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 queue import PriorityQueue
from queue import Queue
import math
from collections import defaultdict
import sys
import operator as op
from functools import reduce


n= int(input())
ar= list(map(int, input().split()))
 
if ar.count(1) > 0:
	print(n- ar.count(1))
else: 
	mi = n + 1
	for k in range(n):
		it = k+1
		g= ar[k]
		while it < n:
			g = math.gcd(g, ar[it])
			if g == 1:
				mi = min(mi, it - k)
				break
			it += 1
	 
	if mi == n+1:
		print(-1)
	else:
		print(mi+ n- 1)






