The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
A. Jeff and Rounding

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputJeff got 2*n* real numbers *a*_{1}, *a*_{2}, ..., *a*_{2n} as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes *n* operations, each of them goes as follows:

- choose indexes
*i*and*j*(*i*≠*j*) that haven't been chosen yet; - round element
*a*_{i}to the nearest integer that isn't more than*a*_{i}(assign to*a*_{i}: ⌊*a*_{i}⌋); - round element
*a*_{j}to the nearest integer that isn't less than*a*_{j}(assign to*a*_{j}: ⌈*a*_{j}⌉).

Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 2000). The next line contains 2*n* real numbers *a*_{1}, *a*_{2}, ..., *a*_{2n} (0 ≤ *a*_{i} ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.

Output

In a single line print a single real number — the required difference with exactly three digits after the decimal point.

Examples

Input

3

0.000 0.500 0.750 1.000 2.000 3.000

Output

0.250

Input

3

4469.000 6526.000 4864.000 9356.383 7490.000 995.896

Output

0.279

Note

In the first test case you need to perform the operations as follows: (*i* = 1, *j* = 4), (*i* = 2, *j* = 3), (*i* = 5, *j* = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/23/2022 11:08:24 (g2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|