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 gcd1(x,y):
    if y==0:
        return x
    else:
        return gcd1(y,x%y)
def minimumCount(a):
    count_one=sum([1 for i in a if i==1])
    if count_one>0:
        return len(a)-count_one
    L=0
    R=1
    G=a[L]
    count=0
    while R!=len(a):
        G=gcd1(G,a[R])
        if gcd1(a[L],a[R])==1:
            count=0
            break
        if G!=1:
            if G!=a[L] or G!=a[R]:
                count=count+1
        L+=1
        R+=1
    if G==1:
        return count+len(a)
    else:
        return -1
if __name__=="__main__":
    n=raw_input()
    list_of_numbers=[int(i) for i in  raw_input().split()]
    print(minimumCount(list_of_numbers))