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.*;
import java.awt.*;

public class Main {
    static int mod=(int)1e9+7;
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        StringBuilder sb = new StringBuilder();
        int n=sc.nextInt();
        int[] arr=new int[n];
        int ones=0;
        for(int i=0;i<n;i++){
            arr[i]=sc.nextInt();
            if(arr[i]==1)ones++;
        }
        if(ones>0){
            System.out.println(n-ones);
            return;
        }
        int min=Integer.MAX_VALUE;
        for(int i=0;i<n;i++){
            int x=arr[i];
            int  j=i+1;
            for(;j<n;j++){
                x=gcd(x,arr[j]);
                if(x==1)break;
            }
            if(x==1)min=Math.min(min,j-i);
        }
        if(min==Integer.MAX_VALUE) System.out.println(-1);
        else System.out.println(min+n-1);
    }
    static int gcd(int a,int b){
        if(b==0)return a;
        else return gcd(b,a%b);
    }
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() { 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;
    }
}