Problem: You are given an array a consisting of n positive integers. You pick two integer numbers l and r from 1 to n, inclusive (numbers are picked randomly, equiprobably and independently). If l > r, then you swap values of l and r. You have to calculate the expected value of the number of unique elements in segment of the array from index l to index r, inclusive (1-indexed).

Input

The first line contains one integer number n (1 ≤ n ≤ 106). The second line contains n integer numbers a1, a2, ... an (1 ≤ ai ≤ 106) — elements of the array.

Output

Print one number — the expected number of unique elements in chosen segment. 

Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 4 — formally, the answer is correct if <image>, where x is jury's answer, and y is your answer.

Examples

Input

2
1 2


Output

1.500000


Input

2
2 2


Output

1.000000

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

	public static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32765);
			tokenizer = null;
		}

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(System.in), 32765);
			tokenizer = null;
		}

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

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

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

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

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

		public int[] nextIntArr(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextInt();
			}
			return arr;
		}

		public Integer[] nextIntegerArr(int n) {
			Integer[] arr = new Integer[n];
			for (int i = 0; i < n; i++) {
				arr[i] = new Integer(this.nextInt());
			}
			return arr;
		}

		public int[][] next2DIntArr(int n, int m) {
			int[][] arr = new int[n][m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					arr[i][j] = this.nextInt();
				}
			}
			return arr;
		}

		public int[] nextSortedIntArr(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextInt();
			}
			Arrays.sort(arr);
			return arr;
		}

		public long[] nextLongArr(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextLong();
			}
			return arr;
		}

		public long[] nextSortedLongArr(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextInt();
			}
			Arrays.sort(arr);
			return arr;
		}

		public char[] nextCharArr(int n) {
			char[] arr = new char[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextChar();
			}
			return arr;
		}
	}

	public static InputReader scn = new InputReader();
	public static PrintWriter out = new PrintWriter(System.out);

	public static void main(String[] args) {
		// InputStream inputStream = System.in; // Useful when taking input other than
		// console eg file handling // check ctor of inputReader
		// To print in file use this:- out = new PrintWriter("destination of file")
		// including extension");

		int n = scn.nextInt();
		int[] arr = new int[n + 1], help = new int[1000001], f = new int[n + 1];

		for (int i = 1; i <= n; i++) {
			arr[i] = scn.nextInt();
			f[i] = help[arr[i]];
			help[arr[i]] = i;
		}

		long count = 0;

		for (int i = 1; i <= n; i++) {
			long sub = 2 * (1L * i - f[i]) * (n - i + 1) - 1;
			count += sub;
		}

		double ans = n;
		ans *= ans;
		ans = count / ans;

		System.out.println(ans);
	}
}