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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define mp              make_pair
#define pb              push_back
#define ff              first
#define ss              second
#define inc(A,B)        A=(A+(B))%MOD
#define mul(A,B)        (ll(A)*ll(B)%ll(MOD))
#define sub(a,b)        (((a)-(b)+MOD)%MOD)

typedef pair < int ,int > pii;
typedef long long ll;
typedef pair < ll ,ll > pll;
typedef complex < ll > pt;

const int MAX_N = 100005;
const int MOD = 1e9 + 7;

int n, pnt;
ll arr[MAX_N];
pll lftRgt[MAX_N], rgtLft[MAX_N];
ll sum, sumPnt;
ll aux[4];

void save ( ll fVal, ll sVal, ll cVal, int ind, pll *arr ) {
  ll fDif = abs ( fVal-sVal ), sDif = abs ( fVal-2*cVal-sVal );
  if ( fDif < sDif )
    arr[ind] = mp ( fVal, sVal );
  else
    arr[ind] = mp ( fVal-cVal, sVal+cVal );
}

int main() {

//  freopen ( "in.txt" , "r" , stdin );
//  freopen ( "out.txt" , "w" , stdout );

  scanf ( "%d", &n );
  for ( int i = 0; i < n; ++i )
    scanf ( "%lld", arr+i );

  sum = arr[0];
  for ( int i = 1; i < n; ++i ) {
    sum += arr[i];
    while ( sumPnt < sum-sumPnt )
      sumPnt += arr[pnt++];
    save ( sumPnt, sum-sumPnt, arr[pnt-1], i, lftRgt );
  }

  sum = arr[n-1];
  sumPnt = 0;
  pnt = n-1;
  for ( int i = n-2; i >= 0; --i ) {
    sum += arr[i];
    while ( sumPnt < sum-sumPnt )
      sumPnt += arr[pnt--];
    save ( sumPnt, sum-sumPnt, arr[pnt+1], i, rgtLft );
  }

  ll mini = LLONG_MAX;
  for ( int i = 1; i < n-2; ++i ) {
    aux[0] = lftRgt[i].ff;
    aux[1] = lftRgt[i].ss;
    aux[2] = rgtLft[i+1].ff;
    aux[3] = rgtLft[i+1].ss;
    mini = min ( mini, *max_element ( aux, aux+4 ) - *min_element ( aux, aux+4 ) );
  }

  printf ( "%lld\n", mini );

  return 0;

}