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 Main {

	public static void main(String[] args) {
		FastScanner sc=new FastScanner();
		PrintWriter pw=new PrintWriter(System.out);
		while(sc.hasNext()){
			int n=sc.nextInt();
			int[]a=new int[2005];
			int[][]g=new int[2005][2005];
			int f=0;
			for(int i=1;i<=n;i++){
				a[i]=sc.nextInt();
				if(a[i]==1)f++;
				int ge=a[i];
				for(int j=i;j>=1;--j){
					ge=gcd(ge,a[j]);
					g[j][i]=ge;
				}
			}
			if(f!=0){
				pw.println(n-f);
				pw.flush();
				return;
			}
			int ans=Integer.MAX_VALUE;
			for(int i=1;i<=n;i++){
				for(int j=i;j<=n;j++){
					if(g[i][j]==1){
						ans=Math.min(ans, j-i+n-1);
					}
				}
			}
			if(ans==Integer.MAX_VALUE){
				ans=-1;
			}
			pw.println(ans);
			pw.flush();
		}

	}
	static int gcd(int a,int b){
		return a==0?b:gcd(b%a,a);
	}
}

class FastScanner {
	BufferedReader br;
	StringTokenizer st;

	public FastScanner() {
		try {
			br = new BufferedReader(new InputStreamReader(System.in),32768);
			st = new StringTokenizer("");
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	public boolean hasNext() {
		while (!st.hasMoreTokens()) {
			String line = nextLine();
			if (line == null) {
				return false;
			}
			st = new StringTokenizer(line);
		}
		return true;
	}

	public String next() {
		while(!st.hasMoreTokens()){
			st=new StringTokenizer(nextLine());
		}
		return st.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public String nextLine() {
		String line = "";
		try {
			line = br.readLine();
		} catch (Exception e) {
			e.printStackTrace();
		}
		return line;
	}
}