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.Scanner;

public class Main {

	private static boolean check(int n) {
		
		for (int i = 0;i < n;i ++) {
			if (input[i] == 1) {
				return true;
			}
		}
		return false;
		
	}
	
	private static int gcd(int a , int b) {
		
		while (b > 0) {
			int t = a;
			a = b;
			b = t % a;
		}
		return a;
		
	}
	
	private static int[] input = new int[10000];
	
	public static void main(String[] args) throws Exception {		
	
		Scanner scan = new Scanner(System.in);	
	
		int i , j , n = scan.nextInt();
		for (i = 0;i < n;i ++) {
			input[i] = scan.nextInt();
		}
		if (check(n)) {
			int ans = 0;
			for (i = 0;i < n;i ++) {
				if (input[i] != 1) {
					ans ++;
				}
			}
			System.out.println(ans);
		} else {
			int ans = - 1;
			for (i = 0;i < n;i ++) {
				for (j = i + 1;j < n;j ++) {
					if (gcd(input[i] , input[j]) == 1) {
						int temp = j - i + n - 1;
						if (temp < ans || ans < 0) {
							ans = temp;
						}
					}
				}
			}			
			for (i = 0;i < n;i ++) {
				int left = i - 1 , right = i + 1;
				if (left >= 0 && right < n) {
					int g = gcd(input[i] , gcd(input[left] , input[right]));
					if (g == 1) {
						int temp = 2 + n - 1;
						if (temp < ans || ans < 0) {
							ans = temp;
						}
					}
				}
			}
			System.out.println(ans);
		}
	
	}
	
	
}








