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 sys import stdin, stdout
from functools import reduce
from math import gcd

n = int(input())
a = list(map(int, input().split()))


g = reduce(gcd, a)
if g != 1:
    print(-1)
    exit()

cnt1 = a.count(1)
if cnt1 > 0:
    ans = n - cnt1
    print(ans)
    exit()


min_len = n
for i in range(n):
    g = 0
    for j in range(i, n):
        g = gcd(g, a[j])
        if g == 1:
            cur_len = j - i
            min_len = min(min_len, cur_len)
            break

ans = min_len + n-1
print(ans)