Mean Absolute Deviation

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given integer observations $a_0,a_1,\ldots,a_{n-1}$, let

and define the mean absolute deviation

Print $D$ with exactly 6 digits after the decimal point.

Input

The first line contains $n$. The second line contains $n$ integers $a_i$.

Output

Print $D$ with exactly 6 digits after the decimal point.

Subtask

Subtask 1 (20 points): $1\le n\le10$, $|a_i|\le10^3$.

Subtask 2 (30 points): $1\le n\le5000$, $|a_i|\le10^6$.

Subtask 3 (50 points): $1\le n\le2\cdot10^5$, $|a_i|\le10^6$.

Example

Input

4
1 2 7 10

Output

3.500000

Explanation

The result follows directly from the mathematical definition above.