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 gcd(a, b):
    if a < b:
        a,b = b,a
    while b > 0:
        r = a % b
        a,b = b,r
    return a

def solve():
    n = int(input())
    al = [int(i) for i in input().split()]
    if 1 in al:
        print(n - al.count(1))
        return
    
    ans = -1
    for i in range(n):
        t = al[i]
        for j in range(i + 1, n):
            t = gcd(t, al[j]) 
            if t == 1:
                if ans == -1:
                    ans = (j - i) + (n - 1)
                else:
                    ans = min(ans, (j - i) + (n - 1))
    print(ans)

if __name__=="__main__":
    solve()
