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>
using namespace std;
int n, a[2006];
int one, g, mn = 1e9;
int gcd(int _a, int _b) { return _b == 0 ? _a : gcd(_b, _a % _b); }
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    g = gcd(g, a[i]);
    if (a[i] == 1) one++;
  }
  if (one != 0) {
    printf("%d\n", n - one);
    return 0;
  }
  if (g != 1) {
    puts("-1");
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    int b = a[i];
    for (int j = i + 1; j <= n; j++) {
      b = gcd(b, a[j]);
      if (b == 1) {
        mn = min(mn, j - i);
        break;
      }
    }
  }
  printf("%d\n", mn + n - 1);
  return 0;
}
