Jeff and Rounding

题意翻译

题意: 你有一个长度为2n的序列,将其中的n个数向下取整,n个数向上取整,求|原序列的和 - 取整后序列的和|的最小值. 输入格式: 第一行一个n. 第二行2n个三位小数x. 输出格式: |ans|的最小值(保留三位小数). 数据范围: x:[0,10000] n:[1,2000] 注意: None. 感谢@尘染梦 提供的翻译

题目描述

Jeff got $ 2n $ 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.

输入输出格式

输入格式

The first line contains integer $ n $ $ (1<=n<=2000) $ . The next line contains $ 2n $ 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.

输出格式

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

输入输出样例

输入样例 #1

3
0.000 0.500 0.750 1.000 2.000 3.000

输出样例 #1

0.250

输入样例 #2

3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896

输出样例 #2

0.279

说明

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 $ .