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.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/*
 public class _892C {

 }

 */
public class _892C {
  public void solve() throws FileNotFoundException {
    InputStream inputStream = System.in;

    InputHelper in = new InputHelper(inputStream);

    // actual solution
    int n = in.readInteger();

    int[] a = new int[n];

    for (int i = 0; i < n; i++) {
      a[i] = in.readInteger();
    }

    int ones = 0;

    for (int i = 0; i < n; i++) {
      if (a[i] == 1) {
        ones++;
      }
    }

    if (ones > 0) {
      System.out.println(n - ones);
      return;
    }

    int fgcd = a[0];

    for (int i = 1; i < n; i++) {
      fgcd = gcd(fgcd, a[i]);
    }

    if (fgcd > 1) {
      System.out.println("-1");
      return;
    }

    int[] la = new int[n];

    int minl = n;

    for (int i = 0; i < n; i++) {

      int al = n;
      int l = 0;
      int cgcd = a[i];
      for (int j = i + 1; j < n; j++) {
        l++;
        cgcd = gcd(cgcd, a[j]);

        if (cgcd == 1) {
          al = l;
          break;
        }
      }

      if (al < minl) {
        minl = al;
      }
    }

    System.out.println(minl + n - 1);
    // end here
  }

  int gcd(int a, int b) {
    if (b == 0) {
      return a;
    } else {
      return gcd(b, a % b);
    }
  }

  public static void main(String[] args) throws FileNotFoundException {
    (new _892C()).solve();
  }

  class InputHelper {
    StringTokenizer tokenizer = null;
    private BufferedReader bufferedReader;

    public InputHelper(InputStream inputStream) {
      InputStreamReader inputStreamReader = new InputStreamReader(inputStream);
      bufferedReader = new BufferedReader(inputStreamReader, 16384);
    }

    public String read() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          String line = bufferedReader.readLine();
          if (line == null) {
            return null;
          }
          tokenizer = new StringTokenizer(line);
        } catch (IOException e) {
          e.printStackTrace();
        }
      }

      return tokenizer.nextToken();
    }

    public Integer readInteger() {
      return Integer.parseInt(read());
    }

    public Long readLong() {
      return Long.parseLong(read());
    }
  }
}
