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 C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
#define FO(x) {freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);}
#define dbg(x) cerr<<#x" = "<<x<<endl
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define rep(i,a,b) for(register int i=(a),i##_end=(b);i<=i##_end;++i)
#define per(i,a,b) for(register int i=(a),i##_st=(b);i>=i##_st;--i)
#define For(i,a,b) for(register int i=(a),i##_end=(b);i<=i##_end;++i)
#define rpg(i,x) for(register int i=fir[x];i;i=e[i].nxt)
#define ull unsigned long long
#define fi first
#define se second
#define pb push_back
#define bin(i) (1<<i)
#define cls(x,y) memset(x,y,sizeof x)
typedef pair<int,int> PII;
typedef long long LL;
const int INF = 0x7fffffff;
/*const int _L = 1e6+5;
char ibuf[_L],*ih=ibuf+_L;
inline char gc(){return (ih==ibuf+_L?fread(ibuf,1,_L,stdin),ih=ibuf:0),*ih++;}
#define  getchar() gc() //*/
template <typename T> inline void rd(T &x) {
    x = 0; int f = 1; char CH = getchar();
    while(!isdigit(CH)) {if(CH=='-')f=0;CH=getchar();}
    while(isdigit(CH)) {x=((x+(x<<2))<<1)+(CH-48);CH=getchar();}
    x=(f==1)?x:-x;  return;
}
const int MXN = 1e5 + 5;
int n,a[MXN];
LL ans=1e19;
inline LL calc(int x) {
	LL tmp=0;
	rep(i,1,n) tmp+=abs(x-a[i]);
	return tmp; 
}
int main() {
#ifdef iloi
//	   freopen("test.in","r",stdin);
#endif
	rd(n);rep(i,1,n) rd(a[i]);
	rep(i,1,n) a[i]-=i;
	sort(a+1,a+1+n);
	int l=a[1],r=a[n];
	while(r-l>3) {
		int mid1=l+(r-l)/3,mid2=r-(r-l)/3;
		LL tmp1=calc(mid1),tmp2=calc(mid2);
		if(tmp2<tmp1) {
			r=mid2;
		} else {
			l=mid1;
		}
	}
	rep(i,l-1,r+1) {
		ans=min(ans,calc(i));
	}
	cout<<ans;
#ifdef iloi
	debug("\nMy Time: %.3lfms\n", (double)clock() / CLOCKS_PER_SEC);
#endif
}