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.*;
import java.util.*;

public class Main {
    private static InputReader in;
    private static PrintWriter out;

    public static void main(String[] args) {
        in = new InputReader();
        out = new PrintWriter(System.out);
        int t = 1;
//        t = in.nextInt();
        for (int i = 0; i < t; ++i) {
            solve();
        }
        out.close();
    }

    private static void solve() throws RuntimeException {
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; ++i) a[i] = in.nextInt();
        int G = 0;
        for (int i = 0; i < n; ++i) {
            G = gcd(a[i], G);
        }
        if (G != 1) {
            out.println(-1);
            return;
        }
        int minLen = n + 1, idx = -1;
        for (int i = 0; i < n; ++i) {
            int g = 0;
            for (int j = i; j < n; ++j) {
                g = gcd(g, a[j]);
                if (g == 1) {
                    if (minLen > j - i) {
                        minLen = j - i;
                        idx = i;
                    }
                    break;
                }
            }
        }
//        for (int i = idx + minLen; i >= idx; --i) {
//            if (i - 1 >= idx) {
//                a[i] = gcd(a[i + 1], a[i]);
//            }
//        }
        boolean[] visited = new boolean[n];
        Queue<Integer> queue = new LinkedList<>();
        queue.add(idx);
        a[idx] = 1;
        visited[idx] = true;
        int moves = minLen;
//        out.println(idx + " | " + minLen);
        while (!queue.isEmpty()) {
            int curr = queue.remove();
            if (curr + 1 < n && !visited[curr + 1]) {
                queue.add(curr + 1);
                visited[curr + 1] = true;
                if (a[curr + 1] != 1) ++moves;
            }
            if (curr - 1 >= 0 && !visited[curr - 1]) {
                queue.add(curr - 1);
                visited[curr - 1] = true;
                if (a[curr - 1] != -1) ++moves;
            }
        }
        out.println(moves);
//        for (int i = 0; i < n; ++i) {
//            if (a[] )
//        }
    }

    private static boolean makeOne(int[] a) {
        for (int i = 1; i < a.length; ++i) {
            int g = gcd(a[i], a[i - 1]);
            out.println("Gcd " + g);
            if (g > 1) continue;
            a[i] = 1;
            return true;
        }
        return false;
    }

    private static int gcd(int a, int b) {
        while (b > 0) {
            int t = a % b;
            a = b;
            b = t;
        }
        return a;
    }

    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}