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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jenish
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        pride solver = new pride();
        solver.solve(1, in, out);
        out.close();
    }

    static class pride {
        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int arr[] = new int[n];
            int ones = 0;
            long gcd = 0;
            for (int i = 0; i < n; i++) {

                arr[i] = in.scanInt();
                if (arr[i] == 1)
                    ones++;


                if (i == 0)
                    gcd = arr[i];
                else
                    gcd = GCD(gcd, arr[i]);
            }


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


            if (gcd != 1) {
                out.println(-1);
                return;
            }


            int minrange = Integer.MAX_VALUE;
            for (int i = 0; i < n; i++) {
                long d = 0;
                for (int j = i; j < n; j++) {
                    if (j == i) {
                        d = arr[j];
                    } else {
                        d = GCD(d, arr[j]);
                    }

                    if (d == 1) {
                        if (j - i + 1 < minrange)
                            minrange = j - i + 1;
                        break;
                    }
                }
            }

            out.println(minrange + n - 1 - 1);


        }

        public long GCD(long A, long B) {
            if (B == 0)
                return A;
            else
                return GCD(B, A % B);
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                    ;
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}

