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

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

    static
    @SuppressWarnings("Duplicates")
    class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();

            if (n == 1) {
                out.print(in.nextInt() == 1 ? 0 : -1);
                return;
            }

            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();

            int gcd = gcd(a[0], a[1]);
            for (int i = 2; i < n; i++) gcd = gcd(gcd, a[i]);
            if (gcd != 1) {
                out.print(-1);
                return;
            }

            int count = 0;
            for (int i = 0; i < n; i++) {
                if (a[i] != 1) count++;
            }

            int res = Integer.MAX_VALUE;
            for (int i = 0; i < n; i++) {
                gcd = 0;
                for (int j = i; j < n; j++) {
                    gcd = gcd(gcd, a[j]);
                    if (gcd == 1) {
                        res = Math.min(res, j - i + count - (a[j] == 1 ? 0 : 1));
                        break;
                    }
                }
            }

            out.print(res);
        }

        private int gcd(int a, int b) {
            if (a < b) {
                int temp = a;
                a = b;
                b = temp;
            }
            while (b != 0) {
                int temp = a % b;
                a = b;
                b = temp;
            }
            return Math.abs(a);
        }

    }

    static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

    }
}

