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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Iterator;
import java.util.StringTokenizer;

public class P {

	static class Pair implements Comparable<Pair> {
		int r, c;

		Pair(int i, int j) {
			r = i;
			c = j;
		}

		@Override
		public int compareTo(Pair o) {
			if (c == o.c)
				return r - o.r;
			return c - o.c;
		}
	}

	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	public static void main(String[] args) throws IOException {

		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int N = sc.nextInt();
		int o = 0;
		int[] a = new int[N];
		for (int i = 0; i < N; ++i) {
			a[i] = sc.nextInt();
			if (a[i] == 1)
				o++;
		}
		if (o != 0) {
			out.println(N - o);
		} else {
			int ans = N + 1;
			for (int i = 0; i < N; ++i) {
				int curGCD = a[i], j = i + 1;
				for (j = i + 1; j < N && curGCD > 1; ++j)
					curGCD = gcd(curGCD, a[j]);

				if (curGCD == 1) {
					ans = Math.min(j - i, ans);
				}
			}
			out.println(ans == N + 1 ? -1 : N + ans - 2);
		}

		out.flush();
		out.close();

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String file) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
	}

}