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;
const int maxn = (int)(1e6) + 2;
const int mod = (int)(1e9) + 7;
int a[maxn];
long long tsum[4 * maxn], n, add[4 * maxn];
int last[maxn];
void push(int v, int tl, int tr) {
  if (add[v]) {
    int tm = (tl + tr) >> 1;
    tsum[v + v] += (tm - tl + 1) * add[v];
    tsum[v + v + 1] += (tr - tm) * add[v];
    add[v + v] += add[v];
    add[v + v + 1] += add[v];
    add[v] = 0;
  }
}
void upd(int v, int tl, int tr, int l, int r, int x) {
  if (l > r || tl > r || l > tr) return;
  if (l <= tl && tr <= r) {
    tsum[v] += (tr - tl + 1) * 1ll * x;
    add[v] += x;
    return;
  }
  push(v, tl, tr);
  int tm = (tl + tr) >> 1;
  upd(v + v, tl, tm, l, r, x);
  upd(v + v + 1, tm + 1, tr, l, r, x);
  tsum[v] = tsum[v + v] + tsum[v + v + 1];
}
long long getsum(int v, int tl, int tr, int l, int r) {
  if (l > r || tl > r || l > tr) return 0;
  if (l <= tl && tr <= r) return tsum[v];
  push(v, tl, tr);
  int tm = (tl + tr) >> 1;
  return getsum(v + v, tl, tm, l, r) + getsum(v + v + 1, tm + 1, tr, l, r);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  long long res = 0;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    upd(1, 1, n, 1, i, 1);
    if (last[a[i]]) upd(1, 1, n, 1, last[a[i]], -1);
    last[a[i]] = i;
    res += 2 * getsum(1, 1, n, 1, i - 1) + 1;
  }
  long long cur = n * (n - 1) + n;
  printf("%.7f", res * 1.0 / cur);
  return 0;
}