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())
A = map(int, raw_input().split())


def c(A):
    def gcd(a,b):
        if a<b:
            a,b=b,a
        while b>=1:
            a,b=b,a%b
        return a
    k=0
    if len(A)==1 and A[0]!=1:
        return -1
    one=0
    for i in range(len(A)):
        if A[i]==1:
            one+=1
    if one>=1:
        return len(A)-one

    while len(A)>=2:
        gx=A[0]
        for i in range(1,len(A),1):
            gx=gcd(gx,A[i])
            ct=gcd(A[i-1],A[i])
            if ct==1:
                return len(A)+k
            A[i-1]=ct
        A.pop()
        k+=2
        if gx>1:
            return -1

print c(A)