You are given n integer numbers a_1, a_2, ..., a_n. Consider graph on n nodes, in which nodes i, j (i≠ j) are connected if and only if, a_i AND a_j≠ 0, where AND denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

Find the length of the shortest cycle in this graph or determine that it doesn't have cycles at all.

Input

The first line contains one integer n (1 ≤ n ≤ 10^5) — number of numbers.

The second line contains n integer numbers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{18}).

Output

If the graph doesn't have any cycles, output -1. Else output the length of the shortest cycle.

Examples

Input


4
3 6 28 9


Output


4

Input


5
5 12 9 16 48


Output


3

Input


4
1 2 4 8


Output


-1

Note

In the first example, the shortest cycle is (9, 3, 6, 28).

In the second example, the shortest cycle is (5, 12, 9).

The graph has no cycles in the third example.
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 *
 * @author pttrung
 */
public class B_Round_580_Div1 {
    public static long MOD = 1000000007;
    static int[] dp;
    static long mask;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        long[] data = new long[n];
        for (int i = 0; i < n; i++) {

            data[i] = in.nextLong();
            //System.out.println(Long.toBinaryString(data[i]));
        }
        ArrayList<Integer>[] map = new ArrayList[64];
        for (int i = 0; i < map.length; i++) {
            map[i] = new ArrayList<>();
        }
        int result = Integer.MAX_VALUE;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < map.length; j++) {
                if (((1L << j) & data[i]) == 0) {
                    continue;
                }
                map[j].add(i);
            }

        }
        for (int i = 0; i < map.length; i++) {
            if (map[i].size() > 2) {
                result = 3;
                break;
            }

        }

        //System.out.println(result);
        dp = new int[n];
        Arrays.fill(dp, -1);
        int[] pa = new int[n];
        boolean[] stack = new boolean[n];
        for (int i = 0; i < map.length && result > 3; i++) {
            if (map[i].size() != 2) {
                continue;
            }

            int v = map[i].get(0);
            Arrays.fill(dp, -1);
            LinkedList<Integer> q = new LinkedList<>();
            dp[v] = 0;
            pa[v] = v;
            q.add(v);
            //System.out.println("Root " + v);

            while (!q.isEmpty()) {
                int node = q.poll();
                //System.out.println("Cur " + node);

                long cur = data[node];
                for (int j = 0; j < map.length; j++) {
                    if (((1L << j) & cur) == 0) {
                        continue;
                    }
                    if (map[j].size() < 2) {
                        continue;
                    }
                    int other = map[j].get(0) == node ? map[j].get(1) : map[j].get(0);
                    if (dp[other] == -1) {
                        dp[other] = 1 + dp[node];
                        pa[other] = node;
                        q.add(other);
                    } else if (other != pa[node] && pa[other] != node) {
                        HashSet<Integer> tmp = new HashSet<>();
                        int check = node;
                        tmp.add(check);
                        while (check != v) {
                            check = pa[check];
                            tmp.add(check);
                        }
                        check = other;
                        while (!tmp.contains(check)) {
                            check = pa[check];
                        }
                        //System.out.println(node + " " + other + " " + tmp + " " + check);
                        result = Integer.min(result, dp[other] + dp[node] + 1 - dp[check]);
                    }
                }
            }
            //System.out.println(Arrays.toString(pa) + " " + Arrays.toString(dp));
        }
        out.println(result == Integer.MAX_VALUE ? -1 : result);

        out.close();
    }


    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }

        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * (val * a);

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}