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 gcd(x, y):
    if x < y:
        x, y = y, x
    while x != y and y != 0:
        x, y = y, x % y
    return x

def one(a):
    b = []
    for i in range(1, len(a)):
        temp = gcd(a[i-1], a[i])
        if temp == 1:
            return True, []
        b.append(temp)
    return False, b

cnt = a.count(1) # there may be more than 1 in a
if cnt > 0:
    print n - cnt
else:
    t, b = one(a)
    while not t and len(b) > 1:
        cnt += 1
        a = b
        t, b = one(a)
    if not t:
        print -1
    else:
        print cnt + n        
        
