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.*;
import java.io.*;

public class File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            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());
        }
    }		
		
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		
		
		int n = sc.nextInt();
		
		// To be possible, some pair of integers must have gcd = 1.
		int[] a = new int[n];
		
		int ones = 0;
		
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			
			if (a[i] == 1) {
				ones++;
			}
		}
		
		if (n == 1) {
			if (a[0] == 1) {
				out.println(0);
			}
			else {
				out.println(-1);
			}
		}
		else {
			if (ones > 0) {
				int moves = n - ones;
				out.println(moves);
			}
			else {
				int gcd = a[0];
				
				for (int i = 1; i < n; i++) {
					gcd = getGCD(gcd, a[i]);
				}
				
				
				
				if (gcd != 1) { // Not possible if gcd of all numbers is not 1.
					out.println(-1);					
				}
				else {
					int closest = n;
					
				    for (int i = 0; i < n; i++) {
				        gcd = a[i];
				        
				        for (int j = i + 1; j < n; j++) {
				            gcd = getGCD(gcd, a[j]);
				            
				            if (gcd == 1) {
				                if (j - i < closest) {
				                    closest = j - i;
				                }
				                
				                break;
				            }
				        }
				    }
					
					int moves = closest + n - 1;
					out.println(moves);
				}
			}
		}
		
		
		
		
		
		out.close();
	}
	
	public static int getGCD(int a, int b) {
		if (b == 0) return a;
		
		return getGCD(b, a % b);
	}
}











	