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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 * Created by MohannadHassanPersonal on 11/17/17.
 */
public class Pride {


    public static void main(String [] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int count = Integer.parseInt(br.readLine());

        String[] input = br.readLine().split(" ");

        int[] numbers = new int[count];

        int equalsOne = 0;

        for (int i = 0; i < count; i++) {
            numbers[i] = Integer.parseInt(input[i]);

            equalsOne += numbers[i] == 1 ? 1 : 0;
        }

        if (equalsOne != 0) {
            System.out.println(count - equalsOne);
        }
        else {
            int [] currentLevel = numbers;
            int [] nextLevel;
            int levelsProcessed = 0;

            boolean hasOne = false;

            while (!hasOne && currentLevel.length > 1) {
                nextLevel = new int[currentLevel.length - 1];

                for (int i = 0; i < nextLevel.length && !hasOne; i++) {
                    nextLevel[i] = gcd(currentLevel[i], currentLevel[i + 1]);
                    hasOne |= nextLevel[i] == 1;
                }

                levelsProcessed += 1;
                currentLevel = nextLevel;
            }

            if (hasOne) {
                System.out.println(levelsProcessed + count - 1);
            }
            else {
                System.out.println("-1");
            }
        }
    }

    private static int gcd(int a, int b) {
        if (b > a) return gcd(b, a);

        if (a % b == 0) return b;

        return gcd(b, a % b);
    }
}
