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 C {
	public static void main(String[] args)throws Throwable {
		MyScanner sc=new MyScanner();
		PrintWriter pw=new PrintWriter(System.out);
		
		int cntOne=0;
		int n=sc.nextInt();
		int [] a=new int [n];
		int g=sc.nextInt();
		a[0]=g;
		if(g==1)
			cntOne++;
		for(int i=1;i<n;i++){
			a[i]=sc.nextInt();
			if(a[i]==1)
				cntOne++;
			g=gcd(g, a[i]);
		}
		if(g!=1)
			pw.println(-1);
		else{
			if(cntOne>0)
				pw.println(n-cntOne);
			else{
				int ans=2*n-2;
				for(int i=0;i<n-1;i++){
					int tmp=1;
					int [] b=Arrays.copyOf(a, n);
					b[i]=gcd(b[i], b[i+1]);
					for(int j=i-1;j>=0;j--){
						b[j]=gcd(b[j], b[j+1]);
						tmp++;
					}
					if(b[0]!=1)
						continue;
					for(int j=1;j<n;j++){
						if(b[j]!=1){
							b[j]=gcd(b[j], b[j-1]);
							tmp++;
						}
					}
					ans=Math.min(ans, tmp);
				}
				
				pw.println(ans);
			}
		}
		
		pw.flush();
		pw.close();
	}
	
	static int gcd(int a,int b){
		return b==0? a : gcd(b, a%b);
	}
	
	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {while (st == null || !st.hasMoreElements()) {
			try {st = new StringTokenizer(br.readLine());}
			catch (IOException e) {e.printStackTrace();}}
		return st.nextToken();}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine(){String str = "";
		try {str = br.readLine();}
		catch (IOException e) {e.printStackTrace();}
		return str;}
	}
}