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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.stream.Stream;

/**
 * Success is not final, failure is not fatal. The courage to continue is what counts.
 * @author bodmas
 */
public class ProblemC {

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

    private int solve(int[] a) {
        int gcd = 0;
        int numOnes = 0;
        for (int i = 0; i < a.length; i++) {
            gcd = gcd(gcd, a[i]);
            if (a[i] == 1)
                numOnes++;
        }
        if (gcd != 1)
            return -1;
        if (numOnes != 0)
            return a.length - numOnes;
        int rounds = 0;
        while (true) {
            for (int i = 0; i < a.length - rounds; i++) {
                if (i != 0) {
                    a[i - 1] = gcd(a[i - 1], a[i]);
                    if (a[i - 1] == 1)
                        return a.length + rounds;
                }
            }
            rounds++;
        }
    }

    public static void main(String[] args) throws IOException {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
                PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out))) {
            in.readLine();
            int[] a = Stream.of(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            out.println(new ProblemC().solve(a));
        }
    }
}
