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.math.BigInteger;

import java.util.*;
public class A_GENERAL {

	public static void main(String[] args) {
		
		MyScanner sc = new MyScanner();
		
		int n = sc.nextInt();
		int ones = 0;
		int[] a = new int[n];
		
		for(int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			if(a[i] == 1)	ones++;
		}
		if(ones > 0) {
			System.out.println(n-ones);
			return;
		}
		
		int min = n+1;
		for(int i = 0; i < n; i++) {
			int x = a[i];
			for(int j = i+1; j < n; j++) {
				x = gcd(x, a[j]);
				if(x == 1) {
					min = Math.min(min, j-i);
					break;
				}
			}
		}
		
		if(min == n+1) {
			System.out.println(-1);
		}
		else {
			System.out.println(n-1+min);
		}
		
	}
	
	static int gcd(int a, int b) {
		return BigInteger.valueOf(a).gcd(BigInteger.valueOf(b)).intValue();
	}
	
	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {while (st == null || !st.hasMoreElements()) {
			try {st = new StringTokenizer(br.readLine());}
			catch (IOException e) {e.printStackTrace();}}
		return st.nextToken();}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine(){String str = "";
		try {str = br.readLine();}
		catch (IOException e) {e.printStackTrace();}
		return str;}
	}
	
}

//10
//10 10 10 10 10 2 4 5 7 6