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 ≤ 10^6). The second line contains n integer numbers a_1, a_2, ... a_{n} (1 ≤ a_{i} ≤ 10^6) — 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 $\operatorname{min}(|x - y|, \frac{|x - y|}{x}) \leq 10^{-4}$, 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

Difficulty: interview

Starter code:

Solutions:
n=int(input())
a=list(map(int,input().split()))

lastocc=[0]*1000006
ans=[0]*n
ans[0]=1
lastocc[a[0]]=1

for i in range(1,n):
    ans[i]=ans[i-1]+(i+1-lastocc[a[i]])
    lastocc[a[i]]=i+1

print((2*sum(ans)-n)/(n*n))


n=int(input())
a=list(map(int,input().split()))

lastocc=[0]*1000006
ans=[0]*n
ans[0]=1
lastocc[a[0]]=1

for i in range(1,n):
    ans[i]=ans[i-1]+(i+1-lastocc[a[i]])
    lastocc[a[i]]=i+1

print((2*sum(ans)-n)/(n*n))


n = int(input())
arr = [0]
arr = arr + list(map(int, input().split(' ')))

def getCounts(arr):
    last = {}
    ans = 0.0
    prev = 0.0
    res = 0.0
    for i in range(1, len(arr)):
        if arr[i] not in last:
            ans = prev + i
        else:
            ans = prev + i - last[arr[i]]
        prev = ans
        res += ans
        last[arr[i]] = i
    return res

ans = (2 * getCounts(arr) - n)/(n*n)
print("%.6f" % ans)


# Accepted on Hacker blocks, giving RTE on test case 6 on Codeforces

lim = 10**7
last_occ = [ 0 for i in range(lim)]

n = int(input())
ans = [0 for i in range(n+1)]

arr = [int(i) for i in input().split()]
arr.insert(0,0 )
#print("arr",arr)

for i in range(1,n+1):
    ans[i] = ans[i-1] + (i-last_occ[arr[i]])
    last_occ[arr[i]] = i

#print("ans",ans)
total_sum = sum(ans)

ans = round((2*(total_sum-n)+n)/n**2,6)
#print(ans)
print(format(ans,'.6f'))