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.
def main():
    n = int(input())
    a = list(map(int, input().split()))

    if gcd_of_array(a) != 1:
        print(-1)
    else:
        if a.count(1) == 0:
            left = 2
            right = n
            best = n

            while left <= right:
                mid = (left + right) // 2
                # print("left = {} - right = {} - mid = {}".format(left, right, mid))
                if check(a, mid):
                    right = mid - 1
                    best = min(mid, best)
                    # print('ok')
                else:
                    # print('f/ailed')
                    left = mid + 1

            ans = n + best - 2

            print(ans)
        else:
            print(n - a.count(1))


def check(a, le):
    # print(len(a) - le)
    for i in range(len(a) - le + 1):
        # print(le, i, i+le-1)
        if gcd_of_array(a[i:i+le]) == 1:
            return True
    return False


def gcd(a, b):
    if a == 0:
        return b
    else:
        return gcd(b % a, a)


def gcd_of_array(a):
    res = a[0]
    for i in a:
        res = gcd(res, i)
        if res == 1:
            break
    return res


main()