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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void rset();
void init_test();
void solve();
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed;
  cout.precision(20);
  init_test();
  return 0;
}
template <typename T>
void chmin(T& a, T b) {
  if (a > b) a = b;
}
template <typename T>
void chmax(T& a, T b) {
  if (a < b) a = b;
}
template <typename T>
void MACRO_rdv2_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_rdv2_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_rdv2_Init(n, rest...);
}
template <typename T>
void MACRO_rdv2_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_rdv2_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_rdv2_Scan(p, rest...);
}
template <typename T>
void wrv(const vector<T>& v) {
  for (int(__ii) = (0); (__ii) < (((int)v.size())); ++(__ii)) {
    if (__ii) cout << ' ';
    cout << v[__ii];
  }
  cout << '\n';
}
template <typename T>
void wrm(const vector<vector<T>>& v) {
  for (int(__ii) = (0); (__ii) < (((int)v.size())); ++(__ii)) {
    for (int(__jj) = (0); (__jj) < (v[__ii].size()); ++(__jj)) {
      if (__jj) cout << ' ';
      cout << v[__ii][__jj];
    }
    cout << '\n';
  }
}
template <typename T>
void sc(T& x) {
  cin >> x;
}
template <typename Head, typename... Tail>
void sc(Head& head, Tail&... tail) {
  cin >> head;
  sc(tail...);
}
template <typename T>
void wr(const T& x) {
  cout << x << '\n';
}
template <typename Head, typename... Tail>
void wr(const Head& head, const Tail&... tail) {
  cout << head << ' ';
  wr(tail...);
}
template <typename T>
void wrf(const T& x) {
  cout << x << endl;
}
template <typename Head, typename... Tail>
void wrf(const Head& head, const Tail&... tail) {
  cout << head << ' ';
  wrf(tail...);
}
template <typename T>
void debug_out(const T& x) {
  cerr << x << '\n';
}
template <typename Head, typename... Tail>
void debug_out(const Head& head, const Tail&... tail) {
  cerr << head << ' ';
  debug_out(tail...);
}
template <typename... T>
void err(const T&... cod) {
  wr(cod...);
  exit(0);
}
void solve() {
  long long n;
  sc(n);
  const int N = 1e6 + 10;
  vector<int> lst(N, 0);
  long double ans = 0;
  for (int(i) = (1); (i) < (n + 1); ++(i)) {
    long long x;
    sc(x);
    ans += ((i - lst[x]) * (n + 1 - i) * 2 - 1);
    lst[x] = i;
  }
  wr(ans / n / n);
}
void init_test() {
  int qq = 1;
  while (qq--) solve();
}