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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class B {
	
	public static void main(String[] args) throws IOException {
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));		
		int n = readInteger(br);
		int[] a = readIntegerArray(br);
		br.close();
		
		int gcdTotal = 0;
		int oneCount = 0;
		for (int number : a) {
			gcdTotal = gcd(gcdTotal, number);
			if (number == 1) oneCount++;
		}
			
		if (gcdTotal > 1) {
			System.out.println(-1);
			return;
		}
		
		if (oneCount > 0) {
			System.out.println(n - oneCount);
			return;
		}
		
		int shortestLength = Integer.MAX_VALUE;
		for (int left = 0; left < n; left++) {
			int curGcd = 0;
			for (int right = left; right < n; right++) {
				if (right - left + 1 >= shortestLength) break;
				curGcd = gcd(curGcd, a[right]);
				if (curGcd == 1) {
					shortestLength = right - left + 1;
					break;
				}
			}
		}
		int ans = (n - 1) + (shortestLength - 1);
		System.out.println(ans);
	}
	
	private static int gcd(int a, int b) {
		if (b == 0) return a;
		return gcd(b, a % b);
	}
	
	private static int readInteger(BufferedReader br) throws IOException {
		return Integer.parseInt(br.readLine().trim());
	}
	
	private static int[] readIntegerArray(BufferedReader br) throws IOException {
		String[] numbersString = br.readLine().trim().split(" ");
		int[] numbers = new int[numbersString.length];
		for (int i = 0; i < numbers.length; i++) {
			numbers[i] = Integer.parseInt(numbersString[i]);
		}
		return numbers;
	}

}
