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.
// package Quarantine;

import javafx.util.Pair;

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.*;

public class ShortestCycle {
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
    public static void main(String[] args)throws IOException {
        Reader s=new Reader();
        int n=s.nextInt();
        long a[]=new long[n+1];
        ArrayList<Integer> count[]=new ArrayList[61];
        HashSet<Integer> graph[]=new HashSet[n+1];
        for(int i=0;i<=60;i++){
            count[i]=new ArrayList<>();
        }
        for(int i=1;i<=n;i++){
            a[i]=s.nextLong();
            graph[i]=new HashSet<>();
            for(int j=0;j<=60;j++){
                long t=1l<<j;
                if((t&a[i])!=0){
                    count[j].add(i);
                }
            }
        }
        for(int i=0;i<=60;i++){
            if(count[i].size()>=3){
                System.out.println(3);
                return;
            }
        }
        HashSet<Pair<Integer,Integer>> edges=new HashSet<>();
        for(int i=0;i<=60;i++){
            for(int j:count[i]){
                for(int k:count[i]){
                    if(j!=k){
                        Pair p=new Pair<>(Math.min(j,k),Math.max(j,k));
                        if(!edges.contains(p)){
                            edges.add(p);
                            graph[j].add(k);
                            graph[k].add(j);
                        }
                    }
                }
            }
        }
        int inf=Integer.MAX_VALUE>>10;
        int min=inf;
        for(Pair<Integer,Integer> p:edges){
            int u=p.getKey();
            int v=p.getValue();
            int dist[]=new int[n+1];
            Queue<Integer> q=new LinkedList<>();
            boolean visited[]=new boolean[n+1];
            q.add(u);
            Arrays.fill(dist,inf);
            dist[u]=0;
            visited[u]=true;
            while(!q.isEmpty()){
                int curr=q.remove();
                for(int j:graph[curr]){
                    if(curr==u&&j==v){
                        continue;
                    }
                    if(!visited[j]){
                        visited[j]=true;
                        dist[j]=dist[curr]+1;
                        q.add(j);
                    }
                }
            }
            if(dist[v]!=inf){
                min=Math.min(min,dist[v]+1);
            }
        }
        if(min!=inf){
            System.out.println(min);
        }
        else{
            System.out.println(-1);
        }
    }
}
