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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class CF892C {
	static int gcd(int a, int b) {
		if (a == 0 || b == 0)
			return a + b; // base case
		return gcd(b, a % b);
	}

	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int[] arr = new int[n];
		int c = 0;
		for (int i = 0; i < arr.length; i++) {
			arr[i] = sc.nextInt();
			if(arr[i] == 1)
				c++;
		}
		if(c != 0){
			pw.println(n-c);
			pw.flush();
			return;
		}
		int dist = 5000;
		int first = -1;
		int last = -1;
		for (int i = 0; i < arr.length; i++) {
			int g = arr[i];
			for (int j = i+1; j < arr.length; j++) {
				g = gcd(g, arr[j]);
				if(g == 1){
					if(j-i < dist){
						dist = j-i;
						first = i;
						last = j;
					}
				}
				//System.out.println(dist + " " + first + " " + last);
			}
		}
		if(first == -1)
			pw.println(-1);
		else
			pw.println(dist*2 + (n-1-last) + first);
		pw.flush();
		pw.close();
	}

	static class MyScanner {
		StringTokenizer st;
		BufferedReader br;

		public MyScanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}
}
