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.reflect.Array;
import java.util.*;
import java.text.*;
import java.math.*;

public class Solution {
	private static Scanner input = new Scanner(System.in);
	
    public static void main(String[] args) {
    	int n = input.nextInt();
    	int a[] = new int[n];
    	
    	int ones = 0;
    	for (int i = 0; i < n; i++) {
    		a[i] = input.nextInt();
    		
    		if (a[i] == 1) {
    			ones++;
    		}
    	}
    	
    	if (ones > 0) {
    		System.out.println(n - ones);
    		return;
    	}
    	
    	int min = Integer.MAX_VALUE;
    	boolean found = false;
    	for (int i = 0; i < n; i++) {
    		int curr = a[i];
    		for (int j = i + 1; j < n; j++) {
    			curr = gcd(curr, a[j]);
    			if (curr == 1) {
    				min = Math.min(j - i, min);
    				found = true;
    			}
    		}
    	}
    	
    	if (!found) {
    		System.out.println(-1);
    	}
    	else {
    		System.out.println(min + n - 1);
    	}
    	
    }
    
    private static int gcd(int number1, int number2) {
    	if (number2 == 0) 
    		return number1;
    	return gcd(number2, number1%number2); 
    }

}