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.InputStreamReader;
import java.util.StringTokenizer;

public class CF0891A_Pride {
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner() {
			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;
		}

	}

	static void print(Object b) {
		System.out.print(b);
	}

	static void println(Object b) {
		System.out.println(b);
	}

	static void println() {
		System.out.println();
	}

	static int solution(int n, int[] arr, int ones) {
		if(ones == n)
			return 0;
		int ans = Integer.MAX_VALUE;
		
		for (int i = 0; i < n; i++) {
			int num = arr[i];
			for (int j = i + 1; j < n; j++) {
				num = gcd(num, arr[j]);
				if (num == 1) {
					ans = Math.min(ans, j - i + n - 1);
					break;
				}
			}
		}
		return ans == Integer.MAX_VALUE ? -1 : ans-ones;
	}

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scanner = new Scanner();
		int n = scanner.nextInt();
		int[] arr = new int[n];
		int ones = 0;
		for (int i = 0; i < n; i++) {
			arr[i] = scanner.nextInt();
			if(arr[i] == 1)
				ones++;}
		println(solution(n, arr, ones));
	}

}
