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.util.StringTokenizer;

public class Test {

    public static void main(String[] args) {
        FastReader in = new FastReader();
        int n = in.nextInt();
        int[] x = new int[n];

        int current = in.nextInt();
        x[0] = current;

        boolean ans = false;
        int ones = current == 1 ? 1 : 0;
        for (int i = 1; i < n; i++) {
            x[i] = in.nextInt();
            int v = gcd(current, x[i]);
            if (x[i] == 1) {
                ones++;
            }
            if (v == 1) {
                ans = true;
            }
            current = x[i];
        }


        if (ans || (x.length == 1 && x[0] == 1)) {
            System.out.println(n - ones);
            return;
        }


        int total = 0;
        for (int i = 0; i + 1 < n; i++) {
            int v = gcd(x[i], x[i + 1]);

            if (v != x[i + 1] && v != 1) {
                total++;
            }

            x[i + 1] = v;

            v = gcd(x[i], x[i + 1]);

            if (v == 1) {
                ans = true;
                total += n;
                break;
            }
        }

        if (ans)
            System.out.println(total);
        else
            System.out.println(-1);
    }

    static int gcd(int a, int b) {
        // Everything divides 0
        if (a == 0 || b == 0)
            return 0;

        // base case
        if (a == b)
            return a;

        // a is greater
        if (a > b)
            return gcd(a - b, b);
        return gcd(a, b - a);
    }
}

class FastReader {

    BufferedReader br;
    StringTokenizer st;

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

    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;
    }
}