Sonya was unable to think of a story for this problem, so here comes the formal description.

You are given the array containing n positive integers. At one turn you can pick any element and increase or decrease it by 1. The goal is the make the array strictly increasing by making the minimum possible number of operations. You are allowed to change elements in any way, they can become negative or equal to 0.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 3000) — the length of the array.

Next line contains n integer ai (1 ≤ ai ≤ 109).

Output

Print the minimum number of operation required to make the array strictly increasing.

Examples

Input

7
2 1 5 11 5 9 11


Output

9


Input

5
5 4 3 2 1


Output

12

Note

In the first sample, the array is going to look as follows:

2 3 5 6 7 9 11

|2 - 2| + |1 - 3| + |5 - 5| + |11 - 6| + |5 - 7| + |9 - 9| + |11 - 11| = 9

And for the second sample:

1 2 3 4 5

|5 - 1| + |4 - 2| + |3 - 3| + |2 - 4| + |1 - 5| = 12
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        ConsoleIO io = new ConsoleIO();
        new Main(io).solve();
        io.close();
    }

    ConsoleIO io;

    Main(ConsoleIO io) {
        this.io = io;
    }

    long MOD = 1_000_000_007;
    int N, M, Q;

    public void solve() {
        N = io.ri();
        int[] a = new int[N];
        for(int i = 0;i<N;i++){
            a[i] = io.ri();
        }

        int[][] pos = new int[N][N];
        for(int i = 0;i<N;i++) {
            Integer[] s = new Integer[N];
            for (int j = 0; j < N; j++)
                s[j] = a[j] + i - j;
            Arrays.sort(s);
            int[] t = new int[N];
            for (int j = 0; j < N; j++)
                t[j] = s[j];
            pos[i] = t;
        }

        long[][] best = new long[N][N];
        for(int i = 0;i<N;i++) {
            long v = Math.abs(a[0] - pos[0][i]);
            if (i > 0) v = Math.min(v, best[0][i - 1]);
            best[0][i] = v;
        }

        for(int i = 1;i<N;i++){
            long[] cur = best[i];
            long[] prev = best[i-1];
            int[] pp = pos[i];
            int[] pr = pos[i-1];
            int q = 0;
            for(int j = 0;j<N;j++){
                int x = pp[j];
                while(q<N-1 && pr[q+1]<x)q++;
                long v = Math.abs(a[i]-pp[j])+prev[q];
                if(j>0) v = Math.min(v, cur[j-1]);
                cur[j] = v;
            }
        }

        io.writeLine(best[N-1][N-1] + "");
    }
}

class ConsoleIO {
    BufferedReader br;
    PrintWriter out;
    public ConsoleIO(){br = new BufferedReader(new InputStreamReader(System.in));out = new PrintWriter(System.out);}
    public void flush(){this.out.flush();}
    public void close(){this.out.close();}
    public void writeLine(String s) {this.out.println(s);}
    public void writeInt(int a) {this.out.print(a);this.out.print(' ');}
    public void writeWord(String s){
        this.out.print(s);
    }
    public void writeIntArray(int[] a, int k, String separator) {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < k; i++) {
            if (i > 0) sb.append(separator);
            sb.append(a[i]);
        }
        this.writeLine(sb.toString());
    }
    public int read(char[] buf, int len){try {return br.read(buf,0,len);}catch (Exception ex){ return -1; }}
    public String readLine() {try {return br.readLine();}catch (Exception ex){ return "";}}
    public long[] readLongArray() {
        String[]n=this.readLine().trim().split("\\s+");long[]r=new long[n.length];
        for(int i=0;i<n.length;i++)r[i]=Long.parseLong(n[i]);
        return r;
    }
    public int[] readIntArray() {
        String[]n=this.readLine().trim().split("\\s+");int[]r=new int[n.length];
        for(int i=0;i<n.length;i++)r[i]=Integer.parseInt(n[i]);
        return r;
    }
    public int[] readIntArray(int n) {
        int[] res = new int[n];
        char[] all = this.readLine().toCharArray();
        int cur = 0;boolean have = false;
        int k = 0;
        boolean neg = false;
        for(int i = 0;i<all.length;i++){
            if(all[i]>='0' && all[i]<='9'){
                cur = cur*10+all[i]-'0';
                have = true;
            }else if(all[i]=='-') {
                neg = true;
            }
            else if(have){
                res[k++] = neg?-cur:cur;
                cur = 0;
                have = false;
                neg = false;
            }
        }
        if(have)res[k++] = neg?-cur:cur;
        return res;
    }
    public int ri() {
        try {
            int r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public long readLong() {
        try {
            long r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public String readWord() {
        try {
            boolean start = false;
            StringBuilder sb = new StringBuilder();
            while (true) {
                int c = br.read();
                if (c!= ' ' && c!= '\r' && c!='\n' && c!='\t') {
                    sb.append((char)c);
                    start = true;
                } else if (start || c == -1) return sb.toString();
            }
        } catch (Exception ex) {
            return "";
        }
    }
    public char readSymbol() {
        try {
            while (true) {
                int c = br.read();
                if (c != ' ' && c != '\r' && c != '\n' && c != '\t') {
                    return (char) c;
                }
            }
        } catch (Exception ex) {
            return 0;
        }
    }
    public char readChar(){try {return (char)br.read();}catch (Exception ex){ return 0; }}
}
class Pair {
    public Pair(int a, long b) {this.a = a;this.b = b;}
    public int a;
    public long b;
}
class Tri {
    public Tri(int a, int b, int c) {this.a = a;this.b = b;this.c = c;}
    public int a;
    public int b;
    public int c;
}
class PairLL {
    public PairLL(long a, long b) {this.a = a;this.b = b;}
    public long a;
    public long b;
}