Problem: Janusz is a businessman. He owns a company "Januszex", which produces games for teenagers. Last hit of Januszex was a cool one-person game "Make it one". The player is given a sequence of n integers a_i.

It is allowed to select any subset of them, and the score is equal to the greatest common divisor of selected elements. The goal is to take as little elements as it is possible, getting the score 1. Now Janusz wonders, for given sequence, how much elements should the player choose?

Input

The first line contains an only integer n (1 ≤ n ≤ 300 000) — the number of integers in the sequence.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 300 000).

Output

If there is no subset of the given sequence with gcd equal to 1, output -1.

Otherwise, output exactly one integer — the size of the smallest subset with gcd equal to 1.

Examples

Input

3
10 6 15


Output

3


Input

3
2 4 6


Output

-1


Input

7
30 60 21 42 70 15 30


Output

3

Note

In the first example, selecting a subset of all numbers gives a gcd of 1 and for all smaller subsets the gcd is greater than 1.

In the second example, for all subsets of numbers the gcd is at least 2. 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.HashSet;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.LinkedHashSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        _1043F solver = new _1043F();
        solver.solve(1, in, out);
        out.close();
    }

    static class _1043F {
        int max = 0;
        int mod = 1000000007;

        int[][] nCr(int n, int r, int mod) {
            int[][] ncr = new int[n + 1][r + 1];

            ncr[0][0] = 1;

            for (int i = 1; i <= n; i++) {
                ncr[i][0] = 1;
            }

            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= r; j++) {
                    ncr[i][j] = ncr[i - 1][j - 1] + ncr[i - 1][j];
                    ncr[i][j] %= mod;
                }
            }

            return ncr;
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();

            int[] a = new int[n];

            in.readArray(a, n, 0);

            LinkedHashSet<Integer> lhs = new LinkedHashSet<>();

            for (int val : a) {
                lhs.add(val);
                max = Math.max(max, val);
            }

            n = lhs.size();

            //int[] mobius = mobius(max);

            int[][] ncr = nCr(max, 7, mod);

            long[][] dp = new long[8][max + 1];

            for (int i = max; i >= 1; i--) {

                int num = 0;
                for (int j = 1; j * i <= max; j++) {
                    if (lhs.contains(j * i)) {
                        num++;
                    }
                }
                for (int j = 1; j <= 7; j++) {
                    dp[j][i] = ncr[num][j];

                    for (int k = 2; k * i <= max; k++) {
                        dp[j][i] -= dp[j][i * k];
                        dp[j][i] %= mod;
                    }
                }
            }

            for (int j = 1; j <= 7; j++) {
                if (dp[j][1] != 0) {
                    out.println(j);
                    return;
                }
            }

            out.println(-1);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }

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

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

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            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 int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public void readArray(int[] a, int n, int offset) {
            for (int i = 0; i < n; i++) {
                a[i] = nextInt() - offset;
            }
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}