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.*;
import java.lang.reflect.Array;
import java.util.*;

public class E_Marbles {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
    }

    private static class Solver {
        private void solve(InputReader inp, PrintWriter out) {
            int n = inp.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = inp.nextInt() - 1;

            int colors = 20;
            int maxMask = 1 << colors;
            // cost to get a color to the from
            long[] dpCost = new long[colors];
            int[] index = new int[colors];
            for (int i = 0; i < n; i++) {
                dpCost[a[i]] += i - index[a[i]];
                index[a[i]]++;
            }
            // mask -> cost
            long[] dpSet = new long[maxMask];
            Arrays.fill(dpSet, Long.MAX_VALUE / 2);
            dpSet[0] = 0;
            // for each color amount of other color after summed
            long[][] dpAfter = new long[colors][colors];
            long[][] cnt = new long[n][colors];
            cnt[0][a[0]] = 1;
            for (int i = 1; i < n; i++) {
                System.arraycopy(cnt[i - 1], 0, cnt[i], 0, colors);
                cnt[i][a[i]]++;
            }
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < colors; j++) {
                    dpAfter[a[i]][j] += cnt[n-1][j] - cnt[i][j];
                    // add values for color a[i]
                }
            }

//            System.out.println("cost: " + Arrays.toString(dpCost));
//            System.out.println("after:");
//            for (long[] i: dpAfter) System.out.println(Arrays.toString(i));

            for (int i = 1; i <= colors; i++) {
                // create mask of i colors taken
                int mask = 0;
                for (int j = 0; j < i; j++) mask |= (1 << j);

                while (mask < maxMask) {
                    //System.out.println("\nchecking mask: " + mask);
                    for (int color = 0; color < colors; color++) {
                        if ((mask & (1 << color)) == 0) continue;
                        //System.out.println("remove color: " + color);
                        // we remove color j from the dp
                        int newMask = mask ^ (1 << color);
                        //System.out.println("prev mask: " + mask + " cost: " + dpSet[newMask]);
                        long cost = dpSet[newMask] + dpCost[color];
                        for (int k = 0; k < colors; k++) {
                            if ((newMask & (1 << k)) != 0) {
                                cost -= dpAfter[k][color];
                            }
                        }
                        dpSet[mask] = Math.min(dpSet[mask], cost);
                    }

                    mask = nextNumberXBits(mask);
                }
            }

            out.println(dpSet[maxMask - 1]);
        }

        private static int nextNumberXBits(int mask) {
            int c = mask & -mask;
            int r = mask + c;
            return (((r ^ mask) >> 2) / c) | r;
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}