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;

public class Pride {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        in.readLine();
        String[] inputs = in.readLine().split("\\s+");
        int[] numbers = new int[inputs.length];
        int oneCounter = 0;
        for (int i = 0; i < inputs.length; i++) {
            numbers[i] = Integer.parseInt(inputs[i]);
            if (numbers[i] == 1) {
                oneCounter++;
            }
        }
        if (oneCounter > 0) {
            System.out.print(numbers.length - oneCounter);
            return;
        }

        System.out.println(solve(numbers));
    }

    private static int solve(int[] numbers) {
        int minMoveToGenerateOne = Integer.MAX_VALUE;
        for (int l = 0; l < numbers.length - 1; l++) {
            int gcd = numbers[l];
            for (int r = l + 1; r < numbers.length; r++) {
                gcd = gcd(gcd, numbers[r]);
                if (gcd == 1) {
                    int numMovesToGenerateOne = r - l;
                    if (numMovesToGenerateOne < minMoveToGenerateOne) {
                        minMoveToGenerateOne = numMovesToGenerateOne;
                    }
                }
            }
        }
        if (minMoveToGenerateOne == Integer.MAX_VALUE) {
            return -1;
        } else {
            return numbers.length - 1 + minMoveToGenerateOne;
        }
    }

    public static int gcd(int a, int b) {
        int max = Math.max(a, b);
        int min = Math.min(a, b);
        return orderedGcd(max, min);
    }

    private static int orderedGcd(int bigger, int smaller) {
        int remaineder = bigger % smaller;
        if (remaineder == 0) {
            return smaller;
        }
        return orderedGcd(smaller, remaineder);
    }
}
