A8907. Building Permutation

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.

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

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.

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 $(1,3,2)$ .