Độ lệch so với trung bình (Deviation from the Mean)

Source: Schaum's Outline of Programming with C

Version: Phuoc Hung OJ Extended

Problem

Given an integer array $a_0,a_1,\ldots,a_{n-1}$.

Its arithmetic mean is

For each index $i$, define the signed deviation from the mean as

Print $d_0,d_1,\ldots,d_{n-1}$, each with exactly 6 digits after the decimal point.

Input

The first line contains integer $n$. The second line contains exactly $n$ integers $a_0,a_1,\ldots,a_{n-1}$.

Output

Print the $n$ real values $d_0,d_1,\ldots,d_{n-1}$ on one line, separated by spaces, each with exactly 6 digits after the decimal point.

Subtask

Subtask 1 (100 points): $1\le n\le2\cdot10^5$; $|a_i|\le10^6$.

Example

Input

4
1 2 3 6

Output

-2.000000 -1.000000 0.000000 3.000000

Explanation

Here $\mu=(1+2+3+6)/4=3$, so the deviations are $-2,-1,0,3$.