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.
var n = +readline();
var a = readline().split(" ").map(Number);
print(solve());

function gcd(a, b) {
  if (!b) return a;
  return gcd(b, a % b);
}

function solve() {
  var cnt = 0
  for (var i = 0; i < n; i++) 
    if (a[i] != 1) 
      cnt++;
  if (cnt < n)
    return cnt;
  var g = a[0];
  for (var i = 0; i < n; i++)
    g = gcd(g, a[i]);
  if (g > 1)
    return -1;
  var ret = n;
  for (var i = 0; i < n; i++) {
    g = a[i];
    for (var j = i; j < n; j++) {
      g = gcd(g, a[j]);
      if (g == 1) {
        ret = Math.min(ret, j - i + 1);
        break;
      }
    }
  }
  return ret - 1 + n - 1;
}