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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static InputReader in;
    static PrintWriter out;
    static long time_start;
    static int cas = 0;
    static double eps = 1e-8;
    static int mod = (int) 1e9 + 9;
    static int inf = 0x3f3f3f3f;
    static long inff = 0x3f3f3f3f3f3f3f3fL;
    static int maxn = (int) 1e5 + 5;

    static int f(int[] arr, int x, int y) {
        if (arr.length <= 2) return 0;
        int ans = Math.abs(x) + Math.abs(y);
        int a = arr[0] + x;
        int b = arr[1] + y;
        int d = b - a;
        for (int i = 2; i < arr.length; ++i) {
            int c = b + d;
            if (Math.abs(c - arr[i]) > 1) return inf;
            ans += Math.abs(c - arr[i]);
            b = c;
        }
        return ans;
    }

    static void solve() {
        while (in.hasNext()) {
            int n = in.nextInt();
            int[] a = in.nextIntArray(n);
            int ans = inf;
            for (int i = -1; i <= 1; ++i) {
                for (int j = -1; j <= 1; ++j) {
                    ans = Math.min(ans, f(a, i, j));
                }
            }
            out.println(ans == inf ? -1 : ans);
        }
    }

    static int lower(long[] arr, int l, int r, long k) {
        int m, ans = l;
        while (l <= r) {
            m = (l + r) / 2;
            if (arr[m] >= k) {
                r = m - 1;
                ans = m;
            } else {
                l = m + 1;
            }
        }
        return ans;
    }

    static void swap(int[] arr, int i, int j) {
        if (arr[i] != arr[j]) {
            arr[i] ^= arr[j];
            arr[j] ^= arr[i];
            arr[i] ^= arr[j];
        }
    }

    static void reverse(int[] arr, int i, int j) {
        while (i < j) {
            swap(arr, i++, j--);
        }
    }

    public static void main(String[] args) {
        openIO();
        solve();
        closeIO();
    }

    static void openIO() {
        try {
            time_start = 0;
            FileInputStream fi = new FileInputStream("night-input");
            System.setIn(fi);
            time_start = System.currentTimeMillis();
        } catch (Exception ex) {
            //hello night_13
        }

        in = new InputReader(System.in);
        out = new PrintWriter(new BufferedOutputStream(System.out));
    }

    static void closeIO() {
        out.flush();

        if (time_start != 0) {
            out.println();
            out.print("time cost: ");
            out.print(System.currentTimeMillis() - time_start);
            out.println(" ms");
        }
        in.close();
        out.close();
    }
}


class InputReader {
    private BufferedReader br;
    private StringTokenizer st;

    public InputReader(InputStream stream) {
        br = new BufferedReader(new InputStreamReader(stream));
        eat("");
    }

    private void eat(String s) {
        st = new StringTokenizer(s);
    }

    public String nextLine() {
        try {
            return br.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    public boolean hasNext() {
        while (!st.hasMoreTokens()) {
            String s = nextLine();
            if (s == null) return false;
            eat(s);
        }
        return true;
    }

    public String next() {
        hasNext();
        return st.nextToken();
    }

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

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

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

    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }

    public BigDecimal nextBigDecimal() {
        return new BigDecimal(next());
    }

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

    public double[] nextDoubleArray(int n) {
        double[] arr = new double[n];
        for (int i = 0; i < n; ++i) {
            arr[i] = nextDouble();
        }
        return arr;
    }

    public char[] nextCharArray() {
        return next().toCharArray();
    }

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

    public double[] nextDoubleArray(int n, int st) {
        n += st;
        double[] arr = new double[n];
        for (int i = st; i < n; ++i) {
            arr[i] = nextDouble();
        }
        return arr;
    }

    public char[] nextCharArray(int st) {
        String temp = "";
        while (st-- > 0) temp += " ";
        return (temp + next()).toCharArray();
    }

    public void close() {
        try {
            br.close();
        } catch (IOException e) {
        }
    }
}