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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;


public class Main {
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) {
		int N = sc.nextInt();
		int a [] = new int [N];
		
	
		for (int i=0; i<N; i++) 
			a[i] = sc.nextInt()-(i+1);
			
		if (N==1) 
			out.println(0);
		
		else {
			Arrays.sort(a);
			
			long ans = 0;
			long min = 2_000_000_000L;
			
			if (N%2==0) {
				for (int j=a[N/2-1]; j<a[N/2]; j++) {
					for (int i=1; i<=N; i++) {
						ans += Math.abs(a[i-1]-j);
					}
					min = Math.min(ans, min);
					ans = 0;
				}	
			}
			
			else {
				for (int j=a[(N-3)/2]; j<=a[(N+1)/2]; j++) {
					for (int i=1; i<=N; i++) {
						ans += Math.abs(a[i-1]-j);
					}
					min = Math.min(ans, min);
					ans = 0;
				}
			}
			out.println(min);
			}
		out.flush();
		}
	
	
		static class FastScanner {
		    private final InputStream in = System.in;
		    private final byte[] buffer = new byte[1024];
		    private int ptr = 0;
		    private int buflen = 0;

		    private boolean hasNextByte() {
		      if (ptr < buflen) {
		        return true;
		      } else {
		        ptr = 0;
		        try {
		          buflen = in.read(buffer);
		        } catch (IOException e) {
		          e.printStackTrace();
		        }
		        if (buflen <= 0) {
		          return false;
		        }
		      }
		      return true;
		    }

		    private int readByte() {
		      if (hasNextByte()) return buffer[ptr++];
		      else return -1;
		    }

		    private static boolean isPrintableChar(int c) {
		      return 33 <= c && c <= 126;
		    }

		    private void skipUnprintable() {
		      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		    }

		    public boolean hasNext() {
		      skipUnprintable();
		      return hasNextByte();
		    }

		    public String next() {
		      if (!hasNext()) throw new NoSuchElementException();
		      StringBuilder sb = new StringBuilder();
		      int b = readByte();
		      while (isPrintableChar(b)) {
		        sb.appendCodePoint(b);
		        b = readByte();
		      }
		      return sb.toString();
		    }

		    public long nextLong() {
		      if (!hasNext()) throw new NoSuchElementException();
		      long n = 0;
		      boolean minus = false;
		      int b = readByte();
		      if (b == '-') {
		        minus = true;
		        b = readByte();
		      }
		      if (b < '0' || '9' < b) {
		        throw new NumberFormatException();
		      }
		      while (true) {
		        if ('0' <= b && b <= '9') {
		          n *= 10;
		          n += b - '0';
		        } else if (b == -1 || !isPrintableChar(b)) {
		          return minus ? -n : n;
		        } else {
		          throw new NumberFormatException();
		        }
		        b = readByte();
		      }
		    }

		    public int nextInt() {
		      return (int) nextLong();
		    }

		    public int[] nextIntArray(int N, boolean oneBased) {
		      if (oneBased) {
		        int[] array = new int[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      } else {
		        int[] array = new int[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      }
		    }

		    public long[] nextLongArray(int N, boolean oneBased) {
		      if (oneBased) {
		        long[] array = new long[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      } else {
		        long[] array = new long[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      }
		    }
		  }

		}