Problem: Monocarp has arranged n colored marbles in a row. The color of the i-th marble is a_i. Monocarp likes ordered things, so he wants to rearrange marbles in such a way that all marbles of the same color form a contiguos segment (and there is only one such segment for each color). 

In other words, Monocarp wants to rearrange marbles so that, for every color j, if the leftmost marble of color j is l-th in the row, and the rightmost marble of this color has position r in the row, then every marble from l to r has color j.

To achieve his goal, Monocarp can do the following operation any number of times: choose two neighbouring marbles, and swap them.

You have to calculate the minimum number of operations Monocarp has to perform to rearrange the marbles. Note that the order of segments of marbles having equal color does not matter, it is only required that, for every color, all the marbles of this color form exactly one contiguous segment.

Input

The first line contains one integer n (2 ≤ n ≤ 4 ⋅ 10^5) — the number of marbles.

The second line contains an integer sequence a_1, a_2, ..., a_n (1 ≤ a_i ≤ 20), where a_i is the color of the i-th marble.

Output

Print the minimum number of operations Monocarp has to perform to achieve his goal.

Examples

Input


7
3 4 2 3 4 2 2


Output


3


Input


5
20 1 14 10 2


Output


0


Input


13
5 5 4 4 3 5 7 6 5 4 4 6 5


Output


21

Note

In the first example three operations are enough. Firstly, Monocarp should swap the third and the fourth marbles, so the sequence of colors is [3, 4, 3, 2, 4, 2, 2]. Then Monocarp should swap the second and the third marbles, so the sequence is [3, 3, 4, 2, 4, 2, 2]. And finally, Monocarp should swap the fourth and the fifth marbles, so the sequence is [3, 3, 4, 4, 2, 2, 2]. 

In the second example there's no need to perform any operations.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakhar897
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        EMarbles solver = new EMarbles();
        solver.solve(1, in, out);
        out.close();
    }

    static class EMarbles {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int arr[] = in.nextIntArray(n);
            int i, j;

            long count[][] = new long[20][20];
            ArrayList<Integer> col[] = new ArrayList[20];
            long dp[] = new long[1 << 20 + 1];

            for (i = 0; i < 20; i++) {
                col[i] = new ArrayList<>();
            }

            for (i = 0; i < n; i++) {
                col[arr[i] - 1].add(i);
            }

            for (i = 0; i < 20; i++) {
                for (j = 0; j < 20; j++) {
                    if (i == j) continue;
                    if (col[i].size() == 0 || col[j].size() == 0)
                        continue;

                    int pos2 = 0;
                    for (int pos1 = 0; pos1 < col[i].size(); pos1++) {
                        while (true) {
                            if (pos2 == col[j].size() - 1 || col[j].get(pos2 + 1) > col[i].get(pos1)) {
                                break;
                            }
                            pos2++;
                        }
                        if (col[i].get(pos1) > col[j].get(pos2)) {
                            count[i][j] += pos2 + 1;
                        }
                    }
                }
            }

            for (i = 0; i < 1 << 20; i++)
                dp[i] = Long.MAX_VALUE - 2;
            dp[0] = 0;

        /*for(i=0;i<20;i++)
            out.println(count[i]);*/

            for (int mask = 0; mask < 1 << 20; mask++) {
                ArrayList<Integer> was = new ArrayList<>();
                for (i = 0; i < 20; i++) {
                    if ((mask & (1 << i)) != 0)
                        was.add(i);
                }

                for (i = 0; i < 20; i++) {
                    if ((mask & (1 << i)) != 0)
                        continue;
                    long sum = 0;
                    for (j = 0; j < was.size(); j++) {
                        sum += count[was.get(j)][i];
                    }
                    int nmask = mask | (1 << i);
                    dp[nmask] = Math.min(dp[nmask], dp[mask] + sum);
                }
            }

            // out.println(dp);

            out.println(dp[(int) (1 << 20) - 1]);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

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

        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 boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}