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 javax.xml.ws.soap.MTOM;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.*;
public class Main {
    public static void main(String []args){
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver=new Task();
        solver.solve(1,in,out);
        out.close();
    }

    static class Task{
        static final int INF = (int)1e9+10;
        public void solve(int testNumber,InputReader in,PrintWriter out) {
            int n = in.nextInt();
            int [] a = new int[n];
            int sum = 0;
            for(int i = 0 ; i < n ; i++){
                a[i] = in.nextInt();
                if(a[i] == 1){
                    sum++;
                }
            }
            if(sum != 0){
                out.println(n - sum);
                return;
            }
            if(n == 1){
                if(a[0] == 1){
                    out.println("0");
                } else {
                    out.println("-1");
                }
                return;
            }
            
            int Min = INF - 10;
            for(int i = 1 ; i < n ; i++){
                int GCD = gcd(a[i-1],a[i]);
                //out.println("GCD=="+GCD);
                int MMin = INF;
                {
                    boolean flag = false;
                    int h = 1;
                    int l = i - 2;
                    for(int j = l ; j >= 0 ;j--){
                        if(GCD == 1){
                            flag = true;
                            break;
                        }
                        h++;
                        int _GCD = gcd(a[j] , GCD);
                        if(_GCD == 1){
                            flag = true;
                            break;
                        } else {
                            GCD = _GCD;
                        }
                    }
                    if(flag) MMin = Math.min(MMin,h);
                }
                {
                    boolean flag = false;
                    GCD = gcd(a[i-1],a[i]);
                    int h = 1;
                    int r = i + 1;
                    for(int j = r ; j < n ; j++){
                        if(GCD == 1){
                            flag = true;
                            break;
                        }
                        h++;
                        int _GCD = gcd(a[j],GCD);
                        if(_GCD == 1){
                            flag = true;
                            break;
                        } else {
                            GCD = _GCD;
                        }

                    }
                    if(flag) MMin = Math.min(MMin,h);
                }
                //out.println("MMin=="+MMin);
                Min = Math.min(Min,MMin + n - 1 );
            }
            if(Min == INF - 10){
                out.println("-1");
            } else {
                out.println(Min);
            }
        }

        private int gcd(int i, int i1) {
            if(i > i1){
                int t= i ;
                i = i1;
                i1 = t;
            }
            while(i > 0){
                int k = i1 % i;
                i1 = i;
                i = k;
            }
            return i1;
        }
    }
    static class InputReader{
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}