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.util.Arrays;
import java.util.Scanner;

public class CF_891A {
 public static void main(String[] args) {
	Scanner sc = new Scanner(System.in);
	
	int n = sc.nextInt();
	int ones =  0;
	int min = Integer.MAX_VALUE;
	int a[] = new int[n];
	int dp[][]=new int[n][n];
	
	for(int i=0;i<n;i++){
		a[i]=sc.nextInt();
		dp[i][i]=a[i];
		if(a[i]==1)ones++;
	}
	
	if(ones>=1){ System.out.println(n-ones);}
	else{
		int k=0;
		boolean f = false;
		for(int i=0;i<n;i++){
			for(int j=i+1;j<n;j++){
				  dp[i][j]=gcd(dp[i][j-1],a[j]);
				  if(dp[i][j]==1){
					  min  = Math.min(min,j-i);
				  }
				 //for(int p=0;p<n;p++)System.out.println(Arrays.toString(dp[p]));
			      //System.out.println("============== min = "+min);
				}
			}
		System.out.println((min==Integer.MAX_VALUE)?-1:min+n-1);
		}
	}

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