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.PrintWriter;
import java.util.Scanner;
import java.util.ArrayList;

public class practise {
    static final int N = 2010;
    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out,true);
    public static void main(String[] args) {
        int n = sc.nextInt();
        int[][] a = new int[N][N];
        int cnt = 0;
        for(int i=0;i<n;i++) {
            a[0][i] = sc.nextInt();
            if(a[0][i]==1) cnt++;
        }
        if(cnt>0) {
            out.println(n-cnt);
            return ;
        }
        for(int i=1;i<n;i++) {
            for(int j=0;j<n-i;j++) {
                a[i][j] = gcd(a[i-1][j],a[i-1][j+1]);
                if(a[i][j] == 1) {
                    out.println(i+n-1);
                    return ;
                }
            }
        }
        out.println("-1");
    }
    public static int gcd(int a,int b) {
        int t = a;
        if(a>b) {
            a = b; b = t;
        }
        while(a!=0) {
            t = b%a;
            b = a;
            a = t;
        }
        return b;
    }
}
