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.
import sys
read = lambda: sys.stdin.readline().strip()
readi = lambda: map(int, read().split())
from collections import *
from math import *

def gcd(a, b):
    while a != b:
        if a > b:
            a = a - b
        else:
            b = b - a
    return a

n = int(read())
nums = list(readi())
ones = nums.count(1)
if ones > 0:
    print(n - ones)
else:
    ans = None
    minimum = float('inf')
    for i in range(n):
        gc = nums[i]
        for j in range(i+1, n):
            gc = gcd(gc, nums[j])
            if gc == 1:
                minimum = min(minimum, j - i)
                break

    if minimum != float('inf'):
        ans = minimum + (n - 1)
        print(ans)
    else:
        print(-1)