Random Query
Description
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).
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.
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 
, where x is jury's answer, and y is your answer.
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 , where x is jury's answer, and y is your answer.
Samples
2
1 2
1.500000
2
2 2
1.000000