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.awt.*;
import java.io.*;
import java.util.*;

public class Abc {
    static int dp[][];
    static int arr[];
    public static void main(String[] args) throws Exception {
//        Scanner sc = new Scanner(System.in);
        FastReader sc=new FastReader();
        int n=sc.nextInt();
        arr=new int[n];
        int one=0;
        for (int i=0;i<n;i++){
            arr[i]=sc.nextInt();
            if (arr[i]==1)one++;
        }
        if (one>0){
            System.out.println(n-one);
            return;
        }
        dp=new int[n][n+1];
        for (int ar[]:dp)Arrays.fill(ar,-1);
        for (int len=2;len<=n;len++){
            for (int i=0;i+len-1<n;i++){
                if (dp(i,len)==1){
                    System.out.println(len-2+n);
                    return;
                }
            }
        }
        System.out.println(-1);
    }
    static int dp(int i,int len){
        if (len==2)return gcd(arr[i],arr[i+len-1]);
        if (len==1)return arr[i];
        if (dp[i][len]!=-1)return dp[i][len];
        return dp[i][len]=gcd(gcd(arr[i],arr[i+len-1]),dp(i+1,len-2));
    }
    static int gcd(int a,int b){
        if (a==0)return b;
        return gcd(b%a,a);
    }
    static 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;
        }
    }
}