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

n=int(input())
l=[int(i) for i in input().split()]
one=0
for i in range(n):
    if(l[i]==1):
       one+=1

if(one>0):
    print(n-one)
else:
    if(len(l)==1):
        print(-1)
    else:
        ans=0
        done=0
        while(done==0):
            gcd1=l
            gcd2=[]
            if(len(gcd1)==0):
                print(-1)
                break
            same=1
            for i in range(len(gcd1)-1):
                if(gcd1[i]!=gcd1[i+1]):
                    same=0
                a=math.gcd(gcd1[i], gcd1[i+1])
                if(a==1):
                    done=1
                    print(len(gcd1)+ans)
                    break
                gcd2.append(a)
            l=gcd2
            ans+=2
            if(same==1):
                print(-1)
                break
            