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.InputStreamReader;
import java.util.*;


public class C2 {
    private static void solve(int[] a) {
        int ans = 500000;
        int n = a.length;
        int ones = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] == 1) {
                ones++;
                ans = 1;
            }
            int res = a[i];
            for (int j = i; j < n; j++) {
                res = gcd(res, a[j]);
                if (res == 1) {
                    ans = Math.min(ans, j - i + 1);
                    break;
                }
            }
        }
        if (ans == 500000) {
            System.out.println(-1);
            return;
        }
        if (ans == 1) {
            System.out.println(n - ones);
        } else {
            System.out.println(Math.max(0, ans + n - 2 - ones));
        }
    }

    static int gcd(int a, int b) {
        if (a % b == 0 || b % a == 0) {
            return Math.min(a, b);
        }
        return gcd(Math.max(a, b) - Math.min(a, b), Math.min(a, b));
    }

    //15 25
    //15 10

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int[] a = sc.readArrayInt(n);
        solve(a);
    }


    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

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

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

        long[] readArrayLong(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        int[] readArrayInt(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

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

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