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 {

    public static void main(String[] args) throws IOException {
//        br = new BufferedReader(new FileReader(new File("subtract.in")));
//        out = new PrintWriter(new File("subtract.out"));
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int PUTEN = 1;
        for (int POMOGI = 0; POMOGI < PUTEN; POMOGI++) {
            int n = nextInt();
            int[] a = new int[n];
            int gg = 0;
            int cnt_one = 0;
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
                if(a[i]== 1)cnt_one++;
                if(i == 0)gg = a[i];
                else gg = gcd(gg, a[i]);
            }
            if(cnt_one != 0){
                out.println(n - cnt_one);
                continue;
            }
            if(gg != 1){
                out.println(-1);
            }else {
                int min = n;
                for (int l = 0; l < n; l++) {
                    int g = 0;
                    for (int r = l; r < n; r++) {
                        g = gcd(a[r], g);
                        if(g == 1) min = Math.min(min, r - l);
                    }
                }
                out.println(n + min - 1);
            }


        }
        out.close();
    }

    static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer in = new StringTokenizer("");

    static String next() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

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

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

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