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 ProblemD {

	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);

	static int gcd(int a, int b) {
		while (b > 0) {
			int temp = b;
			b = a % b;
			a = temp;
		}
		return a;
	}

	public static void main(String[] args) throws IOException {
		int n = sc.nextInt();
		int a[] = new int[n], ones = 0;
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			if (a[i] == 1)
				ones++;
		}
		if (ones > 1) {
			System.out.println(n - ones);
			return;
		}
		int ans = -1;
		for (int i = 0; i < n; i++) {
			int gcd = a[i];
			for (int j = i; j < n; j++) {
				gcd = gcd(gcd, a[j]);
				if (gcd == 1) {
					if (ans == -1)
						ans = j - i;
					else
						ans = Math.min(ans, j - i);
					break;
				}
			}
		}
		pw.println(ans == -1 ? ans : ans + n - 1);
		pw.flush();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(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());
		}
	}
}