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 java.io.BufferedInputStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;


public class C446_D2_Pride {
  public static void main(String []args) throws IOException {
    new Solution().solve();
  }
}

class Solution {
  FastReader fr = new FastReader();
  BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

  public void solve() throws IOException {
    int count = fr.nextInt();
    int []num = new int[count];
    int ones = 0;
    for (int i = 0; i < count; i++) {
      num[i] = fr.nextInt();
      if (num[i] == 1) {
        ones++;
      }
    }

    if (count == 1 && num[0] == 1) {
      System.out.println(0);
      return;
    }

    int ind = count;
    while (ind > 0) {
      for (int i = 1; i < ind; i++) {
        int gcd = gcd(num[i-1], num[i]);
        if (gcd == 1) {
          System.out.println(count + (count - ind) - ones);
          return;
        }
        num[i-1] = gcd;
      }
      ind--;
    }

    System.out.println(-1);

  }

  public int gcd(int n1, int n2) {
    if (n1 < n2) {
      return gcd(n2, n1);
    }
    if (n1 % n2 == 0) {
      return n2;
    }
    return gcd(n2, n1 % n2);
  }
}

class FastReader {
  private InputStream is;
  private int bufferSize = 1 << 17;
  private byte []buffer = new byte[bufferSize];
  private int currentIndex = 0;
  private int lastIndex = 0;

  public FastReader() {
    is = new BufferedInputStream(System.in);
//		try {
//			is = new BufferedInputStream(new FileInputStream(new File("test.txt")));
//		} catch (FileNotFoundException e) {
//			e.printStackTrace();
//		}
  }

  public int nextInt() {
    int result = 0;
    int minus = 1;

    byte character = readNext();

    while (character == ' ' || character == '\n' || character == '\r') {
      character = readNext();
    }

    if (character == '-') {
      minus = -1;
      character = readNext();
    }

    while (character != ' ' && character != '\n' && character != '\r' && character != -1) {
      result = result * 10 + (character - '0');
      character = readNext();
    }

    return minus*result;
  }

  public long nextLong() {
    long result = 0;
    int minus = 1;

    byte character = readNext();

    while (character == ' ' || character == '\n' || character == '\r') {
      character = readNext();
    }

    if (character == '-') {
      minus = -1;
      character = readNext();
    }

    while (character != ' ' && character != '\n' && character != '\r' && character != -1) {
      result = result * 10 + (character - '0');
      character = readNext();
    }

    return minus*result;
  }

  public String nextString() {
    StringBuffer result = new StringBuffer();

    byte character = readNext();

    while (character == ' ' || character == '\n' || character == '\r') {
      character = readNext();
    }

    while (character != ' ' && character != '\n' && character != '\r' && character != -1) {
      result.append((char)character);
      character = readNext();
    }

    return result.toString();
  }

  public String nextLine() {
    StringBuffer result = new StringBuffer();

    byte character = readNext();

    while (character == '\n' || character == '\r') {
      character = readNext();
    }

    while (character != '\n' && character != '\r' && character != -1) {
      result.append((char)character);
      character = readNext();
    }

    return result.toString();
  }

  private byte readNext() {
    if (currentIndex == lastIndex) {
      try {
        lastIndex = is.read(buffer, 0, bufferSize);
      } catch (IOException e) {
        throw new RuntimeException("What?");
      }
      if (lastIndex == -1) {
        buffer[0] = -1;
      }
      currentIndex = 0;
    }

    return buffer[currentIndex++];
  }
}