Building Permutation

题意翻译

给出 $n$ 个整数，通过尽量少的加 $1$ 或者减 $1$ 操作把原数列改造成只含 $1\sim n$（每个数字出现且仅出现一次）的数列。

题目描述

Permutation $ p $ is an ordered set of integers $ p_{1},p_{2},...,p_{n} $ , consisting of $ n $ distinct positive integers, each of them doesn't exceed $ n $ . We'll denote the $ i $ -th element of permutation $ p $ as $ p_{i} $ . We'll call number $ n $ the size or the length of permutation $ p_{1},p_{2},...,p_{n} $ . You have a sequence of integers $ a_{1},a_{2},...,a_{n} $ . In one move, you are allowed to decrease or increase any number by one. Count the minimum number of moves, needed to build a permutation from this sequence.

输入输出格式

输入格式

The first line contains integer $ n $ ( $ 1<=n<=3·10^{5} $ ) — the size of the sought permutation. The second line contains $ n $ integers $ a_{1},a_{2},...,a_{n} $ ( $ -10^{9}<=a_{i}<=10^{9} $ ).

输出格式

Print a single number — the minimum number of moves. Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

输入输出样例

输入样例 #1

2
3 0

输出样例 #1

2

输入样例 #2

3
-1 -1 2

输出样例 #2

6

说明

In the first sample you should decrease the first number by one and then increase the second number by one. The resulting permutation is $ (2,1) $ . In the second sample you need 6 moves to build permutation $ (1,3,2) $ .