#P891A. Pride

    ID: 4078 Type: RemoteJudge 2000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>brute forcedpgreedymathnumber theory*1500

Pride

No submission language available for this problem.

Description

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.

What is the minimum number of operations you need to make all of the elements equal to 1?

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.

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.

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.

Samples

5
2 2 3 4 6

5

4
2 4 6 8

-1

3
2 6 9

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.