWarnings("all")
    private static String nln() throws IOException {
        return r.readLine();
    }

    private static int ni() throws IOException {
        return r.nextInt();
    }

    @SuppressWarnings("all")
    private static long nl() throws IOException {
        return r.nextLong();
    }

    @SuppressWarnings("all")
    private static double nd() throws IOException {
        return r.nextDouble();
    }

    @SuppressWarnings("all")
    private static void p(final Object o) {
        out.print(o);
    }

    @SuppressWarnings("all")
    private static void pn(final Object o) {
        out.println(o);
    }

    @SuppressWarnings("all")
    private static void pn() {
        out.println("");
    }

    @SuppressWarnings("all")
    private static void pi(final Object o) {
        out.print(o);
        out.flush();
    }

    @SuppressWarnings("all")
    private static void pni() {
        out.println("");
        out.flush();
    }

    private static void pni(final Object o) {
        out.println(o);
        out.flush();
    }

    private static class Reader {
        private final int BUFFER_SIZE = 1 << 17;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        // private StringTokenizer st;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        @SuppressWarnings("all")
        public Reader(final String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        final byte[] buf = new byte[SCAN_LINE_LENGTH];

        public String readLine() throws IOException {
            int cnt = 0;
            int c;
            o: while ((c = read()) != -1) {
                if (c == '\n')
                    if (cnt == 0)
                        continue o;
                    else
                        break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public String readToken() throws IOException {
            int cnt = 0;
            int c;
            o: while ((c = read()) != -1) {
                if (!(c >= 33 && c <= 126))
                    if (cnt == 0)
                        continue o;
                    else
                        break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            final boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            final boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            final boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    // static {
    // if (thread)
    // new Thread(null, new Runnable() {
    // @Override
    // public void run() {
    // try {
    // final int testcases = HAS_TEST_CASES ? ni() : 1;
    // for (int i = 1; i <= testcases; i++) {
    // // out.print("Case #" + (i + 1) + ": ");
    // try {
    // solve();
    // } catch (final ArrayIndexOutOfBoundsException e) {
    // e.printStackTrace(System.err);
    // System.exit(-1);
    // } catch (final Exception e) {
    // pni("idk Exception in solve");
    // e.printStackTrace(System.err);
    // System.exit(-1);
    // }
    // }
    // out.flush();
    // } catch (final Throwable t) {
    // t.printStackTrace(System.err);
    // System.exit(-1);
    // }
    // }
    // }, "rec", (1L << 28)).start();
    // }

    @SuppressWarnings({ "all", })
    private static <T> T deepCopy(final T old) {
        try {
            return (T) deepCopyObject(old);
        } catch (final IOException | ClassNotFoundException e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
        return null;
    }

    private static Object deepCopyObject(final Object oldObj) throws IOException, ClassNotFoundException {
        ObjectOutputStream oos = null;
        ObjectInputStream ois = null;
        try {
            final ByteArrayOutputStream bos = new ByteArrayOutputStream(); // A
            oos = new ObjectOutputStream(bos); // B
            // serialize and pass the object
            oos.writeObject(oldObj); // C
            oos.flush(); // D
            final ByteArrayInputStream bin = new ByteArrayInputStream(bos.toByteArray()); // E
            ois = new ObjectInputStream(bin); // F
            // return the new object
            return ois.readObject(); // G
        } catch (final ClassNotFoundException e) {
            pni("Exception in ObjectCloner = " + e);
            throw (e);
        } finally {
            oos.close();
            ois.close();
        }
    }

}