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

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

    static class TaskC {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] arr = new int[n];
            boolean haveOne = false;
            for (int i = 0; i < n; i++) {
                arr[i] = in.nextInt();
                haveOne |= arr[i] == 1;
            }
            int gcd = arr[0];
            int ans = 0;
            for (int i = 1; i < n; i++) gcd = IntMath.gcd(gcd, arr[i]);
            if (gcd != 1) {
                out.println(-1);
                return;
            }
            if (haveOne) {
                for (int i = 0; i < n; i++) {
                    if (arr[i] != 1) {
                        ++ans;
                    }
                }
                out.println(ans);
                return;
            }
            int minMoves = 1000000;
            int[][] g = new int[n][n];
            for (int i = 0; i < n; i++) {
                g[i][i] = arr[i];
                for (int j = i + 1; j < n; j++) {
                    g[i][j] = IntMath.gcd(g[i][j - 1], arr[j]);
                    if (g[i][j] == 1) {
                        minMoves = Math.min(minMoves, j - i + 1);
                    }
                }
            }
            out.println(n - 2 + minMoves);
        }

    }

    static class IntMath {
        public static int gcd(int a, int b) {
            if (b != 0)
                return gcd(b, a % b);
            return a;
        }

    }

    static class FastReader {
        BufferedReader reader;
        StringTokenizer st;

        public FastReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            st = null;
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String line = reader.readLine();
                    if (line == null) {
                        return null;
                    }
                    st = new StringTokenizer(line);
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

    }
}

