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 == 0 :
        return b 
     
    return gcd(b%a, a)
n=input()
a=map(int,raw_input().split(" "))
cnt=0
for i in range(n):
        if(a[i]==1):
                cnt+=1
if(cnt>0):
        print(n-cnt)
else:
        count=9999999999
        for i in range(n-1):
                l=a[i]
                for j in range(i,n):
                        l=gcd(l,a[j])
                        if(l==1):
                                count=min(j-i,count)
                                break
        if(count==9999999999):
                print -1
        else:
                print count+n-1        