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.util.*;

public class Codeforces {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);

        int n = s.nextInt();

        if (n==1) {
            if (s.nextInt() == 1) {
                System.out.print(0);
            } else {
                System.out.print(-1);
            }
        } else {
            int[] input = new int[n];
            for (int i = 0; i < n; i++) {
                input[i] = s.nextInt();
            }

            int min = -1;

            int i =0;

            while (i < n && min != 0){

                int nod = input[i];
                int j = i;
                while (j + 1 < n && nod != 1) {
                    j++;
                    nod = gcd(nod, input[j]);
                }

                if (nod == 1) {
                        if (min == -1) {
                            min = j - i;
                        } else {
                            min = Math.min(min, j - i);
                        }
                }
                i++;
            }

            if (min == 0) {
                int amount = 0;
                for (int j = 0; j < n; j++) {
                    if (input[j] == 1) {
                        amount++;
                    }
                }
                System.out.print(n - amount);
            } else {
                if (min == -1) {
                    System.out.print(-1);
                } else {
                    System.out.print(min + n - 1);
                }
            }
        }
    }

    private static int gcd(int a, int b) {
        if (a % b == 0) {
            return b;
        }
        return gcd(b, a % b);
    }
}