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.*;
import java.util.*;
import java.util.stream.IntStream;

public class A implements Runnable {

    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer tok = new StringTokenizer("");

    private void init() throws FileNotFoundException {
        Locale.setDefault(Locale.US);
        String fileName = "";
        if (ONLINE_JUDGE && fileName.isEmpty()) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            if (fileName.isEmpty()) {
                in = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(fileName + ".out");
            }
        }
    }

    String readString() {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() {
        return Integer.parseInt(readString());
    }

    long readLong() {
        return Long.parseLong(readString());
    }

    double readDouble() {
        return Double.parseDouble(readString());
    }

    int[] readIntArray(int size) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = readInt();
        }
        return a;
    }

    public static void main(String[] args) {
        //new Thread(null, new _Solution(), "", 128 * (1L << 20)).start();
        new A().run();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    @Override
    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            init();
            solve();
            out.close();
            time();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    int[][] buildGraph(int n, int[] u, int[] v) {
        int[][] graph = new int[n][];
        int[] q = new int[n];
        for (int i = 0; i < u.length; i++) {
            q[u[i]]++;
            q[v[i]]++;
        }
        for (int i = 0; i < n; i++) {
            graph[i] = new int[q[i]];
        }
        for (int i = 0; i < u.length; i++) {
            graph[u[i]][--q[u[i]]] = v[i];
            graph[v[i]][--q[v[i]]] = u[i];
        }
        return graph;
    }

    private int aiverson(boolean good) {
        return good ? 1 : 0;
    }

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

    private void solve() {
        int n = readInt();
        int[] a = readIntArray(n);
        int ones = 0;
        for (int i = 0; i < n; i++) {
            ones += aiverson(a[i] == 1);
        }
        if (ones > 0) {
            out.println(n - ones);
            return;
        }
        int minLength = Integer.MAX_VALUE;
        for (int l = 0; l < n; l++) {
            int curGcd = a[l];
            for (int r = l; r < n; r++) {
                curGcd = gcd(curGcd, a[r]);
                if (curGcd == 1) {
                    minLength = Math.min(minLength, r - l + 1);
                }
            }
        }

        if (minLength == Integer.MAX_VALUE) {
            out.println(-1);
        } else {
            out.println((n - 1) + (minLength - 1));
        }
    }
}