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.util.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.io.*;
import java.math.*;
import java.text.DecimalFormat;
public class Prac{     
    static class InputReader { 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        public InputReader(InputStream st) {
            this.stream = st;
        } 
        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
            c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public int[] nia(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public String rs() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                    c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        } 
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        } 
    }
    static PrintWriter w = new PrintWriter(System.out);
    static long mod=998244353L,mod1=1000000007;
    public static class Key {
 
    private final int x;
    private final int y;
 
    public Key(int x, int y) {
        this.x = x;
        this.y = y;
    }
 
    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (!(o instanceof Key)) return false;
        Key key = (Key) o;
        return x == key.x && y == key.y;
    }
 
    @Override
    public int hashCode() {
        int result = x;
        result = 31 * result + y;
        return result;
    }
 
}
    static class Pair{
        int x,y,z,l;
        public Pair(int x,int y,int z,int l){
            this.x=x;
            this.y=y;
            this.z=z;
            this.l=l;
        }
    }
    static int n,len;
    static ArrayList<Integer> arr[];
    public static void main (String[] args)throws IOException{
        InputReader sc=new InputReader(System.in);
        n=sc.ni();
        arr=new ArrayList[n+1];
        String bin[]=new String[n+1];
        for(int i=0;i<=n;i++){
            arr[i]=new ArrayList<>();
        }
        int k=0;
        int count[]=new int[100];
        long cost[]=new long[n+1];
        int nz=0;
        for(int i=1;i<=n;i++){
            long x=sc.nl();
            if(x==0)continue;
            cost[++k]=x;
            
            bin[k]=Long.toBinaryString(x);
            int l=bin[k].length();
            char temp[]=bin[k].toCharArray();
            for(int j=bin[k].length()-1;j>=0;j--){
                if(temp[j]=='1')count[bin[k].length()-1-j]++;
            }
            //k++;
        }
        boolean f=false;
        for(int i=0;i<100;i++){
            if(count[i]>=3){
                f=true;
                break;
            }
        }
        
        if(f)w.println(3);
        else{
            for(int i=1;i<=k;i++){
                for(int j=i+1;j<=k;j++){
                    if(i!=j&&(cost[i]&cost[j])!=0){
                        arr[i].add(j);
                        arr[j].add(i);
                    }
                }
            }
            len=Integer.MAX_VALUE;
            for(int i=1;i<=k;i++){
                int dist[]=new int[k+1];
                int par[]=new int[k+1];
                Arrays.fill(dist,(int)(1e9));
                Arrays.fill(par,-1);
                dist[i]=0;
                Queue<Integer> q=new LinkedList<>();
                q.add(i);
                while(!q.isEmpty()){
                    int x=q.poll();
                    for(int j:arr[x]){
                        if(dist[j]==(int)(1e9)){
                            dist[j]=1+dist[x];
                            par[j]=x;
                            q.add(j);
                        }
                        else if(par[x]!=j&& par[j]!=x){
                            len=Math.min(len,dist[x]+dist[j]+1);
                        }
                    }
                }
            }
            w.println(len==Integer.MAX_VALUE?-1:len);
        }
        w.close();
    }
}