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.
// 作者：杨成瑞先生
import java.io.*;
import java.util.*;

public class cf {

	static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try {
                br = new BufferedReader(new InputStreamReader(System.in));
                st = new StringTokenizer(br.readLine());
            } catch (Exception e){e.printStackTrace();}
        }

        public String next() {
            if (st.hasMoreTokens()) return st.nextToken();
            try {st = new StringTokenizer(br.readLine());}
            catch (Exception e) {e.printStackTrace();}
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            String line = "";
            if(st.hasMoreTokens()) line = st.nextToken();
            else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
            while(st.hasMoreTokens()) line += " "+st.nextToken();
            return line;
        }
    }

    static int mod = 1000000007;
    static long oo = Long.MAX_VALUE;

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

	public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        
        int n = sc.nextInt();
        int[] a = new int[n];
        int count1 = 0;

        for(int i=0;i<n;i++) {
            a[i] = sc.nextInt();
            if(a[i] == 1) count1++;
        }

        if(count1 > 0) {
            pw.println(n - count1);
        }
        else {
            int ans = -1;
            for(int i=0;i<n;i++) {
                int value = a[i];
                for(int j=i;j<n;j++) {
                    value = gcd(value, a[j]);
                    if(value == 1) {
                        int temp = j - i + n - 1;
                        if(temp < ans || ans < 0) {
                            ans = temp;
                        }
                    }
                }
            }
            pw.println(ans);
        }

        pw.close();
    }

}