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.
n=int(raw_input())
l=[int(i) for i in raw_input().split()]
def gcdd(arr):
    gd=0 
    for i in arr:
        gd=gcd(gd,i)
    return gd
def gcd(a,b):
    if b==0: return a 
    return gcd(b,a%b)
g=0 
for i in l: g=gcd(g,i)
if g!=1:
    print(-1)
elif l.count(1)>0:
    print(n-l.count(1))
else:
    mini=10**5 
    for i in range(n):
        g=0 
        for j in range(i,n):
            g=gcd(g,l[j])
            if g==1:
                mini=min(mini,j-i)
    print(mini+n-1)
