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.
def read():
	return list(map(int, input().split()))


def gcd(a, b):
	while b:
		a, b = b, a % b
	return a

def check(l):
	for t in l:
		if t != 1:
			return False
	else:
		return True

def main():
	n = int(input())
	l = read()

	ones = len(list(filter(lambda i: i == 1, l)))
	if ones > 0:
		return n - ones
	sum = 1e10
	for i in range(n - 1):
		g = 0
		for j in range(i, n):
			g = gcd(g, l[j])
			if g == 1:
				sum = min(sum, j - i + n - 1)
	return sum if sum != 1e10 else -1
print(main())