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.
#include <bits/stdc++.h>
long long int gcd(long long int a, long long int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
int main() {
  int n;
  long long int a[2010];
  std::cin >> n;
  bool one = false;
  for (int i = 0; i < n; ++i) {
    std::cin >> a[i];
    if (a[i] == 1) one = true;
  }
  if (one) {
    int ans = 0;
    for (int i = 0; i < n; ++i)
      if (a[i] != 1) ++ans;
    std::cout << ans;
    return 0;
  }
  long long int gcdd = a[0];
  for (int i = 0; i < n; ++i) {
    gcdd = gcd(gcdd, a[i]);
  }
  if (gcdd != 1) {
    std::cout << -1;
    return 0;
  }
  int min = n + 1;
  for (int i = 0; i < n; ++i) {
    int gcdd = a[i];
    for (int j = i + 1; j < n; ++j) {
      gcdd = gcd(gcdd, a[j]);
      if (gcdd == 1) {
        min = std::min(j - i, min);
        break;
      }
    }
  }
  std::cout << min + n - 1;
}
