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 static java.util.Arrays.*;
import static java.lang.Math.*;
import static java.math.BigInteger.*;
import java.util.*;
import java.math.*;
import java.io.*;

public class Main implements Runnable {
    
    void solve() throws IOException {
    	int n = nextInt();
    	int g = 0;
    	int[] a = new int[n];
    	for (int i = 0; i < n; i++) {
    		a[i] = nextInt();
    		g = gcd(g, a[i]);
    	}
    	if (g > 1) {
    		out.println(-1);
    		return;
    	}
    	int countOne = 0;
    	for (int i = 0; i < n; i++)
    		if (a[i] == 1) countOne++;
    	if (countOne > 0) {
    		out.println(n - countOne);
    		return;
    	}
    	int[][] gs = new int[n + 1][n + 1];
    	for (int len = 1; len <= n; len++)
    		for (int i = 0; i + len <= n; i++) {
    			gs[i][len] = gcd(a[i], gs[i + 1][len - 1]);
    			if (gs[i][len] == 1) {
    				out.println(len - 1 + n - 1);
    				return;
    			}
    		}
    }
    
    int gcd(int a, int b) {
    	return b == 0 ? a : gcd(b, a % b);
    }
    
    String next() throws IOException {
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(input.readLine());
        return st.nextToken();
    }
    
    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    
    long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    
    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    
    void debug(Object... o) {
        if (TEST) System.out.println(deepToString(o));
    }
    
    void gcj(Object o) {
        String s = String.valueOf(o);
        out.println("Case #" + test + ": " + s);
        System.out.println("Case #" + test + ": " + s);
    }
    
    BufferedReader input;
    PrintWriter out;
    StringTokenizer st;
    int test;
    boolean TEST = System.getProperty("ONLINE_JUDGE") == null;

    void init() throws IOException {
        if (TEST) input = new BufferedReader(new FileReader("input.in")); 
        else input = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedOutputStream(System.out));
    }
    
    public static void main(String[] args) throws IOException {
        new Thread(null, new Main(), "", 1 << 20).start();
    }
    
    public void run() {
        try {
            init();
            if (TEST) {
                int runs = nextInt();
                for(int i = 0; i < runs; i++) solve();
            } else solve();
            out.close();        
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }
}