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,L,R,M,i,cnt:Longint;
	A:Array[1..200000]of Longint;
	ans:int64;
begin
	read(N);
	for i:=1 to N do begin
		read(A[i]);
		dec(A[i],i);
	end;
	L:=-1000000;
	R:=1000000000;
	while R-L>1 do begin
		M:=(L+R)div 2;
		cnt:=0;
		for i:=1 to N do if A[i]<=M then inc(cnt);
		if cnt*2>=N then R:=M else L:=M;
	end;
	for i:=1 to N do inc(ans,abs(A[i]-R));
	writeln(ans);
end.