Problem:
Score : 300 points

Problem Statement

Snuke has an integer sequence A of length N.

He will freely choose an integer b.
Here, he will get sad if A_i and b+i are far from each other.
More specifically, the sadness of Snuke is calculated as follows:

abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))

Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
    n,i:longint;
    ans:int64;
    a:array[0..200010] of longint;
procedure qsort(l,r:longint);
var
    i,j,mid,t:longint;
begin
    i:=l;j:=r;mid:=a[(i+j) div 2];
    repeat
        while a[i]<mid do inc(i);
        while a[j]>mid do dec(j);
        if i<=j then 
            begin
                t:=a[i];a[i]:=a[j];a[j]:=t;
                inc(i);dec(j);
            end;
    until i>j;
    if l<j then qsort(l,j);
    if i<r then qsort(i,r);
end;
begin
    readln(n);
    for i:=1 to n do
        begin
            read(a[i]);
            a[i]:=a[i]-i;
        end;
    qsort(1,n);
    for i:=1 to n do
        ans:=ans+abs(a[i]-a[n div 2+1]);
    writeln(ans);
end.