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.

// Problem : C. Pride
// Contest : Codeforces Round #446 (Div. 2)
// URL : https://codeforces.com/contest/892/problem/C
// Memory Limit : 256 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cp-editor)

import java.io.*;
import java.util.*;

public class a {
    public static void main(String[] args) throws IOException {
        FastReader scan = new FastReader();
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("taming.out")));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        Task solver = new Task();
        //int t = scan.nextInt();
        int t = 1;
        for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
        out.close();
    }
    static class Task {
        public void solve(int testNumber, FastReader sc, PrintWriter pw) {
        	int n = sc.nextInt();
        	int[] arr=  new int[n];
        	int x = n;
        	for(int i=0;i<n;i++){
        		arr[i]=sc.nextInt();
        		if(arr[i]==1){
        			x--;
        		}
        	}
        	int max = Integer.MAX_VALUE;
        	for(int i=0;i<n;i++){
        		int gcdd = arr[i];
        		for(int j=i+1;j<n;j++){
        			gcdd = gcd(gcdd,arr[j]);
        			if(gcdd==1){
        				max = Math.min(max,j-i+x-1);
        			}
        		}
        	}
        	if(x==0){
        		pw.println(0);return;
        	}
        	if(max==Integer.MAX_VALUE){
        		pw.println(-1);
        		return;
        	}
        	pw.println(Math.max(max,0));
        }
        int gcd(int a, int b){
        	return b==0?a:gcd(b,a%b);
        }

    }
    static class tup implements Comparable<tup>{
        int a, b,c;
        tup(){};
        tup(int a, int b, int c){
            this.a=a;
            this.b=b;
            this.c=c;
        }

        @Override
        public int compareTo( tup o2) {
            return o2.b!=b?Integer.compare(o2.b,b):Integer.compare(o2.a,a);
        }
    }
    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        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;
        }
    }

}