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
import math
import collections
from pprint import pprint
mod = 1000000007


def vector(size, val=0):
    vec = [val for i in range(size)]
    return vec


def matrix(rowNum, colNum, val=0):
    mat = []
    for i in range(rowNum):
        collumn = [val for j in range(colNum)]
        mat.append(collumn)
    return mat


n = int(input())
a = list(map(int, input().split()))
cnt = 0
for i in a:
    if i == 1:
        cnt += 1
if cnt > 0:
    print(n - cnt)
    sys.exit()
ans = 10**4
for i in range(n):
    g = a[i]
    for j in range(i + 1, n):
        g = math.gcd(g, a[j])
        if g == 1:
            ans = min(ans, n - 1 + j - i)
if ans == 10**4:
    print(-1)
else:
    print(ans)
