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.util.*;

public class Codeforces892C {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sp = br.readLine().split(" ");
		int n = Integer.parseInt(sp[0]);
		sp = br.readLine().split(" ");
		int[] lst = new int[n];
		for (int i = 0; i < n; i++) {
			lst[i] = Integer.parseInt(sp[i]);
		}
		
		int[][] gcd = new int[n][n];
		for (int i = 0; i < n; i++) {
			gcd[i][i] = lst[i];
		}
		for (int i = 0; i < n-1; i++) {
			for (int j = i+1; j < n; j++) {
				gcd[i][j] = gcd(gcd[i][j-1], lst[j]);
			}
		}
		
		if (gcd[0][n-1] > 1) {
			System.out.println(-1);
		}
		else {
			int min = n;
			for (int i = 0; i < n; i++) {
				for (int j = i; j < n; j++) {
					if (gcd[i][j] == 1) {
						min = Math.min(min, j-i);
					}
				}
			}
			if (min > 0)
				System.out.println(min+n-1);
			else {
				int counter = 0;
				for (int i = 0; i < n; i++) {
					if (lst[i] != 1) {
						counter++;
					}
				}
				System.out.println(counter);
			}
		}
	}
	
	public static int gcd(int a, int b) {
		if (a == b) {
			return a;
		}
		else if ((a == 0) || (b == 0)) {
			return a+b;
		}
		else if (a > b) {
			return gcd(b, a%b);
		}
		else {
			return gcd(b, a);
		}
	}
}