You have an array a with length n, you can perform operations. Each operation is like this: choose two adjacent elements from a, say x and y, and replace one of them with gcd(x, y), where gcd denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor).

What is the minimum number of operations you need to make all of the elements equal to 1?

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2000) — the number of elements in the array.

The second line contains n space separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the elements of the array.

Output

Print -1, if it is impossible to turn all numbers to 1. Otherwise, print the minimum number of operations needed to make all numbers equal to 1.

Examples

Input

5
2 2 3 4 6


Output

5


Input

4
2 4 6 8


Output

-1


Input

3
2 6 9


Output

4

Note

In the first sample you can turn all numbers to 1 using the following 5 moves:

  * [2, 2, 3, 4, 6]. 
  * [2, 1, 3, 4, 6]
  * [2, 1, 3, 1, 6]
  * [2, 1, 1, 1, 6]
  * [1, 1, 1, 1, 6]
  * [1, 1, 1, 1, 1]



We can prove that in this case it is not possible to make all numbers one using less than 5 moves.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author hsy
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        static final int INF = (int) 1e9 + 10;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n];
            int sum = 0;
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
                if (a[i] == 1) {
                    sum++;
                }
            }
            if (sum != 0) {
                out.println(n - sum);
                return;
            }
            if (n == 1) {
                if (a[0] == 1) {
                    out.println("0");
                } else {
                    out.println("-1");
                }
                return;
            }

            int Min = INF - 10;
            for (int i = 1; i < n; i++) {
                int GCD = gcd(a[i - 1], a[i]);
                //out.println("GCD=="+GCD);
                int MMin = INF;
                {
                    boolean flag = false;
                    int h = 1;
                    int l = i - 2;
                    for (int j = l; j >= 0; j--) {
                        if (GCD == 1) {
                            flag = true;
                            break;
                        }
                        h++;
                        int _GCD = gcd(a[j], GCD);
                        if (_GCD == 1) {
                            flag = true;
                            break;
                        } else {
                            GCD = _GCD;
                        }
                    }
                    if (flag) MMin = Math.min(MMin, h);
                }
                {
                    boolean flag = false;
                    GCD = gcd(a[i - 1], a[i]);
                    int h = 1;
                    int r = i + 1;
                    for (int j = r; j < n; j++) {
                        if (GCD == 1) {
                            flag = true;
                            break;
                        }
                        h++;
                        int _GCD = gcd(a[j], GCD);
                        if (_GCD == 1) {
                            flag = true;
                            break;
                        } else {
                            GCD = _GCD;
                        }

                    }
                    if (flag) MMin = Math.min(MMin, h);
                }
                //out.println("MMin=="+MMin);
                Min = Math.min(Min, MMin + n - 1);
            }
            if (Min == INF - 10) {
                out.println("-1");
            } else {
                out.println(Min);
            }
        }

        private int gcd(int i, int i1) {
            if (i > i1) {
                int t = i;
                i = i1;
                i1 = t;
            }
            while (i > 0) {
                int k = i1 % i;
                i1 = i;
                i = k;
            }
            return i1;
        }

    }
}

