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.
//      これを翻訳している間、あなたはあなたの人生のいくつかの貴重な瞬間を無駄にしました


import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


public class Solution {
    static PrintWriter fop = new PrintWriter(System.out);


    public static void main(String[] args) {
        FastScanner fsca = new FastScanner();

        int n = fsca.nextInt() ;
        int a[] = fsca.readArray(n) ;
        int ct = 0 ;
        for (int i = 0; i <n ; i++)
            if (a[i] == 1)ct++ ;
            if (ct > 0){
                System.out.println(n - ct);
                return;
            }

        int ans = Integer.MAX_VALUE ;
        for (int i = 0; i <n ; i++) {
            int gcd = 0 ;
            for (int j = i; j <n ; j++) {
                gcd = gcd(gcd , a[j]) ;
                if (gcd == 1){
                    ans = Math.min(ans , (j-i + n-1)) ;
                    break;
                }
            }
        }
        if (ans == Integer.MAX_VALUE)
            ans = -1;

        System.out.println(ans);






















        fop.flush();
        fop.close();


    }
    /*-----------------------------------------------------------------------------------------------------------------------------------------------*/
    // template starts from here :

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

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


    static final Random random = new Random();

    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(long[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n);
            long temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }


    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

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

        int[][] readMat(int n, int m) {
            int a[][] = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = nextInt();
            return a;
        }
        char[][] readCharMat(int n, int m) {
            char a[][] = new char[n][m];
            for (int i = 0; i < n; i++) {
                String s = next();
                for (int j = 0; j < m; j++)
                    a[i][j] = s.charAt(j) ;
            }
            return a;
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

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

    static void print(int a[], int n) {
        for (int i = 0; i < n; i++)
            fop.append((a[i]) + " ");
        // fop.append("\n") ;
    }

    static void print(long a[], int n) {
        for (int i = 0; i < n; i++)
            fop.append((a[i]) + " ");
        // fop.append("\n") ;
    }
}
        