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 math


def main():
    input()
    numList = list(map(int, input().split()))
    cnt = numList.count(1)
    if (cnt > 0):
        print(str(len(numList) - cnt))
        return
    minimum = -1
    for L in range(0, len(numList)):
        gcdCounter = -1
        for R in range(L + 1, len(numList)):
            if R == L + 1:
                gcdCounter = math.gcd(numList[L], numList[R])
            else:
                gcdCounter = math.gcd(gcdCounter, numList[R])
            if gcdCounter == 1:
                if minimum == -1:
                    minimum = (R - L) + (len(numList) - 1)
                else:
                    minimum = min(minimum, (R - L) + (len(numList) - 1))
    print(minimum)


if __name__ == '__main__':
    main()
