Polycarp likes arithmetic progressions. A sequence [a_1, a_2, ..., a_n] is called an arithmetic progression if for each i (1 ≤ i < n) the value a_{i+1} - a_i is the same. For example, the sequences [42], [5, 5, 5], [2, 11, 20, 29] and [3, 2, 1, 0] are arithmetic progressions, but [1, 0, 1], [1, 3, 9] and [2, 3, 1] are not.

It follows from the definition that any sequence of length one or two is an arithmetic progression.

Polycarp found some sequence of positive integers [b_1, b_2, ..., b_n]. He agrees to change each element by at most one. In the other words, for each element there are exactly three options: an element can be decreased by 1, an element can be increased by 1, an element can be left unchanged.

Determine a minimum possible number of elements in b which can be changed (by exactly one), so that the sequence b becomes an arithmetic progression, or report that it is impossible.

It is possible that the resulting sequence contains element equals 0.

Input

The first line contains a single integer n (1 ≤ n ≤ 100 000) — the number of elements in b.

The second line contains a sequence b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^{9}).

Output

If it is impossible to make an arithmetic progression with described operations, print -1. In the other case, print non-negative integer — the minimum number of elements to change to make the given sequence becomes an arithmetic progression. The only allowed operation is to add/to subtract one from an element (can't use operation twice to the same position).

Examples

Input

4
24 21 14 10


Output

3


Input

2
500 500


Output

0


Input

3
14 5 1


Output

-1


Input

5
1 3 6 9 12


Output

1

Note

In the first example Polycarp should increase the first number on 1, decrease the second number on 1, increase the third number on 1, and the fourth number should left unchanged. So, after Polycarp changed three elements by one, his sequence became equals to [25, 20, 15, 10], which is an arithmetic progression.

In the second example Polycarp should not change anything, because his sequence is an arithmetic progression.

In the third example it is impossible to make an arithmetic progression.

In the fourth example Polycarp should change only the first element, he should decrease it on one. After that his sequence will looks like [0, 3, 6, 9, 12], which is an arithmetic progression.
/**
 * Created by chiragchandnani on 5/14/18.
 * DA-IICT (B.tech 3rd year)
 */

import java.io.*;
import java.util.*;


public class Q4 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
      
      
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */
        //The Code Starts here
        int noOfElements=sc.nextInt();
        if(noOfElements<=2)
        {
            out.print("0");
            out.close();
            return;
        }

        long b[]=sc.nextLongArray(noOfElements);

        int minCnt=Integer.MAX_VALUE;
        for(int d0=-1;d0<=1;d0++)
        {
            long a[]=new long[noOfElements];

            for(int d1=-1;d1<=1;d1++) {
                boolean valid=true;
                a[0] = b[0] + d0;
                a[1] = b[1] + d1;

                int cnt = Math.abs(d0) + Math.abs(d1);
                for (int i = 2; i < noOfElements; i++) {
                    a[i] = a[0] + (i) * (a[1] - a[0]);
                    if (Math.abs(a[i] - b[i]) > 1)
                    {
                        valid=false;
                        break;
                    }
                    else if (a[i] != b[i]) {
                        cnt++;

                    }
                }
//                debug(a,d0,d1,cnt,maxCnt,valid);
                if(valid)
                {
                    if (minCnt > cnt)
                        minCnt = cnt;
                }

            }
        }
        if(minCnt==Integer.MAX_VALUE)
            out.print("-1");
        else
            out.print(minCnt);


        //The Code ends here
        out.close();
    }


    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        char nextCharacter() {
            return next().charAt(0);
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        public int[][] nextInt2DArray(int m, int n) {
            int[][] arr = new int[m][n];
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++)
                    arr[i][j] = nextInt();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }

    public static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }

    public static class Pair implements Comparable<Pair> {
        long u;
        long v;

        public Pair(long u, long v) {
            this.u = u;
            this.v = v;
        }


        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }

        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }

        public int compareTo(Pair other) {
            return Long.compare(u, other.u) != 0 ? Long.compare(u, other.u) : Long.compare(v, other.v);
        }

        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
    //--------------------------------------------------------


    // Different other methods

    public static long pow(long n, long p, long mod) {
        if (p == 0)
            return 1;
        if (p == 1)
            return n % mod;
        if (p % 2 == 0) {
            long temp = pow(n, p / 2, mod);
            return (temp * temp) % mod;
        } else {
            long temp = pow(n, p / 2, mod);
            temp = (temp * temp) % mod;
            return (temp * n) % mod;

        }
    }

    public static long pow(long n, long p) {
        if (p == 0)
            return 1;
        if (p == 1)
            return n;
        if (p % 2 == 0) {
            long temp = pow(n, p / 2);
            return (temp * temp);
        } else {
            long temp = pow(n, p / 2);
            temp = (temp * temp);
            return (temp * n);

        }
    }

    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd(y % x, x);
    }

    static long modInverse(long a, long m) {
        long m0 = m, t, q;
        long x0 = 0, x1 = 1;

        if (m == 1)
            return 0;

        while (a > 1) {
            // q is quotient
            q = a / m;

            t = m;

            // m is remainder now, process
            // same as Euclid's algo
            m = a % m;
            a = t;

            t = x0;

            x0 = x1 - q * x0;

            x1 = t;
        }

        // Make x1 positive
        if (x1 < 0)
            x1 += m0;

        return x1;
    }

    public static boolean isPrime(int n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }

    public static class DisjointSet {
        HashMap<Integer, Node> map = new HashMap<Integer, Node>();

        class Node {
            int data;
            int rank;
            Node parent;

            Node(int data) {
                this.data = data;
                this.rank = 0;
                this.parent = this;
            }
        }

        void makeSet(int data) {
            map.put(data, new Node(data));
        }

        Node findSet(int data) {
            return findSet(map.get(data));
        }

        boolean isConnected(int d1, int d2) {
            return findSet(d1) == findSet(d2);
        }

        Node findSet(Node node) {
            Node parent = node.parent;
            if (parent == node)
                return parent;
            node.parent = findSet(node.parent);
            return node.parent;
        }

        void union(int data1, int data2) {
            Node d1 = map.get(data1);
            Node d2 = map.get(data2);

            Node p1 = findSet(d1);
            Node p2 = findSet(d2);

            if (p1.data == p2.data)
                return;

            if (p1.rank >= p2.rank) {
                p1.rank = (p1.rank == p2.rank) ? p1.rank + 1 : p1.rank;
                p2.parent = p1;
            } else {
                p1.parent = p2;
            }
        }

    }
}
