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.
from fractions import gcd
n=int(raw_input())
a=list(map(int,raw_input().split()))

def num_of_ones(a):
    one_cnt=0
    for i in a:
        if i==1:
            one_cnt+=1
    return one_cnt

def reti(a):
    if a[0]==1:
        return 0
    for i in xrange(len(a)):
        for j in xrange(len(a)-i-1):
            a[j] = gcd(a[j],a[j+1])
            if a[j]==1:
                return i

one_cnt = num_of_ones(a)
level = reti(a)
if level==None:
    print -1
else:
    print len(a)-one_cnt+level