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.*;
import java.lang.Math;
import java.util.*;

public class Pride{


public static int gcd(int a, int b){
	int min = Math.min(a, b);
	int max = Math.max(a, b);
	int remainder = max % min;
	while(remainder != 0){
		max = min;
		min = remainder;
		remainder = max % min;
	}
	return min;
	
}

public static int countNumberinArray(int[] a, int key){
	int c = 0;
	for(int i : a){
		if (i == key){
			c++;
		}
	}
	return c;
}
public static int devisors(int[] a, int n){
	if (countNumberinArray(a, 1) > 0){
		return n - countNumberinArray(a, 1);
	}
	boolean possible = false;
	int l = n;
	
	for (int i = 0; i < n - 1; i++){
		int agcd = a[i];
		for (int j = i + 1; j < n; j++){
			agcd = gcd(agcd, a[j]);
			if (agcd == 1){
				possible = true;
				if (j - i < l){
					l = j - i;
				}
			}	
		}
	}
	if (possible == true){	
		return l + n - 1;
	}
	return -1;
	
}	

public static void main (String[] args) throws IOException{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	String arrayLength = br.readLine();
	int n = Integer.parseInt(arrayLength);
	String[] inputArray = br.readLine().split(" ");
	int[] a = new int[n];
	for (int i = 0; i < n; i++){
		a[i] = Integer.parseInt(inputArray[i]);
	}
	System.out.println(devisors(a, n));
	 	
}

}
