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.
//package Round892;

import java.util.Scanner;

public class C {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();

        int a[] = new int[n];
        int count1 = 0;

        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
            if (a[i] == 1)
                count1++;
        }

        if (count1 > 0) {
            System.out.println(n - count1);
            System.exit(0);
        }

        int gcd[][] = new int[n][n]; // from to
        int minLength = Integer.MAX_VALUE;

        for (int i = 0; i < n; i++) {
            gcd[i][i] = a[i];
            for (int j = i - 1; j >= 0; j--) {
                gcd[j][i] = gcd(gcd[j][i - 1], a[i]);
                if (gcd[j][i] == 1 && i - j < minLength)
                    minLength = i - j;
            }
        }

        if (minLength == Integer.MAX_VALUE)
            System.out.println(-1);
        else
            System.out.println(n + minLength - 1);
    }

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