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.*;
import java.util.*;

public class A implements Runnable{
	public static void main (String[] args) {new Thread(null, new A(), "_cf", 1 << 27).start();}

	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);

		int n = fs.nextInt(), a[] = new int[n];
		int res = (int)1e9, cnt = 0;
		for(int i = 0; i < n; i++) {
			a[i] = fs.nextInt();
			if(a[i] == 1) cnt++;
		}
		
		if(cnt > 0) {
			out.println(n-cnt);
			out.flush();
			return;
		}
		
		
		for(int i = 0; i < n; i++) {
			int gcd = a[i];
			for(int j = i; j < n; j++) {
				gcd = gcd(gcd, a[j]);
				if(gcd == 1) {
					int len = j-i;
					len += n-1;
					res = Math.min(res, len);
				}
			}
		}
		
		if(res == (int)1e9) res = -1;
		out.println(res);
		out.close();
	}
	
	int gcd (int a, int b) {
		if(a == 0) return b;
		return gcd(b%a, a);
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner() {
			try	{
				br = new BufferedReader(new InputStreamReader(System.in));
				//                br = new BufferedReader(new FileReader("testdata.out"));
				st = new StringTokenizer("");
			} catch (Exception e){e.printStackTrace();}
		}
		public String next() {
			if (st.hasMoreTokens())	return st.nextToken();
			try {st = new StringTokenizer(br.readLine());}
			catch (Exception e) {e.printStackTrace();}
			return st.nextToken();
		}
		public int nextInt() {return Integer.parseInt(next());}
		public long nextLong() {return Long.parseLong(next());}
		public double nextDouble() {return Double.parseDouble(next());}

		public String nextLine() {
			String line = "";
			try {line = br.readLine();}
			catch (Exception e) {e.printStackTrace();}
			return line;
		}
		public Integer[] nextIntegerArray(int n) {
			Integer[] a = new Integer[n];
			for(int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for(int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
		public char[] nextCharArray() {return nextLine().toCharArray();}
	}

}
