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.util.*;
import java.io.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static int mod = 998244353;
	static long inf = (long) 1e18 + 1;
	static int[] col;
	static int n, m;
	static TreeSet<Integer>[] ad;
	static long[] memo,cnt[];
	static HashSet<Integer> h;
	static int[] pos, ones;
	static char[][] g;
	static boolean[][] vis;
	static boolean f;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		n = sc.nextInt();
		int[] a = new int[n];
		TreeSet<Integer> ts = new TreeSet<>();
		HashMap<Integer, Integer> hm = new HashMap<>();
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			ts.add(a[i]);
		}
		int id = 0;
		m = ts.size();
		while (!ts.isEmpty()) {
			hm.put(ts.pollFirst(), id++);
		}
		for (int i = 0; i < n; i++)
			a[i] = hm.get(a[i]);
		pos = new int[1 << m];
		ad = new TreeSet[m];
		for (int i = 0; i < m; i++)
			ad[i] = new TreeSet<>();
		for (int i = 0; i < n; i++)
			ad[a[i]].add(i);
		memo = new long[1 << m];
		cnt = new long[m][m];
		int []cnts=new int[20];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				if (j != a[i]) {	
					cnt[a[i]][j] += cnts[j];
				}
			}
			cnts[a[i]]++;
		}
		Arrays.fill(memo, -1);
		System.out.println(dp(0));
		out.flush();
	}

	static long dp(int mask) {
		if (mask == (1 << m) - 1)
			return 0;
		if (memo[mask] != -1)
			return memo[mask];
		long ans = Long.MAX_VALUE;
		for (int i = 0; i < m; i++) {
			if ((mask & (1 << i)) == 0) {
				long tem = 0;
				for (int k = 0; k < m; k++)
					if ((mask & (1 << k)) != 0)
						tem += cnt[k][i];
				ans = Math.min(ans, tem + dp(mask | (1 << i)));
			}
		}
		return memo[mask] = ans;
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}