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())
arr = list(map(int, input().split()))


def GCD(x, y):
    if y > 0:
        return GCD(y, x % y)
    else:
        return x


allGCD = arr[0]
for i in arr:
    allGCD = GCD(allGCD, i)

if allGCD > 1:
    print(-1)
else:
    ones = 0
    for i in arr:
        if i == 1:
            ones += 1

    if ones > 1:
        print(n - ones)
    else:
        res = 2000000000
        for i in range(n):
            tmp = arr[i]
            for j in range(i, n):
                tmp = GCD(tmp, arr[j])
                if tmp == 1:
                    res = min(res, j-i)
        print(n + res - 1)





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85% copied. LEL

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