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, ... a_n (1 ≤ a_i ≤ 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 $\text{[math]}$ , where x is jury's answer, and y is your answer.

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