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.
//package codeforces;

import java.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class C892 {

    public static void main(String[] args) throws IOException {
        InputReader ir = new InputReader(System.in);

        int n = ir.readInt();

        int[] numbers = ir.readIntArray(n);

        int result = computeMinIteration(numbers);

        System.out.println(result);
    }

    private static int computeMinIteration(int[] numbers) {
        int onesCount = 0;

        for (int n : numbers) {
            if (n == 1) {
                onesCount++;
            }
        }

        if (onesCount > 0) {
            return numbers.length - onesCount;
        }

        int minSegLength = Integer.MAX_VALUE;

        for (int i = 0; i < numbers.length; i++) {
            int leftSegmentGcd = numbers[i];

            for (int j = i + 1; j < numbers.length; j++) {
                if ((leftSegmentGcd = gcd(leftSegmentGcd, numbers[j])) == 1) {
                    minSegLength = Math.min(minSegLength, j - i);
                    break;
                }
            }
        }

        if (minSegLength == Integer.MAX_VALUE) {
            return -1;
        }

        return minSegLength + numbers.length - 1;
    }

    private static int gcd(int a, int b) {
        if (b % a == 0) {
            return a;
        }

        return gcd(b % a, a);
    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int read() {
            try {
                if (curChar >= numChars) {
                    curChar = 0;
                    numChars = stream.read(buf);
                    if (numChars <= 0)
                        return -1;
                }
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return buf[curChar++];
        }

        public int readInt() {
            return (int) readLong();
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
                if (c == -1) throw new RuntimeException();
            }
            boolean negative = false;
            if (c == '-') {
                negative = true;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += (c - '0');
                c = read();
            } while (!isSpaceChar(c));
            return negative ? (-res) : (res);
        }

        public int[] readIntArray(int size) {
            int[] arr = new int[size];
            for (int i = 0; i < size; i++) arr[i] = readInt();
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}