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.
import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class Main {

    public static int BP(long[] mas, long k){
        int l = 0, r = mas.length;
        int mid = (l + r) / 2;
        while (l + 1 < r){
            if(mas[mid] > k){
                r = mid;
            }
            else l = mid;
            mid = (l + r) / 2;
        }

        if(mas[mid] > k) return l;
        else return r;
    }

    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        FastPrinter out = new FastPrinter(System.out);
        //FastScanner in = new FastScanner(new InputStreamReader(new FileInputStream(new File("mars.in"))));
        //FastPrinter out = new FastPrinter(new OutputStreamWriter(new FileOutputStream(new File("mars.out"))));
        int n = in.nextInt();
        int[] mas = new int[n];
        int[] masCopy = new int[n];
        int ans = Integer.MAX_VALUE;
        for(int i = 0; i < n; i++){
            mas[i] = in.nextInt();
            masCopy[i] = mas[i];
        }
        if(n == 1 || n == 2) System.out.println(0);
        else {
            int k = mas[1] - mas[0];
            boolean flag = true;
            int v = 0;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[0]--;

            k = mas[1] - mas[0];
            flag = true;
            v = 1;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[0]--;
            mas[1]--;

            k = mas[1] - mas[0];
            flag = true;
            v = 2;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[0]--;
            mas[1]++;

            k = mas[1] - mas[0];
            flag = true;
            v = 2;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[0]++;

            k = mas[1] - mas[0];
            flag = true;
            v = 1;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[0]++;
            mas[1]++;

            k = mas[1] - mas[0];
            flag = true;
            v = 2;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[0]++;
            mas[1]--;

            k = mas[1] - mas[0];
            flag = true;
            v = 2;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[1]++;

            k = mas[1] - mas[0];
            flag = true;
            v = 1;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }

            mas[1]--;

            k = mas[1] - mas[0];
            flag = true;
            v = 1;
            for(int i = 1; i < n - 1; i++){
                if(mas[i+1] + 1 - mas[i] == k) {mas[i+1]++; v++;}
                else if(mas[i+1] - 1 - mas[i] == k) {mas[i+1]--; v++;}
                else if (mas[i+1] - mas[i] != k) {flag = false; break;}
            }
            if(flag) ans = Math.min(ans, v);
            for(int i = 0; i < n; i++){
                mas[i] = masCopy[i];
            }
            if(ans == Integer.MAX_VALUE) System.out.println(-1);
            else System.out.println(ans);
        }
        out.close();
    }
}
class FastPrinter {
    private final PrintWriter writer;

    public FastPrinter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public FastPrinter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void close() {
        writer.close();
    }

    public void println(long i) {
        writer.println(i);
    }

    public void println(double d) {
        writer.println(d);
    }

    public void println(String s) {
        writer.println(s);
    }

    public void println(String format, Object... args) {
        println(String.format(format, args));
    }

    public void println() {
        writer.println();
    }

    public void print(long i) {
        writer.print(i);
    }

    public void print(char c) {
        writer.print(c);
    }

    public void print(double d) {
        writer.print(d);
    }

    public void print(String s) {
        writer.print(s);
    }

    public void print(String format, Object... args) {
        print(String.format(format, args));
    }

    public void flush() {
        writer.flush();
    }
}

class FastScanner {

    private BufferedReader reader;
    private StringTokenizer st;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public FastScanner(InputStream stream) {
        this.reader = new BufferedReader(new InputStreamReader(stream));
        this.st = new StringTokenizer("");
    }

    public FastScanner(InputStreamReader stream) {
        this.reader = new BufferedReader(stream);
        this.st = new StringTokenizer("");
    }

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

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

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

    public String next() {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(readLine());
        }
        return st.nextToken();
    }

    public String nextLine() {
        st = new StringTokenizer("");
        return readLine();
    }

    public String tryNextLine() {
        st = new StringTokenizer("");
        return tryReadLine();
    }

    private String readLine() {
        String line = tryReadLine();
        if (line == null) throw new InputMismatchException();
        return line;
    }

    private String tryReadLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

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

    public int[][] nextIntTable(int rowCount, int columnCount) {
        int[][] table = new int[rowCount][];
        for (int i = 0; i < rowCount; i++)
            table[i] = nextIntArray(columnCount);
        return table;
    }

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

    public long[][] nextLongTable(int rowCount, int columnCount) {
        long[][] table = new long[rowCount][];
        for (int i = 0; i < rowCount; i++)
            table[i] = nextLongArray(columnCount);
        return table;
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\t' || isEOL(c);
    }

    public static boolean isEOL(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}