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(input())
ai = list(map(int,input().split()))
num = 0
ar = [[0] * n for i in range(n)] 
for i in range(n):
    ar[0][i] = ai[i]
    if ai[i] == 1:
        num += 1
def gcd(i,j):
    a = ar[i][j-1]
    b = ai[j]
    while b != 0:
        a, b = b, a % b
    ar[i+1][j] = a
    return a
if num == 0:
    ans = -1
    for i in range(1,n):
        for j in range(i,n):
            if gcd(i-1,j) == 1:
                ans = n - 1 + i
        if ans != -1:
            break
    print(ans)
else:
    print(n - num)
