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.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;


public class Main {
    
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        InputReader inputReader = new InputReader(in);
        PrintWriter out = new PrintWriter(System.out);

        int n = inputReader.getNextInt();
        int[] arr = new int[n];
        int ones = 0;

        for(int i = 0; i < n; i++) {
            arr[i] = inputReader.getNextInt();
            if(arr[i] == 1) {
                ones++;
            }
        }

        int dist = n + 1;
        for(int i = 0; i < n; i++) {
            int gcd = arr[i];
            int j = i + 1;
            while(j < n) {
                gcd = gcd(arr[j], gcd);
                if(gcd == 1) {
                    break;
                } else {
                    j++;
                }
            }

            if(gcd == 1) {
                dist = Math.min(dist, j - i);
            }
        }

        if(dist == n + 1) {
            out.println(-1);
        } else {
            out.println(n - 1 + dist - ones);
        }

        in.close();
        out.close();
    }

    public static int gcd(int x, int y) {
        while(y > 0) {
            int aux = x % y;
            x = y;
            y = aux;
        }
        return x;
    }

    public static class InputReader {

        static final String SEPARATOR = " ";

        String[] split;
        int head = 0;
        BufferedReader in;

        public InputReader(BufferedReader in) {
            this.in = in;
        }

        private void fillBuffer() throws IOException {
            if(split == null || head >= split.length) {
                head = 0;
                split = in.readLine().split(SEPARATOR);
            }
        }

        public String getNextToken() throws IOException {
            fillBuffer();
            return split[head++];

        }

        public int getNextInt() throws IOException {
            return Integer.parseInt(getNextToken());
        }

        public long getNextLong() throws IOException {
            return Long.parseLong(getNextToken());
        }
    }

}