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.*;
import java.util.Map.Entry;

public class main {
	static HashMap<Integer, Integer>[] dp;
	static TreeMap<Integer, Integer> map = new TreeMap<>();
	public static void main(String[] args) {

		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] arr = new int[n];
		for(int i=0;i<arr.length;i++) arr[i] = in.nextInt();
		if(n == 1) {
			System.out.println(arr[0] == 1 ? 0 : -1);
			return;
		}
		int cnt = 0;
		for(int i=0;i<arr.length;i++) cnt += arr[i] == 1 ? 0 : 1;
		int i = 0;
		while(reduce(arr)) i++;
		for(int j=0;j<arr.length;j++) if(arr[j] == 1) {
			System.out.println(i + cnt);
			return;
		}
		System.out.println(-1);
	}
	
	public static boolean reduce(int[] arr) {
		boolean change = false;
		int pre = arr[0];
		arr[0] = gcd(arr[0], arr[1]);
		for(int i=1;i<arr.length;i++) {
			int c = gcd(pre, arr[i]);
			pre = arr[i];
			if(pre != c) change = true;
			arr[i] = c;
			if(c == 1) return false;
		}
		return change;
	}
	
	public static int gcd(int a, int b) {
		if(b == 0) return a;
		return gcd(b, a%b);
	}
	
	public static boolean same(int[] arr) {
		int c = arr[0];
		for(int i:arr) if(c != arr[i]) return false;
		return true;
	}
}
