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Examples

Example 1

Input

3

10 20 30

Output

1.833333

Explanation:

So all possible permutations are:

{10 20 30}

{10 30 20}

{20} {10 30}

{20 30} {10}

{30} {10 20}

{30 20} {10}

So here there are total 6 permutations, and total number of groups are 11.

So, output is 11/6 = 1.833333

Example 2

Input

4

56 78 13 92

Output

2.083333

Explanation:

So here there are total 24 permutations,

For example:

{56 78 13 92}

{92} {13 78 56}

{56} {13 92 78}

{78 92} {13 56}

.

.

So on and so forth. The total number of groups are 50.

So, the output is 50/24 = 2.083333