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 (GCC 5.4.1) (judge verdict: Accepted)

//c.c C-Linear Approximation
#include<stdio.h>
#include<stdlib.h>
typedef long long lld;


int cmp(const void *a,const void *b){
    if(*(lld*)a<*(lld*)b){
        return -1;
    }else{
        return 1;
    }
    return 0;
}
lld iabs(lld x){
    if(x<0){
        return -x;
    }
    return x;
}

int main(void){
    int n;
    scanf("%d",&n);
    lld a[n];
    for(int i=0;i<n;++i){
        scanf("%lld",&a[i]);
    }

    lld b[n];
    for(lld i=0;i<n;++i){
        b[i] = a[i] - i - 1;
    }

    qsort(b,n,sizeof(lld),cmp);

    lld ansnum1,ansnum2,ansnum,ans1=0,ans2=0,ans=0;
    if(n%2!=0){
        ansnum = n/2;
        for(int i=0;i<n;++i){
            ans += iabs(a[i]-b[ansnum]-(i+1));
        }
    }else{
        ansnum1 = n/2 - 1;
        ansnum2 = n/2;
        for(int i=0;i<n;++i){
            ans1 += iabs(a[i]-b[ansnum1]-(i+1));
            ans2 += iabs(a[i]-b[ansnum2]-(i+1));
        }
        if(ans1>ans2){
            ans = ans2;
        }else{
            ans = ans1;
        }
    }
    printf("%lld\n",ans);
    return 0;
}