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.*;
import java.util.*;
/*

4
2 1 1 1

6
6 15 10 6 15 10
 */
public class a {
	public static void main(String[] arg) throws IOException {
		new a();
	}
	public a() throws IOException {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		int[] vs = new int[n];
		for(int i = 0; i < n; i++) {
			vs[i] = in.nextInt();
		}
		int run = vs[0];
		for(int i = 1; i < n; i++) run = gcd(run, vs[i]);
		if(run != 1) out.println(-1);
		else {
			int minDist = n-1;
			int numOnes = 0;
			for(int i = 0; i < n; i++) {
				if(vs[i] == 1) numOnes++;
				int val = vs[i];
				for(int j = i; j < n; j++) {
					val = gcd(val, vs[j]);
					if(val == 1) {
						minDist = Math.min(minDist, Math.abs(i-j));
					}
				}
			}
			if(numOnes == n) out.println(0);
			else if(numOnes > 0) out.println(n-numOnes);
			else out.println(n-numOnes-1+minDist);
		}
		in.close(); out.close();
	}
	int gcd(int a, int b) {
		return b==0?a:gcd(b, a%b);
	}
	class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
			st = new StringTokenizer("");
		}
		public void close() throws IOException {
			br.close();
		}
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		public String next() throws IOException {
			while(!st.hasMoreElements()) st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
	}
}
