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.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;






public class Main{
	static class MyScanner {
	    BufferedReader br;
	    StringTokenizer st;

	    public MyScanner() {
	       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;
	    }
	}
		
	
		 public static void main(String[] args) throws IOException {
			 	PrintWriter out = new PrintWriter(System.out);
			    MyScanner sc = new MyScanner();
			 	Main solver = new Main();
				solver.solve(out, sc);
				out.flush();
				out.close();
				
		}
	
		
		 
		 
		
 		void solve(PrintWriter out, MyScanner sc) throws IOException{	
 		
 			int n = sc.nextInt();
 			int[] a = new int[n];
 			int one = 0;
 			for(int i = 0 ; i < n ; ++i) {
 				a[i] = sc.nextInt();
 				if(a[i] == 1) one++;
 			}
 			if(one > 0) {
 				out.print(n - one);return;
 			}
 			int min = Integer.MAX_VALUE;
 			for(int i = 0 ; i < n ; ++i) {
 				if(a[i] == 1) {
 					out.print(n - 1);return;
 				}else {
 					int g = a[i];
 					for(int j = i + 1; j < n ; ++j) {
 						g = gcd(g, a[j]);
 						if(g == 1) {
 							min = Math.min(min, j - i);
 							break;
 						}
 					}
 				}
 			}
 			if(min != Integer.MAX_VALUE) out.print(min + n - 1);
 			else out.print(-1);
 			
 			
 				
 		}
 		
 		int gcd(int a, int b) {
 			if(a % b == 0) return b;
 			return gcd(b , a% b);
 		}
 		
 		
 		
 		
 		
 		
 		
 		


 		
 		

 	
		
	
			
		
		
		
		
		
		
		
		
	
	
}