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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main {

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

	}
	static boolean isPrime(long k){
		if(k==2)
			return true;
		int size= (int) Math.sqrt(k)+1;
		for(int i=2;i<=size;i++)
			if(k%i==0)
				return false;
		return true;
	}

	static class TaskA {
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			
			int n;
			n= in.nextInt();
			int []array= new int[n];
			int nonZero=0;
			for(int i=0;i<n;i++){
				array[i]= in.nextInt();
				if(array[i]!=1)
					nonZero++;
			}
			
			int gcd=array[0];
			for(int i=0;i<n;i++){
				gcd= GCD(array[i],gcd);
			}
			
			if(gcd!=1){
				out.println("-1");
				return;
			}
			
			if(nonZero!=n){
				out.println(nonZero);
				return;
			}
			
			int minReplace= Integer.MAX_VALUE;
			for(int i=0;i<n-1;i++){
				gcd=array[i];
				for(int j=i+1;j<n;j++){
					gcd=GCD(array[j],gcd);
					if(gcd==1)
						minReplace= Math.min(minReplace, j-i);
				}
				
			}
			
			int ans= minReplace+n-1;
			out.println(ans);
		}

		

	}

	private static int GCD(int a, int b) {
		if(a>b){
			int temp=a;
			a=b;
			b=temp;
		}
		if(b%a==0)
			return a;
		return GCD(b%a,a);
	}
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}

}
