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.
#!/usr/bin/python2
# -*- coding: utf-8 -*-

import sys
from fractions import gcd

def rl(proc=None):
    if proc is not None:
        return proc(sys.stdin.readline())
    else:
        return sys.stdin.readline().rstrip()

def srl(proc=None):
    if proc is not None:
        return map(proc, rl().split())
    else:
        return rl().split()

def main():
    rl()
    A = srl(int)
    if 1 in A:
        print len([x for x in A if x > 1])
        return
    g = reduce(gcd, A)
    if g != 1:
        print -1
        return

    N = len(A)
    r = 2 * N
    for i in xrange(len(A)):
        j = i + 1
        g = A[i]
        t = N - 1
        while g > 1 and j < len(A) and t < r:
            g = gcd(g, A[j])
            j += 1
            t += 1
        if g == 1:
            r = t
    print r




if __name__ == '__main__':
    main()
