Compute the Variance of an Integer Sequence

Little Keke has recently learned the definition of variance. Given a sequence of integers of length \(n\), compute its variance defined as follows:

\[ \sigma = \frac{(a_1 - \overline{a})^2 + (a_2 - \overline{a})^2 + \cdots + (a_n - \overline{a})^2}{n} \]

where \(\overline{a}\) is the average of the sequence, i.e., \[ \overline{a} = \frac{a_1 + a_2 + \cdots + a_n}{n}. \]

It is guaranteed that all intermediate and final results are integers.

inputFormat

The first line contains a single integer \(n\) representing the number of elements in the sequence.

The second line contains \(n\) space-separated integers \(a_1, a_2, \ldots, a_n\), representing the elements of the sequence.

outputFormat

Output one integer representing the variance \(\sigma\) of the sequence.

sample

5
1 2 3 4 5

2