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)

{$R-,S-,Q-,I-,O+}
var n,i,sad,l,r,m1,m2,temp1,temp2:int64;
    a:array[1..200000] of int64;

function f(b:int64):int64;
var i,ret:int64;
begin
  ret:=0;
  for i:=1 to n do inc(ret,abs(a[i]-b));
  f:=ret;
end;

function min(x,y:int64):int64;
begin
  if x>y then min:=y else min:=x;
end;

begin
  read(n);
  for i:=1 to n do begin read(a[i]);dec(a[i],i);end;
  r:=1000000000;
  l:=-1000000;
  sad:=min(f(l),f(r));
  while l<=r do begin
    m1:=(2*l+r) div 3;
    temp1:=f(m1);
    m2:=(l+2*r) div 3;
    temp2:=f(m2);
    if temp1 < temp2 then begin
      if sad>temp1 then sad:=temp1;
      r:=m2-1;
    end else begin
      if sad>temp2 then sad:=temp2;
      l:=m1+1;
    end;
  end;
  writeln(sad);
end.