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.DataInputStream;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;

public class C {

    private static void run() throws IOException {
        int n = in.nextInt();
        Integer[] i_a = new Integer[n];
        for (int i = 0; i < n; i++) {
            i_a[i] = new Integer(in.nextInt());
        }
        Arrays.sort(i_a);
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = i_a[i];
        }

        long ans = Long.MAX_VALUE;
        long[][] dp = new long[n + 1][n];
        for (int i = 2; i <= n; i++) {
            for (int j = 0; j < n; j++) {
                dp[i][j] = Long.MAX_VALUE;
            }
        }
        for (int i = 2; i <= n; i++) {
            for (int j = 0; j < n; j++) {
                int current_right_pos = j + i - 1;
                if (current_right_pos >= n) continue;

                long right_is_new = dp[i - 1][j] + a[current_right_pos] - a[j];
                long left_is_new = dp[i - 1][j + 1] + a[current_right_pos] - a[j];
                dp[i][j] = Math.min(right_is_new, left_is_new);
            }
        }

        for (int i = 0; i < n; i++) ans = Math.min(ans, dp[n][i]);
        out.println(ans);
    }

    public static void main(String[] args) throws IOException {
        in = new Reader();
        out = new PrintWriter(new OutputStreamWriter(System.out));

//        int t = in.nextInt();
//        for (int i = 0; i < t; i++) {
//        }
        run();

        out.flush();
        in.close();
        out.close();
    }

    private static int gcd(int a, int b) {
        if (a == 0 || b == 0)
            return 0;
        while (b != 0) {
            int tmp;
            tmp = a % b;
            a = b;
            b = tmp;
        }
        return a;
    }

    static final long mod = 1000000007;

    static long pow_mod(long a, long b) {
        long result = 1;
        while (b != 0) {
            if ((b & 1) != 0) result = (result * a) % mod;
            a = (a * a) % mod;
            b >>= 1;
        }
        return result;
    }

    private static long multiplied_mod(long... longs) {
        long ans = 1;
        for (long now : longs) {
            ans = (ans * now) % mod;
        }
        return ans;
    }

    @SuppressWarnings("FieldCanBeLocal")
    private static Reader in;
    private static PrintWriter out;

    private static void print_array(int[] array) {
        for (int now : array) {
            out.print(now);
            out.print(' ');
        }
        out.println();
    }

    private static void print_array(long[] array) {
        for (long now : array) {
            out.print(now);
            out.print(' ');
        }
        out.println();
    }

    static class Reader {
        private static final int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

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

        public String readLine() throws IOException {
            final byte[] buf = new byte[1024]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    break;
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextSign() throws IOException {
            byte c = read();
            while ('+' != c && '-' != c) {
                c = read();
            }
            return '+' == c ? 0 : 1;
        }

        private static boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        public int skip() throws IOException {
            int b;
            // noinspection ALL
            while ((b = read()) != -1 && isSpaceChar(b)) {
                ;
            }
            return b;
        }

        public char nc() throws IOException {
            return (char) skip();
        }

        public String next() throws IOException {
            int b = skip();
            final StringBuilder sb = new StringBuilder();
            while (!isSpaceChar(b)) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = read();
            }
            return sb.toString();
        }

        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 {
            din.close();
        }

    }
}