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.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/**
 * Created by Katushka on 27.01.2020.
 */
public class Pride {

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

        return gcd(b, a % b);
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        int ones = 0;
        int g = -1;
        int minMoves = 0;
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            if (a[i] == 1) {
                ones++;
            }
            if (g == -1) {
                g = a[i];
            } else {
                if (g != 1) {
                    g = gcd(g, a[i]);
                    minMoves++;
                }
            }
        }
        if (g != 1) {
            System.out.println("-1");
            return;
        }
        if (ones > 0) {
            System.out.println(n - ones);
            return;
        }
        if (minMoves == 1) {
            System.out.println(n);
            return;
        }
        for (int i = 1; i < n; i++) {
            g = a[i];
            int moves = 0;
            for (int j = i + 1; j < n; j++) {
                g = gcd(g, a[j]);
                moves += 1;
                if (g == 1) {
                    break;
                }
            }
            if (g == 1 && moves < minMoves) {
                minMoves = moves;
            }
            if (minMoves == 1) {
                break;
            }
        }
        System.out.println(minMoves + n - 1);

    }

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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    final String str = reader.readLine();
                    tokenizer = new StringTokenizer(str);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

        public long nextLong() {
            return Long.parseLong(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }
    }
}
